Relationship Between Age and Numerical Ability: A Correlational Analysis
Relationship Between Age and Numerical Ability: A Correlational Analysis
Rajesh Patel
Submitted in partial requirement for the
degree of Bachelor of Psychology Science (Honours)
ISN Psychology
Institute for Social Neuroscience
Ivanhoe, Victoria, Australia, 3079
Date: May 22, 2023
Supervisor: Dr Jian Chen
Word Count: 3449
Thesis Declaration
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AbstractNumerical ability is imperative in meeting the financial challenge posed on the health and welfare systems by the increasing lifespan and growth in the aged population. A positive correlation has been observed between age and symbolic numerical ability, which is defined as numerical ability related to processing numbers denoted by symbols. However, existing literature fails to provide clear conclusions concerning the relationship between age and non-symbolic numerical ability, which is the numerical processing of a collection of items.
Therefore, this study investigates the strength and direction of the relationship between age and symbolic and non-symbolic numerical ability and hypothesizes that there exists a strong negative correlation between age and both symbolic and non-symbolic numerical ability. Correlation analysis was conducted on the non-symbolic numerical and symbolic numerical ability measured by the accuracy and speed of identifying the number of dots using the Dot Enumeration Test and Wide Range Achievement Test Math Computation subscale, respectively. One hundred and forty Australian volunteers in the age range of 18 and 80 completed the online test. Insight into the relationship between age and symbolic and non-symbolic numerical processing ability brings additional conclusive insight about the Australian population to the existing literature. Furthermore, it also provide validation for future studies in the maintenance and enhancement of numerical ability, thereby facilitating the well-being of a fast-growing ageing Australian population.
principle findings and implications
Relationship Between Age and Numerical Ability: A Correlational Analysis
Increasing lifespan, coupled with financial liberalisation and continuous technology advancements, requires people to maintain their numerical ability for longer (Australian Institute of Health and Welfare, 2022; Lusardi & Mitchell, 2011). Numerical ability is categorised into symbolic and non-symbolic processing, and symbolic numerical ability is found to be associated with financial well-being (Norris et al., 2015; Sunderaraman et al., 2022). Symbolic numerical processing is associated with number sense related to digits ('1') or number words ('one'), and non-symbolic numerical processing is related to collections or quantities of items such as dots (Norris et al., 2015). The non-symbolic numerical skill has been demonstrated to improve in typical development and serves as a foundation for acquiring the symbolic, acquired later in development through comprehensive formal education (Norris et al., 2015). Symbolic processing is associated with financial well-being, and non-symbolic ability provides the foundation for its development, making both processing modes vital.
An individuals socioeconomic status has been reported to potentially make it difficult for an adult to lead a balanced life (Parsons & Bynner, 2005) and is positively correlated with a lower numerical ability (Ritchie & Bates, 2013). Numerical ability, which includes the representation and processing of numbers, is proficiency in solving arithmetic computations and relatively simple word problems (Landerl, 2013; Thurstone, 1973). Studies by Parsons and Bynner (2005), Ritchie and Bates (2013) and Sunderaraman et al. (2022) indicate that lower numerical ability adversely impacts financial well-being, socioeconomic status, and quality of life. Financial well-being is described as a good and positive financial condition comprising objective (material resources possessed by an individual) and subjective (perception of one's financial situation) criteria (Sorgente & Lanz, 2017). Numerical ability is vital for helping individuals meet their subjective and objective measures of a balanced life.
A decline in numerical ability has been correlated with increasing age resulting from deterioration in attention and working memory (Norris, 2015). Age is defined as the passing of chronological time, a time-dependent functional decline that impairs sensory, motor, and cognitive functions and adversely affects the quality of life (Patridge et al., 2018). In the context of the growing number of aged people and increasing lifespan, it is essential to consider Izquierdo et al. (2021) findings that cognitive skills, such as numerical ability, decline with age. Australian Institute of Health and Welfare (2022) reported that compared to those born between 1891 and 1900, people born between 2018 and 2020 are expected to live about 30 years more, concluding that the number of aged people (i.e., individuals of age 60 years and above) in Australia is increasing due to increased life expectancy. This report makes it critical to understand the challenges brought about by the longer lifespan of Australians. A study conducted by Norris et al. (2015) involving fifty participants comprising 25 participants of age 19 to 25 and 25 participants of age 60 to 77 reported that numerical ability declines with age. A growing ageing population and the relationship between numerical processing ability and well-being (financial and socio-economic) make it imperative to investigate the strength and direction of the relationship between age and numerical ability. Insight into the relationship between age and numerical ability could set the basis for future study in the maintenance and enhancement of numerical ability, thereby supporting well-being (financial and socio-economic) in a fast-ageing Australian demographic.
Literature Review: The Relationship Between Age and Numerical Ability
Numerical ability has been found to be stable over time, with Siegler and Braithwaite (2017) observing the ease of predictability of numerical ability at age fifteen based on numerical ability in kindergarten. However, a component analysis conducted by Salthouse and Kersten (1993) with 104 participants revealed that older group participants made fewer errors in symbolic numerical processing (arithmetic tasks using digits) than the younger group and reported that older group participants had lower accuracy in non-symbolic numerical ability than younger group participants. The study attributed the decline in the numerical ability to the speed of processing caused by ageing rather than to deteriorated arithmetical skills or ability. However, analyses of variance on mean latencies of correctly solved problems conducted by Duverne and Lemaire (2004) with a sample size of 138 participants found that arithmetic accuracy declines in older age. The above studies characterise numerical ability as stable (no change with age), negatively correlated with age (decline in speed due to age), unrelated to age (no impact of age on ability), and negatively correlated with age (decline in speed and accuracy), which seem contrary and unproductive. These mixed findings from the above studies suggest that existing research on the relationship between age and numerical ability remains inconclusive.
After reviewing over seven years of published studies, Rechel et al. (2013) opined that with increased lifespan, keeping the proportion of life lived in good health constant would require enhanced resources and necessitate higher financial well-being. Furthermore, Rechel et al. (2013) asserted that aging results in an increasing number of older people with various health problems. Positive correlation between aging and health challenges and moral obligation to increase the proportion of life lived in good health together place a considerable impact not only on the health and welfare systems but also on the long-term care provisions highlighting the need for ensuring improved financial well-being. It could be argued that as higher numerical ability sustains financial well-being, facilitating higher numerical ability would enable resource availability to deal with increased lifespan-driven healthcare costs. This underlines the importance of understanding numerical ability.
Rationale: Benefits to Understanding Correlation between Age and Numerical Ability
After performing mediation analysis to estimate the statistical significance of indirect associations and compare the performance in symbolic and non-symbolic processing in a sample of 66 participants with equal representation from Germany and China, Lonnemann et al. (2017) reported that the ability to distinguish between different sets of numerical quantities was present in preverbal infants and was found to increase up to the age of about 30. The authors also failed to find any evidence of changes in numerical ability in participants older than 30; however, previous literature has reported the impact of aging on symbolic numerical ability considering complex abilities, including arithmetical problems (Duverne & Lemaire, 2004; Lemaire & Arnaud, 2008). This is the key reason why Siegler and Braithwaite (2017) highlighted the need to gain insight into why for some people, numerical processing is difficult and vice versa. This confirms that the existing literature fails to provide conclusive insights into the relationship between numerical ability and age, highlighting the need for further insight into the relationship. Such insight would stimulate the development of effective strategies to maintain and enhance numerical ability, resulting in improved well-being.
The literature review highlights the importance of numerical ability for an individual. Noticeably, Norris et al. (2015) highlighted that a limited number of studies had investigated non-symbolic numerical processing in older adults and added that the methods and stimuli used had varied widely, with some contradictory results. Specifically, Norris et al. (2015) noted that Trick et al. (1996) reported the involvement of different processes in enumerating small and large numbers of items and concluded that processing for small numbers made minimal demands on attention and concluded that developmental improvements without any decline in old age; but counting larger numbers requires sophisticated coordination of attention, which improves at first and then decline over the life span. Whereas Norris et al. (2015) noted that Watson et al. (2005) measured the response time for young and older adults in enumeration tasks and found no deficit in enumeration rates either with or without distractors; and Gandini et al. (2009) associated aging with poorer estimation speed but not accuracy, concluding that slower estimation in aging could reflect a decline in processing speed rather than a decline in numerical abilities. In contrast, Norris et al. (2015) reported that the study by Lemaire and Lecacheur (2007) reported scant difference in symbolic numerical processing between age groups and cited the influence of physical features of very large numbers as the cause of the difference.
Norris et al. (2015) added that not many studies present in the existing literature provided clear conclusions concerning the influence of ageing on numerical ability and affirmed the importance of gaining insight into cognitive ageing to identify the difference between non-normal and normal ageing aiding early detection of alterations in pathological processes. Inspecting the relationship between age and symbolic and non-symbolic numerical ability will help address the current state of contradictory and inconclusive findings and deliver the opportunity to identify early changes in pathological processes.
AimThe aim of the present study is to investigate the strength and direction of the relationship between age and symbolic and non-symbolic numerical ability.
HypothesisThis study hypothesises that a strong negative correlation exists between age and symbolic and non-symbolic numerical ability. To assess this assertion, the below hypothesis was tested:
H1: There exists a strong negative correlation between age and symbolic numerical ability.
H2: There exists a strong negative correlation between age and non-symbolic numerical ability.
MethodDesignA quantitative correlational research design was conducted wherein participants completed the Wide Range Achievement Test Math Computation subscale (WRAT-4) and Dot Enumeration Task (DET). The variables for this proposed study are participant age, symbolic numerical ability, and non-symbolic numerical ability. The score on WRAT-4 is used to measure symbolic numerical ability, and the median score of three non-symbolic objects in DET is used to measure non-symbolic numerical ability.
Participants
One hundred and forty participants of age ranging from 18 to 80 years from Australia with proficiency in reading English of a minimum grade eight level completed the online test fully. Perugini et al. (2018) emphasised the importance of the replicability of the study and recommend using a value of .80 for power with a large population effect size, r = .37, in a priori analysis to determine sample size. The minimum sample size was determined by performing a priori analysis for a Pearson correlation between age and symbolic and non-symbolic numerical ability using the G*Power Version 3.1.9.6 (Faul et al., 2007), considering an effect size of 0.80 (or 80%) at = .05 and r = .37. G*Power output is provided in Appendix A. Completed responses received exceeded the minimum sample size requirement.
Recruitment of participants was conducted by approaching a network of friends and acquaintances, social media such as Facebook, Instagram, and other electronic bulletins. Visually impaired individuals and persons with English proficiency level below grade 8 or post-graduate qualification in science or mathematics were not invited for this study and thereby excluded from participation. Project details were briefly described to the participants during the initial recruitment conversation. In addition, individuals between the ages of 18 and 80 were individually provided with an email containing the online test link and a document detailing the study details. The contact particulars of the study organisers obtained ethics approval, and details of support services available (in case participants experience any distress) were included in the study details document.
MaterialsWide Range Achievement Test Math Computation subscale (WRAT-4)
WRAT-4, a norm-referenced skills assessment instrument, includes subscales that measure reading, maths, spelling, and comprehension skills for use with individuals aged 5 through 94 (Dell et al., 2008). The Math Computation subscale is designed to measure an individual's ability to perform basic mathematics computations through counting, identifying numbers, and calculating mathematics problems (Dell et al., 2008). The oral section of the Math Subscale was excluded as this proposed study participants will be older than 18 years of age. WRAT-4 includes the blue and green forms, which can be used interchangeably, permitting retesting within a short period. This study will employ only the blue form of the 2006 version of WRAT-4, which has been reported to have a standard error of measurement of 5 with a reliability coefficient of = 0.96, item separation reliability of 1.0 and internal reliability measures of .87 to .93 (IvyPanda, 2021, February 10). The internal consistency of the Math computation subscale of WRAT-4 for an age-based sample blue form is = 0.89 (IvyPanda, 2021, February 10). Abreu-Mendoza et al. (2019) were satisfied with the criterion validity.
The Math Computation component of the math subscale comprised 40 problems to be solved (without using calculators). The questions were arranged as per the difficulty level, providing insight into how people of varied ages scored within time limitations. The participant was awarded one point for each correct answer, and unanswered questions and incorrect answers were scored zero. For each participant, the scores were summed up, reflecting the individual's performance. High scores reflect high symbolic numerical ability and vice versa. The Math Computation subscale is provided in Appendix C.
Dot Enumeration Task
DET comprises a set of randomly arranged dots ranging from one to nine, which participants were required to enumerate as quickly as possible by simultaneously entering the number on their computer. DET evaluated arithmetic ability and response time to assess enumeration accuracy and speed. The 48 arithmetic ability tests were presented in a fixed pseudo-random order with no dot number occurring twice in succession (interstimulus-interval: 1120 ms). Two grey displays of the same surface area with different numbers of yellow squares were presented side by side on the screen, and participants were required to select the numerically larger one as quickly as possible by keypress response. Working memory assessment involved displays presented between 20 and 72 squares, and numerical distances between the two displays ranging from eight to 25 squares. After three practice trials with feedback, 72 test trials (four for each numerical distance) were presented in a fixed pseudo-random order (interstimulus-interval: 300 ms). A short response time in DET signified high non-symbolic numerical ability and vice versa. Gray and Reeve (2014) confirmed that DET scores (enumeration efficiency) predicted numerical ability over and above the influence of general cognitive functions. An example of a question in DET is provided in Appendix D.
Procedure
Participants were required to fully complete the online test comprising the WRAT-4 and DET estimated to take about 30 minutes in a quiet environment with minimal distractions in one session on their computer at a location of their preference. Participants were allowed to adjust the brightness and contrast of the display and place their chair at personal convenience. Before commencing the test, participants could complete five practice examples. The test began with details of the study followed by the informed consent form, acceptance of which initiated the test. Non-acceptance of informed consent was treated as a withdrawal from participation. An incentive of $10 (as an electronic gift voucher from a major grocery chain) was provided to participants upon test completion. The online test ended with the participant providing details about where the gift voucher was to be emailed, thanking them for participation along with confirmation of anonymity and confidentiality.
Proposed AnalysisSPSS (version 28) was used to analyse the data in this correlational study wherein the participant's age and the scores of the WRAT-4 and DET are the variables. Each participant was allowed to complete the test only once, and participant selection criteria included steps aimed at ensuring that a participant's score is not influenced by other participants, thereby ensuring the independence of data.
Missing Value Analysis
Missing data can reduce statistical power, produce biased estimates and lead to invalid conclusions. To minimise missing values and ensure the completion of all questions, before commencing the online test, participants were reminded to completely answer each question before progressing to the next question. Participants could advance to the next question after answering the current question or expiry of time, ensuring each question received a score. Initial screening of the data was conducted to identify responses received from software applications programmed to execute specific tasks as part of another computer program or to simulate human activity (bots). Once the responses from bots were identified and removed, the remaining responses were assessed for missing values before analysis to mitigate the impact of missing values. The mean substitution approach was undertaken to deal with any missing values. Mean substitution is a method in whichmissing observations for a score are replaced by the average of observed data for that score in other participants.
Assumption Testing
Outliers potentially decrease the value of a correlation coefficient; hence an outlier management approach consisting of determining outliers using visual inspection of box plots is included. Median values are least affected by non-symmetrical distributions (Field, 2018). Hence outliers identified by box plots will be replaced with the median values. The assumptions of data linearly and normality will be validated through the visual inspection of scatterplots and the Shapiro-Wilk test, respectively. The correlation coefficient provides a reliable measure of the strength of the linear relationship only if the relationship between the variables, age and symbolic and non-symbolic numerical ability, is linear (Field, 2018). As recommended by Field (2018), a visual inspection of the plot of the participant's age against the WRAT-4 and DET scores will be conducted to confirm if the linearity assumption is satisfied. A non-significant value provided by the Shapiro-Wilk test will be used to confirm satisfaction of the normality assumption. Descriptive statistics will be computed upon completion of outlier management and presented in a table. As Enders and Bandalos (2001) recommended, the Missing at Random assumption is adopted for this study and missing data will be substituted using the Maximum Likelihood Estimation approach. Bivariate correlations and significance testing for mean comparisons will be completed using the estimate of standard errors. Pearson's Correlation Analysis
Correlation coefficients are widely used to measure the association between variables measured, which is expected to range from -1.0 to +1.0 (Taylor, 1990). This study proposes to compute the strength and direction of the correlation between age and symbolic and non-symbolic numerical ability by calculating the correlation coefficient (r). A negative value of r will signify that symbolic and non-symbolic numerical ability decreases with age, whereas a positive value of r will convey the contrary. A zero value of r will indicate an absence of relationship, and the degree of closeness of r to +1 or -1 will convey the strength of association. The square of the correlation coefficient (or r square after ignoring decimal points) will signify the variance in age (by percentage) that is related to the variance (by percentage) in symbolic and non-symbolic numerical ability. Statistical significance will also be reported, along with sample size, indicating the likelihood of the reported correlation resulting from chance in the form of random sampling error.
Woodrow (2014) recommends that the decision about how significant the results of correlation analysis is informed by the study purpose, and if the study hypothesises a strong correlation between variables, then a correlation coefficient value, such as r = .37, would suffice. The aim of this study aims is to examine the strength and direction of the relationship between age and symbolic and non-symbolic numerical ability. Hence relying on Woodrow's recommendation, r = .37 with = .05 will be used for both variables. Results will be significant if the computed value of p < 0.05. The correlation between age and symbolic and non-symbolic numerical ability calculated from the proposed data collection will be presented as separate graphs.
Open Science Framework
Data collected, analysis conducted, findings, and any other information relevant to the replication of this study, along with the ethics approval, will be uploaded on the Open Science Framework (OSF) maintained and developed bythe Center for Open Science. It is not intended to collect any identifying data during the data-gathering process. Nevertheless, data will be scanned to ensure anonymity before conducting analysis and once again before uploading on OSF. The data analysis process will be written in easy-to-understand language with assumptions and outlier management clearly stated.
Results
Descriptive and inferential statistical analyses
Missing data and outliers
Assumptions of correlation are tested and is it clearly explained (and justified) what was done if assumptions were violated? Is it clear how the data were analyzed and can an academic who is not an expert in the field understand what was done and why?
Are the results appropriately described in APA format?Students also need to provide effect sizes and confidence intervals
Is it clear how the analyses can be replicated? Are the tables and figures clear and in line with APA format?
Discussion
Are aim and hypotheses clearly and concisely restatedIs it clear if hypotheses were supported or not? you also need to interpret the effect size and confidence interval/reliability of the finding.
How do these results (and the effect size) relate to previous studies on this topic. Are they similar/different (again not only in relation to significance but more importantly in relation to effect size)? Are theoretical and/or practical implications of the findings discussed?
Are strengths, limitations and future directions discussed? Is there a final conclusion.
Appendix A: G*Power Output
091440000Appendix B: Project details
TitleRelationship between Age and Numerical Ability: A Correlational Analysis
Ethics Approval Number210505
Principal InvestigatorDr Jian Chen
Associate InvestigatorMr Rajesh Patel
Introduction
You are invited to participate in this research project conducted by ISN Psychology called Relationship between Age and Numerical Ability: A Correlational Analysis. This Participant Information Sheet outlines the research project. It explains the processes involved with taking part. Knowing what is involved will help you decide if you want to participate in the research.
Please read this information carefully. Ask questions about anything you don't understand or want to know more about. Before deciding to participate, you might want to talk about it with a relative or friend. Participation in this research is voluntary. If you don't wish to participate, you don't have to.
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Understand what you have read
Consent to take part in the research described
What is the purpose of this research?
The aim of the present study is to investigate the strength and direction of the relationship between age and numerical ability. Numerical ability is made of the symbolic numerical ability, which is associated with digits or number words, and non-symbolic numerical ability related to collections or quantities of items (such as dots). In the context of the growing number of aged people and increasing lifespan, it is important to understand the relationship between age and numerical ability, as this ability has been found to influence financial well-being and quality of life. Though a limited number of studies have investigated basic non-symbolic numerical processing in older adults, the methods and stimuli used have varied widely, with some contradictory results.
Insight into the relationship between age and numerical processing ability would contribute to the existing literature. Furthermore, it would also provide validation for future studies in the maintenance and enhancement of numerical processing ability, thereby facilitating the well-being of a fast-growing ageing Australian demographic.
What does participation in this research involve?
Formal acceptance of this consent form is required before participating in this study.
To be eligible to participate in this study, you confirm that
You are more than 20 years of age
You are proficient in English (higher than grade 8 level)
You confirm that you have good vision
You do not have a post-graduate qualification in science or mathematics
This test is estimated to take about 30 to 40 minutes and can be completed anytime at a place convenient to you, but it needs to be completed in a single session. You will need to complete both parts of this test fully. The first part will require confirmation of the number of dots on the screen. In the second part, you will be required to perform simple calculations. Each question needs to be answered within the defined time limit. Only after the question is answered or the time limit is over will you be allowed to progress to the next question.
Please be assured we will not be collecting personal information, ensuring that data collection remains anonymous. Consent to participate and test results remain confidential. Over the next three days, we will contact you to answer any questions that you may have and seek feedback and suggestions.
Study findings are expected to be available after three months. Please let us know if you would be interested in a summary of the findings. As a token of appreciation, upon completion of the test, we will email you an electronic gift card for $10 for Coles Supermarket within two days.
Do I have to take part in this research project?
Participation in any research project is voluntary. If you do not wish to participate, you do not have to. If you decide to participate and change your mind, you are free to withdraw from the project at any stage. If you choose to withdraw from the project, please notify a research team member, and you will be asked to complete and sign a 'Withdrawal of Consent' form.
Your decision whether to take part or not to take part, or to take part and then withdraw, will not affect your relationship with ISN Psychology or the researchers.
What are the possible benefits of taking part?
We estimate the findings of this study to provide validation for future studies in the maintenance and enhancement of numerical processing ability, thereby facilitating the well-being of a fast-growing ageing Australian demographic. There will be no clear benefit to you from participating in this research. As a token of appreciation for your participation, we will provide you with a $10 gift voucher from Coles Supermarkets upon completing this study.
What are the possible risks and disadvantages of taking part?
You may feel that some of our questions are stressful or upsetting. If you do not wish to answer a question, you may skip it and go to the next question, or you may stop immediately. If you become upset or distressed due to your participation in the research project, please contact the chief investigator Rajesh Patel at research@isn.edu.au.
Additionally, you may wish to contact one of the following third-party counselling services:
Lifeline Australia Crisis Support: 13 11 14 (available 24 hours)
Beyond Blue: 1300 22 4636
What will happen to information about me?
All collected data will be non-identifiable. Data will be stored on the institute server, with access restricted only to the project team. Server access is controlled by a password along with a 2-Factor Authentication. Non-identifiable data will be retained only on our server for five years and destroyed. By participating in this study, you consent us to use the test scores and your age. No other information will be collected and/or stored. Your information will only be used for this research project and will only be disclosed with your permission, except as required by law.
It is anticipated that the results of this research project will be published and/or presented in various forums. In any publication and/or presentation, information will be provided so that you cannot be identified.
Who has reviewed the research project?
All research in Australia involving humans is reviewed by an independent group called the Human Research Ethics Committee (HREC). The ethical aspects of this research project have been approved by the ISN Psychology HREC (approval number [approval number].) This project will be carried out according to the National Statement on Ethical Conduct in Human Research (2007). This Statement has been developed to protect the interests of people who agree to participate in human research studies.
Further information and who to contact
The person you may need to contact will depend on the nature of your query. If you want any further information concerning this project or if you have any problems which may be related to your involvement in the project, you can contact the research contact person below:
Research contact person
NameDr Jian Chen
PositionPrincipal Investigator
Telephone0418 331 332
Emailresearch@isn.edu.au
If you have any complaints about any aspect of the project, the way it is being conducted or any questions about being a research participant in general, then you may contact Reviewing HREC approving this research and the HREC Secretary's details
Reviewing HREC nameISN Psychology HREC
HREC SecretaryMelissa Mulraney
Emailethics@isn.edu.au
Appendix C: Wide Range Achievement Test Math Computation subscale (WRAT-4)
Appendix D: Dot Enumeration Test (DET)
Short-term memory test: Placing dots online based on memory
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Ritchie, S. J., & Bates, T. C. (2013). Enduring links from childhood mathematics and reading achievement to adult socioeconomic status.Psychological Science,24(7), 1301-1308. https://doi.org/10.1177/09567976124662Salthouse, T.A., Kersten, A.W. Decomposing adult age differences in symbol arithmetic.Memory & Cognition21, 699710 (1993). https://doi.org/10.3758/BF03197200
Siegler, R. S., & Braithwaite, D. W. (2017). Numerical development.Annual Review of Psychology,68, 187-213. https://doi.org/10.1146/annurev-psych-010416-044101Sorgente, A., & Lanz, M. (2017). Emerging adults' financial well-being: A scoping review. Adolescent Research Review, 2(4), 255-292. https://doi.org/10.1007/s40894-016-0052-x
Sunderaraman, P., Barker, M., Chapman, S., & Cosentino, S. (2022). Assessing numerical reasoning provides insight into financial literacy.Applied Neuropsychology: Adult,29(4), 710-717. https://doi.org/10.1080/23279095.2020.1805745Taylor, R. (1990). Interpretation of the correlation coefficient: a basic review. Journal of Diagnostic Medical Sonography, 6(1), 35-39. https://doi.org/10.1177/875647939000600Trick, L. M., Enns, J. T., and Brodeur, D. A. (1996). Life span changes in visual enumeration: the number discrimination task. Developmental Psychology. 32 (5), 925932. https://doi.org/10.1037/0012-1649.32.5.925Thurstone, L. L. (1973). Primary mental abilities. In The measurement of intelligence (pp. 131-136). Springer, Dordrecht. https://doi.org/10.1007/978-94-011-6129-9_8
Watson, D. G., Maylor, E. A., & Bruce, L. A. M. (2005). Search, Enumeration, and Aging: Eye Movement Requirements Cause Age-Equivalent Performance in Enumeration but Not in Search Tasks.Psychology and Aging, 20(2), 226240.https://doi.org/10.1037/0882-7974.20.2.226Woodrow, L. (2014). Writing about Quantitative Research. Applied Linguistics. http://dx.doi.org/10.1057/9780230369955
Relationship Between Age and Numerical Ability: A Correlational Analysis
Rajesh Patel
Submitted in partial requirement for the
degree of Bachelor of Psychology Science (Honours)
ISN Psychology
Institute for Social Neuroscience
Ivanhoe, Victoria, Australia, 3079
Date: May 22, 2023
Supervisor: Dr Jian Chen
Word Count: 3449
Thesis Declaration
Student
I acknowledge that the work contained in this thesis is my own and that appropriate acknowledgement of sources and/or data has been provided.
I have uploaded the de-identified data, stimuli, analyses, and explanation of the analyses used for this project in the assignment provided in Moodle in a manner that is clear and will allow for full replication of my study. When working with confidential data that cannot be shared for ethical reasons, the data is at least available to my supervisor. The statistical output of the analyses should always be available. Provide a detailed statement here regarding what has been uploaded and where.
Please provide a statement here on how the data, stimuli and analyses can be accessed:
If your thesis required ethical approval from the ISN ethics committee, you need to submit the final report to the ethics committee. Ethics approval was obtained from ISN ethics committee (approval number 210505), and if the final report has been submitted.
Provide a detailed statement here regarding the ethics of your project.
I provided my supervisor with a draft of this thesis in a timely manner that would allow for a sufficient critical review of the contents.
_______________ ____________
(Students signature) Date
Supervisor
I can confirm that the analyses, data collected and stimuli used for this project is uploaded to Moodle and/or provided to me in a manner that is clear and will allow for replication of the results.
I have read no more than one final draft of all sections of this thesis with the exception of the discussion.
The student has provided me with a draft on time in order for me to provided critical feedback for this thesis in a timely manner.
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(Supervisors signature) Date
AbstractNumerical ability is imperative in meeting the financial challenge posed on the health and welfare systems by the increasing lifespan and growth in the aged population. A positive correlation has been observed between age and symbolic numerical ability, which is defined as numerical ability related to processing numbers denoted by symbols. However, existing literature fails to provide clear conclusions concerning the relationship between age and non-symbolic numerical ability, which is the numerical processing of a collection of items.
Therefore, this study investigates the strength and direction of the relationship between age and symbolic and non-symbolic numerical ability and hypothesizes that there exists a strong negative correlation between age and both symbolic and non-symbolic numerical ability. Correlation analysis was conducted on the non-symbolic numerical and symbolic numerical ability measured by the accuracy and speed of identifying the number of dots using the Dot Enumeration Test and Wide Range Achievement Test Math Computation subscale, respectively. One hundred and forty Australian volunteers in the age range of 18 and 80 completed the online test. Insight into the relationship between age and symbolic and non-symbolic numerical processing ability brings additional conclusive insight about the Australian population to the existing literature. Furthermore, it also provide validation for future studies in the maintenance and enhancement of numerical ability, thereby facilitating the well-being of a fast-growing ageing Australian population.
principle findings and implications
Relationship Between Age and Numerical Ability: A Correlational Analysis
Increasing lifespan, coupled with financial liberalisation and continuous technology advancements, requires people to maintain their numerical ability for longer (Australian Institute of Health and Welfare, 2022; Lusardi & Mitchell, 2011). Numerical ability is categorised into symbolic and non-symbolic processing, and symbolic numerical ability is found to be associated with financial well-being (Norris et al., 2015; Sunderaraman et al., 2022). Symbolic numerical processing is associated with number sense related to digits ('1') or number words ('one'), and non-symbolic numerical processing is related to collections or quantities of items such as dots (Norris et al., 2015). The non-symbolic numerical skill has been demonstrated to improve in typical development and serves as a foundation for acquiring the symbolic, acquired later in development through comprehensive formal education (Norris et al., 2015). Symbolic processing is associated with financial well-being, and non-symbolic ability provides the foundation for its development, making both processing modes vital.
An individuals socioeconomic status has been reported to potentially make it difficult for an adult to lead a balanced life (Parsons & Bynner, 2005) and is positively correlated with a lower numerical ability (Ritchie & Bates, 2013). Numerical ability, which includes the representation and processing of numbers, is proficiency in solving arithmetic computations and relatively simple word problems (Landerl, 2013; Thurstone, 1973). Studies by Parsons and Bynner (2005), Ritchie and Bates (2013) and Sunderaraman et al. (2022) indicate that lower numerical ability adversely impacts financial well-being, socioeconomic status, and quality of life. Financial well-being is described as a good and positive financial condition comprising objective (material resources possessed by an individual) and subjective (perception of one's financial situation) criteria (Sorgente & Lanz, 2017). Numerical ability is vital for helping individuals meet their subjective and objective measures of a balanced life.
A decline in numerical ability has been correlated with increasing age resulting from deterioration in attention and working memory (Norris, 2015). Age is defined as the passing of chronological time, a time-dependent functional decline that impairs sensory, motor, and cognitive functions and adversely affects the quality of life (Patridge et al., 2018). In the context of the growing number of aged people and increasing lifespan, it is essential to consider Izquierdo et al. (2021) findings that cognitive skills, such as numerical ability, decline with age. Australian Institute of Health and Welfare (2022) reported that compared to those born between 1891 and 1900, people born between 2018 and 2020 are expected to live about 30 years more, concluding that the number of aged people (i.e., individuals of age 60 years and above) in Australia is increasing due to increased life expectancy. This report makes it critical to understand the challenges brought about by the longer lifespan of Australians. A study conducted by Norris et al. (2015) involving fifty participants comprising 25 participants of age 19 to 25 and 25 participants of age 60 to 77 reported that numerical ability declines with age. A growing ageing population and the relationship between numerical processing ability and well-being (financial and socio-economic) make it imperative to investigate the strength and direction of the relationship between age and numerical ability. Insight into the relationship between age and numerical ability could set the basis for future study in the maintenance and enhancement of numerical ability, thereby supporting well-being (financial and socio-economic) in a fast-ageing Australian demographic.
Literature Review: The Relationship Between Age and Numerical Ability
Numerical ability has been found to be stable over time, with Siegler and Braithwaite (2017) observing the ease of predictability of numerical ability at age fifteen based on numerical ability in kindergarten. However, a component analysis conducted by Salthouse and Kersten (1993) with 104 participants revealed that older group participants made fewer errors in symbolic numerical processing (arithmetic tasks using digits) than the younger group and reported that older group participants had lower accuracy in non-symbolic numerical ability than younger group participants. The study attributed the decline in the numerical ability to the speed of processing caused by ageing rather than to deteriorated arithmetical skills or ability. However, analyses of variance on mean latencies of correctly solved problems conducted by Duverne and Lemaire (2004) with a sample size of 138 participants found that arithmetic accuracy declines in older age. The above studies characterise numerical ability as stable (no change with age), negatively correlated with age (decline in speed due to age), unrelated to age (no impact of age on ability), and negatively correlated with age (decline in speed and accuracy), which seem contrary and unproductive. These mixed findings from the above studies suggest that existing research on the relationship between age and numerical ability remains inconclusive.
After reviewing over seven years of published studies, Rechel et al. (2013) opined that with increased lifespan, keeping the proportion of life lived in good health constant would require enhanced resources and necessitate higher financial well-being. Furthermore, Rechel et al. (2013) asserted that aging results in an increasing number of older people with various health problems. Positive correlation between aging and health challenges and moral obligation to increase the proportion of life lived in good health together place a considerable impact not only on the health and welfare systems but also on the long-term care provisions highlighting the need for ensuring improved financial well-being. It could be argued that as higher numerical ability sustains financial well-being, facilitating higher numerical ability would enable resource availability to deal with increased lifespan-driven healthcare costs. This underlines the importance of understanding numerical ability.
Rationale: Benefits to Understanding Correlation between Age and Numerical Ability
After performing mediation analysis to estimate the statistical significance of indirect associations and compare the performance in symbolic and non-symbolic processing in a sample of 66 participants with equal representation from Germany and China, Lonnemann et al. (2017) reported that the ability to distinguish between different sets of numerical quantities was present in preverbal infants and was found to increase up to the age of about 30. The authors also failed to find any evidence of changes in numerical ability in participants older than 30; however, previous literature has reported the impact of aging on symbolic numerical ability considering complex abilities, including arithmetical problems (Duverne & Lemaire, 2004; Lemaire & Arnaud, 2008). This is the key reason why Siegler and Braithwaite (2017) highlighted the need to gain insight into why for some people, numerical processing is difficult and vice versa. This confirms that the existing literature fails to provide conclusive insights into the relationship between numerical ability and age, highlighting the need for further insight into the relationship. Such insight would stimulate the development of effective strategies to maintain and enhance numerical ability, resulting in improved well-being.
The literature review highlights the importance of numerical ability for an individual. Noticeably, Norris et al. (2015) highlighted that a limited number of studies had investigated non-symbolic numerical processing in older adults and added that the methods and stimuli used had varied widely, with some contradictory results. Specifically, Norris et al. (2015) noted that Trick et al. (1996) reported the involvement of different processes in enumerating small and large numbers of items and concluded that processing for small numbers made minimal demands on attention and concluded that developmental improvements without any decline in old age; but counting larger numbers requires sophisticated coordination of attention, which improves at first and then decline over the life span. Whereas Norris et al. (2015) noted that Watson et al. (2005) measured the response time for young and older adults in enumeration tasks and found no deficit in enumeration rates either with or without distractors; and Gandini et al. (2009) associated aging with poorer estimation speed but not accuracy, concluding that slower estimation in aging could reflect a decline in processing speed rather than a decline in numerical abilities. In contrast, Norris et al. (2015) reported that the study by Lemaire and Lecacheur (2007) reported scant difference in symbolic numerical processing between age groups and cited the influence of physical features of very large numbers as the cause of the difference.
Norris et al. (2015) added that not many studies present in the existing literature provided clear conclusions concerning the influence of ageing on numerical ability and affirmed the importance of gaining insight into cognitive ageing to identify the difference between non-normal and normal ageing aiding early detection of alterations in pathological processes. Inspecting the relationship between age and symbolic and non-symbolic numerical ability will help address the current state of contradictory and inconclusive findings and deliver the opportunity to identify early changes in pathological processes.
AimThe aim of the present study is to investigate the strength and direction of the relationship between age and symbolic and non-symbolic numerical ability.
HypothesisThis study hypothesises that a strong negative correlation exists between age and symbolic and non-symbolic numerical ability. To assess this assertion, the below hypothesis was tested:
H1: There exists a strong negative correlation between age and symbolic numerical ability.
H2: There exists a strong negative correlation between age and non-symbolic numerical ability.
MethodDesignA quantitative correlational research design was conducted wherein participants completed the Wide Range Achievement Test Math Computation subscale (WRAT-4) and Dot Enumeration Task (DET). The variables for this proposed study are participant age, symbolic numerical ability, and non-symbolic numerical ability. The score on WRAT-4 is used to measure symbolic numerical ability, and the median score of three non-symbolic objects in DET is used to measure non-symbolic numerical ability.
Participants
One hundred and forty participants of age ranging from 18 to 80 years from Australia with proficiency in reading English of a minimum grade eight level completed the online test fully. Perugini et al. (2018) emphasised the importance of the replicability of the study and recommend using a value of .80 for power with a large population effect size, r = .37, in a priori analysis to determine sample size. The minimum sample size was determined by performing a priori analysis for a Pearson correlation between age and symbolic and non-symbolic numerical ability using the G*Power Version 3.1.9.6 (Faul et al., 2007), considering an effect size of 0.80 (or 80%) at = .05 and r = .37. G*Power output is provided in Appendix A. Completed responses received exceeded the minimum sample size requirement.
Recruitment of participants was conducted by approaching a network of friends and acquaintances, social media such as Facebook, Instagram, and other electronic bulletins. Visually impaired individuals and persons with English proficiency level below grade 8 or post-graduate qualification in science or mathematics were not invited for this study and thereby excluded from participation. Project details were briefly described to the participants during the initial recruitment conversation. In addition, individuals between the ages of 18 and 80 were individually provided with an email containing the online test link and a document detailing the study details. The contact particulars of the study organisers obtained ethics approval, and details of support services available (in case participants experience any distress) were included in the study details document.
MaterialsWide Range Achievement Test Math Computation subscale (WRAT-4)
WRAT-4, a norm-referenced skills assessment instrument, includes subscales that measure reading, maths, spelling, and comprehension skills for use with individuals aged 5 through 94 (Dell et al., 2008). The Math Computation subscale is designed to measure an individual's ability to perform basic mathematics computations through counting, identifying numbers, and calculating mathematics problems (Dell et al., 2008). The oral section of the Math Subscale was excluded as this proposed study participants will be older than 18 years of age. WRAT-4 includes the blue and green forms, which can be used interchangeably, permitting retesting within a short period. This study will employ only the blue form of the 2006 version of WRAT-4, which has been reported to have a standard error of measurement of 5 with a reliability coefficient of = 0.96, item separation reliability of 1.0 and internal reliability measures of .87 to .93 (IvyPanda, 2021, February 10). The internal consistency of the Math computation subscale of WRAT-4 for an age-based sample blue form is = 0.89 (IvyPanda, 2021, February 10). Abreu-Mendoza et al. (2019) were satisfied with the criterion validity.
The Math Computation component of the math subscale comprised 40 problems to be solved (without using calculators). The questions were arranged as per the difficulty level, providing insight into how people of varied ages scored within time limitations. The participant was awarded one point for each correct answer, and unanswered questions and incorrect answers were scored zero. For each participant, the scores were summed up, reflecting the individual's performance. High scores reflect high symbolic numerical ability and vice versa. The Math Computation subscale is provided in Appendix C.
Dot Enumeration Task
DET comprises a set of randomly arranged dots ranging from one to nine, which participants were required to enumerate as quickly as possible by simultaneously entering the number on their computer. DET evaluated arithmetic ability and response time to assess enumeration accuracy and speed. The 48 arithmetic ability tests were presented in a fixed pseudo-random order with no dot number occurring twice in succession (interstimulus-interval: 1120 ms). Two grey displays of the same surface area with different numbers of yellow squares were presented side by side on the screen, and participants were required to select the numerically larger one as quickly as possible by keypress response. Working memory assessment involved displays presented between 20 and 72 squares, and numerical distances between the two displays ranging from eight to 25 squares. After three practice trials with feedback, 72 test trials (four for each numerical distance) were presented in a fixed pseudo-random order (interstimulus-interval: 300 ms). A short response time in DET signified high non-symbolic numerical ability and vice versa. Gray and Reeve (2014) confirmed that DET scores (enumeration efficiency) predicted numerical ability over and above the influence of general cognitive functions. An example of a question in DET is provided in Appendix D.
Procedure
Participants were required to fully complete the online test comprising the WRAT-4 and DET estimated to take about 30 minutes in a quiet environment with minimal distractions in one session on their computer at a location of their preference. Participants were allowed to adjust the brightness and contrast of the display and place their chair at personal convenience. Before commencing the test, participants could complete five practice examples. The test began with details of the study followed by the informed consent form, acceptance of which initiated the test. Non-acceptance of informed consent was treated as a withdrawal from participation. An incentive of $10 (as an electronic gift voucher from a major grocery chain) was provided to participants upon test completion. The online test ended with the participant providing details about where the gift voucher was to be emailed, thanking them for participation along with confirmation of anonymity and confidentiality.
Proposed AnalysisSPSS (version 28) was used to analyse the data in this correlational study wherein the participant's age and the scores of the WRAT-4 and DET are the variables. Each participant was allowed to complete the test only once, and participant selection criteria included steps aimed at ensuring that a participant's score is not influenced by other participants, thereby ensuring the independence of data.
Missing Value Analysis
Missing data can reduce statistical power, produce biased estimates and lead to invalid conclusions. To minimise missing values and ensure the completion of all questions, before commencing the online test, participants were reminded to completely answer each question before progressing to the next question. Participants could advance to the next question after answering the current question or expiry of time, ensuring each question received a score. Initial screening of the data was conducted to identify responses received from software applications programmed to execute specific tasks as part of another computer program or to simulate human activity (bots). Once the responses from bots were identified and removed, the remaining responses were assessed for missing values before analysis to mitigate the impact of missing values. The mean substitution approach was undertaken to deal with any missing values. Mean substitution is a method in whichmissing observations for a score are replaced by the average of observed data for that score in other participants.
Assumption Testing
Outliers potentially decrease the value of a correlation coefficient; hence an outlier management approach consisting of determining outliers using visual inspection of box plots is included. Median values are least affected by non-symmetrical distributions (Field, 2018). Hence outliers identified by box plots will be replaced with the median values. The assumptions of data linearly and normality will be validated through the visual inspection of scatterplots and the Shapiro-Wilk test, respectively. The correlation coefficient provides a reliable measure of the strength of the linear relationship only if the relationship between the variables, age and symbolic and non-symbolic numerical ability, is linear (Field, 2018). As recommended by Field (2018), a visual inspection of the plot of the participant's age against the WRAT-4 and DET scores will be conducted to confirm if the linearity assumption is satisfied. A non-significant value provided by the Shapiro-Wilk test will be used to confirm satisfaction of the normality assumption. Descriptive statistics will be computed upon completion of outlier management and presented in a table. As Enders and Bandalos (2001) recommended, the Missing at Random assumption is adopted for this study and missing data will be substituted using the Maximum Likelihood Estimation approach. Bivariate correlations and significance testing for mean comparisons will be completed using the estimate of standard errors. Pearson's Correlation Analysis
Correlation coefficients are widely used to measure the association between variables measured, which is expected to range from -1.0 to +1.0 (Taylor, 1990). This study proposes to compute the strength and direction of the correlation between age and symbolic and non-symbolic numerical ability by calculating the correlation coefficient (r). A negative value of r will signify that symbolic and non-symbolic numerical ability decreases with age, whereas a positive value of r will convey the contrary. A zero value of r will indicate an absence of relationship, and the degree of closeness of r to +1 or -1 will convey the strength of association. The square of the correlation coefficient (or r square after ignoring decimal points) will signify the variance in age (by percentage) that is related to the variance (by percentage) in symbolic and non-symbolic numerical ability. Statistical significance will also be reported, along with sample size, indicating the likelihood of the reported correlation resulting from chance in the form of random sampling error.
Woodrow (2014) recommends that the decision about how significant the results of correlation analysis is informed by the study purpose, and if the study hypothesises a strong correlation between variables, then a correlation coefficient value, such as r = .37, would suffice. The aim of this study aims is to examine the strength and direction of the relationship between age and symbolic and non-symbolic numerical ability. Hence relying on Woodrow's recommendation, r = .37 with = .05 will be used for both variables. Results will be significant if the computed value of p < 0.05. The correlation between age and symbolic and non-symbolic numerical ability calculated from the proposed data collection will be presented as separate graphs.
Open Science Framework
Data collected, analysis conducted, findings, and any other information relevant to the replication of this study, along with the ethics approval, will be uploaded on the Open Science Framework (OSF) maintained and developed bythe Center for Open Science. It is not intended to collect any identifying data during the data-gathering process. Nevertheless, data will be scanned to ensure anonymity before conducting analysis and once again before uploading on OSF. The data analysis process will be written in easy-to-understand language with assumptions and outlier management clearly stated.
Results
Descriptive and inferential statistical analyses
Missing data and outliers
Assumptions of correlation are tested and is it clearly explained (and justified) what was done if assumptions were violated? Is it clear how the data were analyzed and can an academic who is not an expert in the field understand what was done and why?
Are the results appropriately described in APA format?Students also need to provide effect sizes and confidence intervals
Is it clear how the analyses can be replicated? Are the tables and figures clear and in line with APA format?
Discussion
Are aim and hypotheses clearly and concisely restatedIs it clear if hypotheses were supported or not? you also need to interpret the effect size and confidence interval/reliability of the finding.
How do these results (and the effect size) relate to previous studies on this topic. Are they similar/different (again not only in relation to significance but more importantly in relation to effect size)? Are theoretical and/or practical implications of the findings discussed?
Are strengths, limitations and future directions discussed? Is there a final conclusion.
Appendix A: G*Power Output
091440000Appendix B: Project details
TitleRelationship between Age and Numerical Ability: A Correlational Analysis
Ethics Approval Number210505
Principal InvestigatorDr Jian Chen
Associate InvestigatorMr Rajesh Patel
Introduction
You are invited to participate in this research project conducted by ISN Psychology called Relationship between Age and Numerical Ability: A Correlational Analysis. This Participant Information Sheet outlines the research project. It explains the processes involved with taking part. Knowing what is involved will help you decide if you want to participate in the research.
Please read this information carefully. Ask questions about anything you don't understand or want to know more about. Before deciding to participate, you might want to talk about it with a relative or friend. Participation in this research is voluntary. If you don't wish to participate, you don't have to.
If you decide to participate in the research project, you will be asked to sign the consent section. By signing it, you are telling us that you:
Understand what you have read
Consent to take part in the research described
What is the purpose of this research?
The aim of the present study is to investigate the strength and direction of the relationship between age and numerical ability. Numerical ability is made of the symbolic numerical ability, which is associated with digits or number words, and non-symbolic numerical ability related to collections or quantities of items (such as dots). In the context of the growing number of aged people and increasing lifespan, it is important to understand the relationship between age and numerical ability, as this ability has been found to influence financial well-being and quality of life. Though a limited number of studies have investigated basic non-symbolic numerical processing in older adults, the methods and stimuli used have varied widely, with some contradictory results.
Insight into the relationship between age and numerical processing ability would contribute to the existing literature. Furthermore, it would also provide validation for future studies in the maintenance and enhancement of numerical processing ability, thereby facilitating the well-being of a fast-growing ageing Australian demographic.
What does participation in this research involve?
Formal acceptance of this consent form is required before participating in this study.
To be eligible to participate in this study, you confirm that
You are more than 20 years of age
You are proficient in English (higher than grade 8 level)
You confirm that you have good vision
You do not have a post-graduate qualification in science or mathematics
This test is estimated to take about 30 to 40 minutes and can be completed anytime at a place convenient to you, but it needs to be completed in a single session. You will need to complete both parts of this test fully. The first part will require confirmation of the number of dots on the screen. In the second part, you will be required to perform simple calculations. Each question needs to be answered within the defined time limit. Only after the question is answered or the time limit is over will you be allowed to progress to the next question.
Please be assured we will not be collecting personal information, ensuring that data collection remains anonymous. Consent to participate and test results remain confidential. Over the next three days, we will contact you to answer any questions that you may have and seek feedback and suggestions.
Study findings are expected to be available after three months. Please let us know if you would be interested in a summary of the findings. As a token of appreciation, upon completion of the test, we will email you an electronic gift card for $10 for Coles Supermarket within two days.
Do I have to take part in this research project?
Participation in any research project is voluntary. If you do not wish to participate, you do not have to. If you decide to participate and change your mind, you are free to withdraw from the project at any stage. If you choose to withdraw from the project, please notify a research team member, and you will be asked to complete and sign a 'Withdrawal of Consent' form.
Your decision whether to take part or not to take part, or to take part and then withdraw, will not affect your relationship with ISN Psychology or the researchers.
What are the possible benefits of taking part?
We estimate the findings of this study to provide validation for future studies in the maintenance and enhancement of numerical processing ability, thereby facilitating the well-being of a fast-growing ageing Australian demographic. There will be no clear benefit to you from participating in this research. As a token of appreciation for your participation, we will provide you with a $10 gift voucher from Coles Supermarkets upon completing this study.
What are the possible risks and disadvantages of taking part?
You may feel that some of our questions are stressful or upsetting. If you do not wish to answer a question, you may skip it and go to the next question, or you may stop immediately. If you become upset or distressed due to your participation in the research project, please contact the chief investigator Rajesh Patel at research@isn.edu.au.
Additionally, you may wish to contact one of the following third-party counselling services:
Lifeline Australia Crisis Support: 13 11 14 (available 24 hours)
Beyond Blue: 1300 22 4636
What will happen to information about me?
All collected data will be non-identifiable. Data will be stored on the institute server, with access restricted only to the project team. Server access is controlled by a password along with a 2-Factor Authentication. Non-identifiable data will be retained only on our server for five years and destroyed. By participating in this study, you consent us to use the test scores and your age. No other information will be collected and/or stored. Your information will only be used for this research project and will only be disclosed with your permission, except as required by law.
It is anticipated that the results of this research project will be published and/or presented in various forums. In any publication and/or presentation, information will be provided so that you cannot be identified.
Who has reviewed the research project?
All research in Australia involving humans is reviewed by an independent group called the Human Research Ethics Committee (HREC). The ethical aspects of this research project have been approved by the ISN Psychology HREC (approval number [approval number].) This project will be carried out according to the National Statement on Ethical Conduct in Human Research (2007). This Statement has been developed to protect the interests of people who agree to participate in human research studies.
Further information and who to contact
The person you may need to contact will depend on the nature of your query. If you want any further information concerning this project or if you have any problems which may be related to your involvement in the project, you can contact the research contact person below:
Research contact person
NameDr Jian Chen
PositionPrincipal Investigator
Telephone0418 331 332
Emailresearch@isn.edu.au
If you have any complaints about any aspect of the project, the way it is being conducted or any questions about being a research participant in general, then you may contact Reviewing HREC approving this research and the HREC Secretary's details
Reviewing HREC nameISN Psychology HREC
HREC SecretaryMelissa Mulraney
Emailethics@isn.edu.au
Appendix C: Wide Range Achievement Test Math Computation subscale (WRAT-4)
Appendix D: Dot Enumeration Test (DET)
Short-term memory test: Placing dots online based on memory
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Australian Institute of Health and Welfare. (2022). Life expectancy. Australian Institute of Health and Welfare. https://www.aihw.gov.au/reports/life-expectancy-death/deaths-in-australia/contents/life-expectancy.
Dell, C. A., Harrold, B., & Dell, T. (2008). Test review of Wide Range Achievement TestFourth Edition.Rehabilitation Counseling Bulletin,52(1), 5760. https://doi.org/10.1177/0034355208320076
Duverne, S., & Lemaire, P. (2004). Age-related differences in arithmetic problem-verification strategies.The Journals of Gerontology Series B: Psychological Sciences and Social Sciences,59(3), 135-142. https://doi.org/10.1093/geronb/59.3.P135Enders, C. K., & Bandalos, D. L. (2001). The relative performance of full information maximum likelihood estimation for missing data in structural equation models. Structural Equation Modeling, 8(3), 430-457.
Faul, F., Erdfelder, E., Lang, A., & Buchner, A. (2007). G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behavior Research Methods, 39(2), 175-191. doi:10.3758/bf03193146
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