Statistics and Data Analysis for Social and Behavioural Sciences

Question 1

The principal of a primary school in Singapore read about the potential benefits of omega-3 supplements on cognitive health. He wanted to find out whether this is true among students in his school. He tasked his teachers to do a survey among the students. Due to time constraints, the teachers could only obtain responses from a small proportion of students. Based on the survey responses from 209 students, 94 of them reported that they consume omega-3 supplements regularly. Among students who fared better academically (top 5% of their cohort, based on marks from latest Math exam), 39 of them consume omega-3 supplements regularly while 28 do not.

1. Identify the independent and dependent variables.

• Identify the most appropriate non-parametric statistical test and explain why it is the most appropriate. Assume that all assumptions of the statistical test you identified are met and there are no concerns about small sample size.

• Using Jamovi, conduct the statistical test that you identified in b) to analyse the given dataset to address the principal’s objective. Show the Jamovi output by copying and pasting ALL the output that is necessary to interpret the results in your answer.

Note:

• All Jamovi screenshots must be easy to read at 100% zoom setting in Microsoft Word. No marks will be given for Jamovi output that are too small or difficult to read.
  • The identified statistical test must be taught in HBC203.
  • Use an alpha level of .05two-tailed to determine statistical significance.
  • To copy the output, either take a screenshot of the output (preferred) or right click on the respective table(s) and select Copy from the dropdown menu.

• Report the results in APA format and interpret the results in relation to the principal’s objective.
• Besides the small proportion of students who answered the quick survey, identify 2 other limitations of the survey that was done. For each limitation, discuss 1 way to improve the survey.

Question 2

A team of researchers examined the benefits of omega-3 supplements and/or walnuts on cognitive development (numeracy skills and memory) among children aged 6 to 10. They were also interested in studying the relationship between numeracy skills and memory. To address these research objectives, they formulated two Research Questions (RQs):

RQ1. Do children who take omega-3 supplements and/or walnuts have better numeracy skills (as measured by a Math test)?

RQ2. Do children perform better on a Math test because they have better memory?

They recruited 283 children and randomly assigned them to 1 of the following interventions.

• Group A: Omega-3 supplement (0.9g to 1.2g, depending on age and gender)
  • Group B: Walnuts (45g)
  • Group C: Omega-3 supplement (0.9g to 1.2g, depending on age and gender) + Walnuts (45g)

Each child took the omega-3 supplement and/or walnuts every day for 3 months. After that, they completed a Math test and a memory test.

For each Research Question (RQ), answer parts a) to d). Present your answer to each RQ separately and in sequence (i.e., RQ1, followed by RQ2).

1. Identify the independent and dependent variables.

• Identify the most appropriate parametric statistical test and explain why it is the most appropriate. Assume that all assumptions of the statistical test you identified are met and there are no concerns about small sample size.

• Using Jamovi, conduct the statistical test that you identified in Q2b) to analyse the given dataset to address the research objectives. Show the Jamovi output by copying and pasting ALL the output that is necessary to interpret the results in your answer.

Question 3 (30 marks)

1. Should the principal in Question 1 encourage his students to consume walnuts to improve their cognitive development? Clearly state your answer. Then, discuss your answer using the findings in Question 2 and at least 2 academic journal articles.

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Expert Answers on Above Statistics Analysis Assignment

1: Independent and dependent variables – The consumption of Omega-3 supplements is the independent variable whereas the dependent variable is the academic performance.
Most appropriate nonparametric test – The most appropriate nonparametric test is the chi-square test of independence because both the variables for analysis are categorical, and this test is quite useful in analyzing the association between two categorical variables. It will help in evaluating whether Omega-3 supplement consumption would have any effect on academic performance.

Statistical test using Jamovi

The statistical analysis indicates that there is a positive association between omega-3 supplement consumption and academic performance as the chi Square result at 5% significance shows .007. This implies that the students that have consumed omega-3 supplements are more likely to be among the top performers in the maths which implies the existence of a positive relationship between Omega-3 intake and academic achievement.

Two other limitations and improvements

Self reported supplement consumption – there are possibilities that the students may forget to take Omega-3 supplements, and the improvement can be to collect parental confirmation of the same.
No control for adult influencing factors – there are possibilities that academic performance can also be affected by factors like diet, study habits or intelligence. The Improvement can be to include control variables so does the study time and parental education.

Do children who take omega-3 supplements and/or walnuts have better numeracy skills?

The independent variable is the type of intervention such as Omega-3, walnuts and the dependent variable is numeracy skills.
Appropriate parametric test – one way Anova because there is one categorical independent variable within three groups and one continuous dependent variable i.e math score.
Statistical analysis – the performance of statistical analysis using one way Anova shows that the p-value is significant which implies that at least one intervention group differs significantly in numeracy scores.

Should the principal encourage students to consume walnuts?

Yes but it needs to be done in a preventive way. It is evaluated from the findings that omega-3 supplement and walnuts can improve numeracy skills and nutrients also support better cognitive functioning which could enhance academic outcomes.

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