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 n1 values in the first sample, n2 values in the second sample, and so on until we have nk values in the kth sample. The null and alternative hypotheses for ANOVA are:
H0: μ1 = μ2 = μ3
Ha: 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).
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