Statistics and Data Analysis for the Social and Behavioral Sciences

Question 1

A beverage company conducted a study examining whether people preferred the taste of their soft drinks to the taste of their competitors’ soft drinks. In the study, there were 216 Chinese, 171 Malays, 103 Indians, and 90 people from other ethnic groups (Others).

The company wants to know whether the proportion of people in each ethnic group in the sample is the same as the corresponding proportion in the population. According to census data, as of 2021, the proportions of the ethnic groups in the population are: Chinese (74.25%), Malays (13.66%), Indians (8.90%) and Others (3.19%).

Identify the most appropriate statistical test to conduct if the company wants to determine whether the proportion of people in each ethnic group in the sample is different from that in the population. Explain why this is the most appropriate statistical test by providing two reasons in the context of this study.

Then, using hand calculations, analyse the data by conducting the statistical test you identified. Show all working. Interpret the results of your
data analysis. Explain your answer with reference to the p value and the alpha level. Use an alpha level of .05. You do not need to report the results in APA format for this question.

Question 2

In 2017, a group of behavioural scientists at National Environment Agency (NEA) wanted to find out if giving out free tissue packets (with a reminder to return the tray to the tray area) would improve tray return rates in hawker centres. They randomly selected 10 hawker centres for a 3-week field study. In the first week (pre-intervention phase), they observed the 10 hawker centres’ customers to establish a baseline tray return rate.

In the second week (intervention phase), they recruited volunteers to give out the free tissue packets and recorded the tray return rate during the week. In the final week (post-intervention phase), they stopped giving out the free tissue packets and recorded the tray return rate for each hawker centre.
The average tray return rates (%) in the 10 hawker centres for each phase are presented below.

Based on the study design, identify the most appropriate statistical test to conduct. Explain why this is the most appropriate statistical test by providing two reasons in the context of this study. Then, assuming all the assumptions of the statistical test you identified are met and there are no concerns about small sample size, analyse the data using jamovi. Show the jamovi spreadsheet by taking a screenshot of the spreadsheet (i.e., what you see when you
click the DATA tab) and pasting it in your answer.

The jamovi spreadsheet should be correctly formatted. Further, paste all the output necessary for interpretation of the results in your answer. Interpret fully the results of your data analysis. Explain your answer with reference to the p values and the alpha level, using an alpha level of .05. Discuss how NEA
can use the findings to inform its policy. You do not need to report the results in APA format for this question

Question 3

Paul wants to know whether the obesity of politicians in a country predicts the corruption levels in that country. Using a computer vision algorithm that analysed frontal face images to calculate body-mass index (BMI), he estimated the BMI of 299 cabinet ministers from 15 post-Soviet countries who were in office in 2017.

For each country, he then calculated the median estimated BMI for the cabinet ministers. Higher values on the median estimated BMI represent greater obesity. He also recorded the Transparency International Corruption
Perceptions Index (CPI) score for each country. Lower scores on the CPI represent higher (perceived) levels of corruption in the country, with scores ranging from 0 (highly corrupt) to 100 (not corrupt). The data are shown below.

a. For this question, assume that the scale of measurement for both variables is interval. Based on this information and the study design, identify the most appropriate statistical test to conduct.

Explain why this is the most appropriate statistical test by providing two reasons in the context of this study. Then, assuming all the assumptions of the statistical test you identified are met and there are no concerns about small sample size, analyse the data using jamovi. Show the jamovi spreadsheet by taking a screenshot of the spreadsheet (i.e., what you see when you click the DATA tab) and pasting it in your answer.

The jamovi spreadsheet should be correctly formatted. Further, paste all the output necessary for interpretation of the results in your answer. Report the results in APA format. Use an alpha level of .05 to determine if the result is statistically significant.

b. Discuss the changes you would make to Paul’s study if you wanted to generalize the findings of the study to all the countries in the world and explain why you made those changes