Question

Team SASK is studying distractions while driving.

They watched people driving, and recorded any distractions they saw. If someone had more than one distraction, they recorded that fact.

They will analyze each distraction separately. For each, they want to know how common each distraction is.

* What hypothesis test and/or confidence interval can you use for this?

• Single-sample t-test
• One sample proportion test (Chi-square test)
• Chi-square goodness-of-fit test
• Two-sample t-test
• Paired t-test
• One-way ANOVA
• Repeated-measures ANOVA
• Multi-way ANOVA
• Test for Pearson's correlation
• Linear regression
• Create two-way table and compare two proportions (z-test or chi-square test of independence)

* What are the main assumptions of the test and/or CI?

• All individuals being studied are independent of each other
• Either the outcome variable is normally distributed OR n is large (rule of thumb: n ≥ 30 for each group) OR both
• For each group i, n_i * p_i (the expected frequency) is large (rule of thumb: np ≥ 5 for every group)
• All the variables must all be approximately normally distributed
• The outcome variable y must all be approximately normally distributed, but the explanatory variable x does not need to be normal
• There are no extreme outliers or influential points
• The x-y relationship is linear
• Variance is similar for all levels of the input variable

Answer 1

In this question there are more than two distractions are possible.

So we compare more than two different groups.

For comparison of more than two groups, multi way ANOVA test is used.

So answer of first question is multi-way ANOVA test is required for given study.

Now we discuss second question.

Main assumption of the test and /or CI are below.

1)All individuals being studied are independent of each other

2)Either the outcome variable is normally distributed OR n is large (rule of thumb: n ≥ 30 for each group) OR both

3)All the variables must all be approximately normally distributed.

4)Variance is similar for all levels of the input variable.

So these are main assumption for multi-way ANOVA test.

I hope you understand.

Thank you.