In this lesson you’ll continue with t-tests, but this time for independent samples. In this case, we have two groups of subjects (which should be randomly placed into these groups) and we can either observe certain data or do an experiment. An experiment involves direct interaction of some sort with the subjects.
Observation examples:
1. You’re the CEO of a machine manufacturing company with two plants that produce approximately equal numbers of products, and you want to know if one plant is more efficient than the other in terms of product quality. To test this, you observe the proportion of defective equipment made each quarter at each plant. Your data would look something like this:
| Year, Quarter | Plant 1 | Plant 2 |
| Y1Q1 | 0.29 | 0.51 |
| Y2Q2 | 0.14 | 0.23 |
| Y3Q3 | 0.17 | 0.37 |
| … | … | … |
In this example n will be the same for each sample, but this doesn’t have to be the case to do an independent-samples t-test.
2. You’re the superintendent of a school district and want to know if AP History scores are about equal among two high schools in your district. To test this, you collect the AP History test scores of everyone in the two high schools who took the test. Your data will look something like this:
| Student | High School 1 | High School 2 |
| 1 | 2.5 | 1.5 |
| 2 | 3.0 | 4 |
| 3 | 2.0 | 3.0 |
| … | … | … |
| n | 1.5 | 2.5 |
| … | … | |
| k | 5.0 |
In this example, the number in each sample is different: High School 1 has k students who took the AP History test; High School 2 has n students who did so.
Experiment examples:
1. You want to know if exercise affects creativity differently in males than females. You have a group of 36 female volunteers and 42 male volunteers take a creativity test, then exercise for 30 minutes and retake the test. You then compare the differences in creativity between males and females.
2. You want to compare the effects of two acne medications to determine which is more effective. You have two random groups of people (about the same age and of both genders) take each medication and after four weeks you compare the results.
Hopefully you now understand the difference between dependent and independent samples. Let’s now discuss how to conduct this type of t-test.
Our hypotheses and basic t-statistic remain the same. The only thing that changes is the standard error, which is now based on two samples from different populations, each with its own sample size and standard deviation.
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Continue to Lesson 12, or select a lesson below.
Lesson 1: Introduction to Statistical Research Methods
Lesson 2: Visualizing Data
Lesson 3: Central Tendency
Lesson 4: Variability
Lesson 5: Standardizing
Lesson 6: Normal Distribution
Lesson 7: Sampling Distributions
Lesson 8: Estimation
Lesson 9: Hypothesis Testing
Lesson 10: t-Tests for Dependent Samples
Lesson 11: t-Tests for Independent Samples
Lesson 12: Intro to One-Way ANOVA
Lesson 13: One-Way ANOVA: Test significance of differences
Lesson 14: Correlation
Lesson 15: Linear Regression
Lesson 16: Chi-Squared Tests
Afterward
Index