Statistical Decision Tree and Analysis Guide

1. The Null Hypothesis ($H_0$): The assumption that there is no effect, no difference, or no relationship.
2. The Alternative Hypothesis ($H_a$): The claim that there is a significant effect or relationship.

To make a decision, you must follow a rigorous six-step process:

1. Define $H_0$ and $H_a$.
2. Pick your statistical test, your significance level ($\alpha$), whether it is a 1-tailed or 2-tailed test, and calculate your Degrees of Freedom (df).
3. Find the critical value using a statistical table.
4. Calculate your test statistic (such as $t$ or $F$).
5. Make a decision: either reject $H_0$ (the result is significant) or retain $H_0$ (the result is not significant).
6. Write a conclusion that includes both words and the statistical evidence.

Exam Tip: Always remember that "retaining $H_0$" does not prove the null hypothesis is true; it simply means you do not have enough evidence to reject it.

Choosing Your Test: A Decision Tree

The most critical skill is selecting the correct test. To do this, you must identify your variables: the Independent Variable (the factor you manipulate or use to group subjects) and the Dependent Variable (the outcome you measure).

Step 1: Check Data Type

First, ask: "Is my data qualitative (categorical) or quantitative (numerical)?"

• Qualitative Data: If you are comparing observed counts against expected values in a table, use the Chi Square test.
• Quantitative Data: If you are dealing with measurements, proceed to analyze the relationship or difference between variables.

Step 2: Relation vs. Manipulation

Next, determine if you are looking for a Relation (association) or a Manipulation (cause and effect).

Correlational Analysis and Regression

If you want to see if two variables move together, use Correlational Analysis. This measures the size and direction of a relationship. To test if a correlation ($r$) is significantly different from zero, you use a $t$-test with $df = N - 2$. If your goal is to use one variable to predict the outcome of another, you move from simple correlation to Regression.

Comparing Groups (t-tests and ANOVA)

If you are comparing groups, the choice depends on how many groups you have and how they are connected:

If you have 2 groups:

• 1-sample t-test: Comparing one group mean to a known value ($df = N - 1$).
• Independent samples t-test: Comparing two entirely different groups (e.g., Men vs. Women) ($df = N - 2$).
• Dependent (Repeated Measures) t-test: Comparing the same people at two different times or matched pairs ($df = N - 1$).

If you have 3 or more groups:

• 1-way ANOVA: Used when you have three or more independent groups to compare.
• Repeated Measures ANOVA: Used when the same participants are measured across three or more time points or conditions.

Summary Table of Statistical Decisions