Exploring Two–Variable Data
When constructing segmented bar graphs to show percentages within each category of a categorical variable, what needs to be consistent across all segments?
The scale representing percentages should remain constant for all bars.
The order of segments should be randomized to avoid bias in interpretation by viewers.
Segment widths should differ based on their percentage values within each bar for clarity purposes.
Each segment's color or shade should vary by bar to display differences clearly.
Which graph is commonly used to represent the distribution of a single categorical variable?
Bar chart
Pie chart (commonly but less ideally used for this purpose)
Dot plot
Time-series plot
When constructing a two-way table from a survey about exercise habits and study time among students, which would be the most appropriate way to summarize the relationship between the two variables?
Calculate the conditional percentages of study time given each exercise habit category.
Create a bar graph showing only the distribution of exercise habits.
List all individual student responses without grouping or summarizing them.
Compute the mean study time for all students regardless of their exercise habits.
In a study comparing two categorical variables, which test should be used to determine if there is an association between the variables in the population?
Chi-square test for independence
One-way ANOVA
Two-sample t-test
Linear regression analysis
Which of the following graphical representations consists of two separate bar charts, one for each categorical variable, plotted next to each other to compare the proportions of data points?
Mosaic plots
Segmented bar graphs
Two-way tables
Side-by-side bar graphs
What kind of table would best display the relationship between two categorical variables?
Box plot
Histogram
Two-way table
Scatterplot
When examining the relationship between two categorical variables in a contingency table, what should you look at to determine if there's an association?
Overall mean of the table entries
Conditional percentages across rows or columns
Total number in each cell only
Differences between maximum and minimum values in cells

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When evaluating the relationship between two categorical variables, why is it important to consider the sample size in a contingency table?
Sample size does not affect the relationship between variables, only their individual distributions.
Larger sample sizes can provide more reliable estimates of the population parameters.
The sample size determines which statistical test should be used to analyze the data.
Smaller sample sizes make calculations more manageable and less time-consuming.
When comparing response rates from mailed surveys about recycling habits across four age groups, which measure would best capture an association that does not depend on the overall sample sizes within each group?
Pearson correlation coefficient (r)
Cramér's V coefficient
Risk difference (RD)
Odds ratio (OR)
What does it mean for two variables to be associated in the context of bivariate categorical data?
There is a cause-and-effect relationship between the variables
The variables have a strong correlation
There is a pattern or trend in the data suggesting a relationship
The variables have identical categories