PURCHASE A DIGITAL COPY PURCHASE A HARD COPY 

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  tTests for Dependent Samples 
Lesson 11  tTests for Independent Samples 
Lesson 12  Intro to OneWay ANOVA 
Lesson 13  OneWay ANOVA: Test significance of differences 
Lesson 14  Correlation 
Lesson 15  Linear Regression 
Lesson 16  ChiSquared Tests 
Afterward  
Index 
tTests 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 ttests (AB, AC, BC); for four samples (A, B, C, and D) we would have to do 6 ttests (AB, AC, AD, BC, BC, CD); for five samples 10 ttests; 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. Oneway 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:
: At least two populations are significantly different
Recall that the tstatistic 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).
When we compare three or more samples, we want the same thing: some kind of variability between means (betweengroup variability) divided by
a standard error (withingroup variability). We’ll call this the Fstatistic.
To continue learning, purchase StreetSmart Stats: A Friendly Introduction to Statistical Research Methods.
Click here for a hard copy
Click here for a digital copy