t-tests only test for a significant difference between *two* samples. If we have three samples (A, B, and C), we would have to do 3 different t-tests (AB, AC, BC); for four samples (A, B, C, and D) we would have to do 6 t-tests (AB, AC, AD, BC, BC, CD); for five samples 10 t-tests; etc. **ANOVA**, which stands for “analysis of variance”, allows us to do one test for more than two samples, and tells us if at least two samples are significantly different. One-way ANOVA is used when we only have one variable, or factor.

Henceforth, we’ll denote the number of samples as k. So we have k samples, with n_{1} values in the first sample, n_{2} values in the second sample, and so on until we have n_{k} values in the kth sample. The null and alternative hypotheses for ANOVA are:

H_{0}: μ_{1} = μ_{2} = μ_{3}

H_{a}: At least two populations are significantly different

Recall that the t-statistic tells us whether or not two populations are most likely significantly different (based on the collected samples), and is a function of how far apart samples are from each other (the numerator, which is the difference between means), and the standard error (the denominator). Remember, the standard error is the estimated standard deviation of our expected population distribution (where this population is either based on a sample or the difference between dependent samples, or the result of subtracting two estimated populations based on two independent samples).

**This is a preview of Lesson 12. To access the full book, please purchase a hard copy or a digital version. If you opt for the digital version, you will receive a link via email within 1 business day.**

Continue to Lesson 13, 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