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TipStudy instructions
Work through each section in order — every concept builds on the last.
Complete every Knowledge Check before moving on. Your running score appears in the bottom-right corner of the screen.
Fully expand and interact with the Decision Trees and Flashcards when you encounter them.
Use the APA Builder to practice writing your results.
Click Reveal My Score at the end to see your final result and targeted study advice.
Start here: complete the pre-check, then work through each section.
📋 Pre-Check
A researcher wants to compare the vertical jump heights of soccer players, basketball players, and volleyball players. Why shouldn't they just run three separate paired t-tests (Soccer vs BBall, Soccer vs VBall, BBall vs VBall)?
1. The Logic of Variance (Signal-to-Noise)
ANOVA heavily relies upon breaking down total variance into two distinct compartments. Understanding these two components explains the entire statistical mechanism underlying the F-statistic.
We partition variance into two pools: 1. Between-Groups Variance: The difference between our distinct samples (e.g., the gap between the Training Method and the Control). We want this to be high! This is our signal. 2. Within-Groups Variance: The random, uncontrolled scatter of scores belonging to individuals inside the exact same group. We want this to be low! This is our error/noise.
By measuring these two components, we can synthesize the F-statistic.
🧠 Knowledge Check
If your F-ratio computation generates a value hovering around ~1.00, what is the most scientifically sound interpretation?
2. Reading the Sources of Variance
When mapping out ANOVA, the mathematical steps break down sequentially into Sums of Squares, Mean Squares, and finally the F-ratio itself. This builds the famous Source Table.
🧠 Knowledge Check
To calculate the final F-statistic in a One-Way ANOVA, you divide:
3. Assumptions and Violations
Because ANOVA is a parametric procedure, it rests heavily upon Normality and Homogeneity of Variance.
While ANOVA is relatively robust to mild departures (because of the Central Limit Theorem), violations of equal variance (Homoscedasticity) are serious red flags. Levene’s Test checks this.
🧠 Knowledge Check
SPSS reveals that your Levene's Test for Homogeneity of Variances has a p-value of .021. Because this is less than .05, what is your next course of action?
4. Post-Hoc Triangulation
A significant Omnibus F-test only warns you that at least one difference exists somewhere. It blindly points out the fire but won’t tell you the location, which necessitates deploying Post Hoc (After the Fact) methodology.
The overarching rule is that you never run Post Hoc calculations if the Omnibus F is non-significant.
There are two primary paradigms: - Tukey’s HSD: The standard approach for pairwise comparisons that maintains strong power while safely throttling Familywise error rates. - Bonferroni: Extremely stringent. Takes your alpha level (.05) and forcefully divides it by the total number of comparisons. Best for a small quantity of vital comparisons, as it is aggressively punishing to statistical power overall.
🧠 Knowledge Check
When evaluating the results between 5 distinct resistance training methodologies on vertical leap, what is the primary downside of relying entirely upon the Bonferroni adjustment methodology over Tukey's HSD?
5. Mapping the Effect Sizes (\(\eta^2\) vs \(\omega^2\)).
Flip through these flashcards to familiarize yourself with ANOVA effect size metrics:
Click cards to flip • Review before knowledge check
Eta-Squared (η²)
Evaluates the total percentage of variance in the dependent variable explained by the condition. However, it applies purely to the sample itself and heavily upwardly biases the effect size measurement if the sample is small.
Omega-Squared (ω²)
A more conservative and statistically honest estimation. It attempts to define the variance explained within the generalized population, not just the isolated sample box. Essential when dealing with small groups.
Cohen's f
An effect size used primarily alongside G*Power to evaluate standard deviations across means in an ANOVA in order to proactively compute necessary required sample sizes.
🧠 Knowledge Check
In a One-Way ANOVA with a relatively small sample (N=22), SPSS outputs both an Eta-Squared and an Omega-Squared coefficient. Why should the movement scientist report Omega-Squared?
6. One-Way ANOVA APA Writing Practice
Use the inputs to build the final APA format statement. Ensure you include standard F-syntax. (Example format: F( dfB, dfW ) = 4.22)
APA Statement Builder
Construct your paragraph by entering mock data (or data from lab) into the blanks below.
7. Finish and Reveal Results
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References
1. Furtado, O., Jr. (2026). Statistics for movement science: A hands-on guide with SPSS (1st ed.). https://drfurtado.github.io/sms/
