Lab_Wk04_2023

STAT251 Fundamentals of Biostatistics LABORATORY NOTES Week 4 Exploring Associations: Categorical Variables and Probability Aim: The focus of this lab is exploring associations involving two categorical variables. This lab also consolidates the concepts of independence and conditional probability. Go to Moodle Week 4 Section and download the data file StudentData.csv. Open Jamovi and import the file: select the triple-bar icon, and select Open . Then Browse to the location that data file is in and open the file. To save your analyses in the following sections, save the file as a .omv file at the end of your session. 1. Categorical Response and Categorical Explanatory Variable Let’s see if we can detect any evidence of a relationship between a person’s birthplace and their sex. This information is in the two categorical variables Sex and Born. We will do this by examination of evidence generated in the following three ways: 1. Comparisons of proportions in a contingency table of the variables concerned; 2. Comparison of the column heights in bar charts; 3. Mathematical determination of statistical independence. First check the variable definition and any coding for the variables concerned. It is helpful to look at the frequencies of a categorical variable first to check that the observations have all been entered as the codes or categories suggest. That is, check that the number of categories is as expected and names are consistently spelled. For example, for Sex, check observations have not been entered as both Male and male or both Female and f as that would show as 4 categories. Select Analyses → Exploration →Descriptives. Put Sex and Born into the Variables box, and tick the Frequency Tables box. Discussion : What are the categories for the Born variable? What percentage of students were born in each? Are there any missing values for either variable? 2.1 Contingency Table of Raw Data Now we can obtain the two-way table of counts (or frequencies) for the two nominal variables: Sex and Born . Select Analyses→Frequencies→Independent Samples . Put the variable Born into Rows and Sex into Columns . In the Cells menu, select the Row , Column and Total options under Percentages . STAT251 Laboratory Notes Week 4 1

Contingency Tables sex Born Female Male Total Australia n Observed 23 85 108 % within row 21.30 % 78.70 % 100.00 % % within column 63.89 % 55.56 % 57.14 % % of total 12.17 % 44.97 % 57.14 % Oversea s Observed 13 68 81 % within row 16.05 % 83.95 % 100.00 % % within column 36.11 % 44.44 % 42.86 % % of total 6.88 % 35.98 % 42.86 % Total Observed 36 153 189 % within row 19.05 % 80.95 % 100.00 % % within column 100.00 % 100.00 % 100.00 % % of total 19.05 % 80.95 % 100.00 % STAT251 Laboratory Notes Week 4 2