Module 8: Two Sample Hypothesis Tests

Difference between One sample tests and Two Sample Tests

• One sample: comparing it to a known/hypothesized population parameter (e.g. mean/proportion)

• Two sample: comparing two distinct groups/population to each other

Two Main Types of Two-Sample Tests

1. Independent Samples: Two seperate groups with no links or pairings (e.g. comparing test scores from two different classes)

2. Dependent/Paired Samples: (think of it as one person doing 2 different tests) each observation in one group is directly paired with another (e.g. comparing pre-test and post-test

Two Sample T-Tests: When do we use it and Steps

• when samples are independent from each other (unrelated), using it to compare two population means.Sample size (n) greater than or equal to 30

Step 1: State your null and alternate hypothesis

Null: both means equal each other

Alternate: mean1 > mean2 or mean1 < mean2

Step 2: find the sample mean, sample standard deviation and sample size for each group. If only given data/file, use the appropriate section on RStudio.

Step 3: Use R to calculate test statistic, then the p value - make sure to also know if its left or right tailed

Step 4: Make a decision to significance value 0.05 (or otherwise shown)

Step 5: Make statement (e.g. Students using method A performed significantly better than students using method B)

What if you find the word “compares” in a two-sample t-test

actually means different - which is two-tailed

Paired Sample T-Test: Definition, Steps to Perform it

• Subject involves Before and After

Step 1: State the null (null = 0). You will also need before and after values

Step 2: Find the alternate hypothesis : alternate is either ud not equal to 0, ud < 0 (EXPECT A DECREASE) or ud > 0 (EXPECT AN INCREASE)

• Ensure to find the value of After - Before

Step 2: Enter data into RStudio (before and after)

Step 3: Compare with significance level or 0.05

Step 4: Write a Conclusion

Two Sample Hypothesis Tests: Definition, Conditions,. Steps to Perform it

Definition: Used when comparing the proportion of success between two independent groups - ensure there are categorical outcomes (yes/no)