Statistical Power in Regression
Power analysis in regression helps you determine whether your sample size is large enough to detect an effect of a certain size with a given level of confidence. It’s essential when planning studies to avoid wasting resources or missing true relationships (Type II errors).
🎯 What Is Statistical Power?
Statistical power is the probability of correctly rejecting a false null hypothesis (i.e., detecting a true effect). Conventionally:
- Power ≥ 0.80 is considered adequate
- Power depends on:
- Effect size (e.g., R_squared, f_squared)
- Sample size (N)
- Significance level (α), typically 0.05
- Number of predictors (k)
📐 Effect Size Metric in Regression Power Analysis: f²
f_squared=R_squared/(1−R_squared)
Cohen’s (1988) guidelines for f_squared:
- 0.02 = small
- 0.15 = medium
- 0.35 = large
🧮 How to Do Power Analysis for Regression
✅ Using G*Power (Free tool)
- Open G*Power
- Select:
- Test family: F tests
- Statistical test: Linear multiple regression: Fixed model, R² deviation from zero
- Choose:
- Type of power analysis: A priori (to calculate required sample size)
- Input parameters:
- Effect size f_squared
- α = 0.05 (default)
- Power = 0.80 or 0.90
- Number of predictors
👉 Click “Calculate” – G*Power will give you the required sample size.
🔁 Example
You want to detect a medium effect (f² = 0.15) with:
- α = 0.05
- Power = 0.80
- Predictors = 4
G*Power says you need ~85 participants.
✅ How to Do Power Analysis for Regression in SPSS (v28/v29+)
🔁 Scenario
You want to determine how many cases (sample size) are needed to detect a medium effect size in a linear regression model with 4 predictors, at 80% power, and a significance level of 0.05.
🧭 Step-by-Step Instructions
🔹 Step 1: Access Power Analysis
- Go to:
Analyze > Power Analysis > Linear Regression
🔹 Step 2: Choose the Type of Analysis
In the dialog box, choose from one of the following:
- Compute required sample size (A priori)
- Compute power given sample size
- Compute effect size
- Compute α error probability
For planning, choose: Compute required sample size
🔹 Step 3: Define Model Parameters
Fill in the following fields:
- Effect size (f²):
- 0.02 = small
- 0.15 = medium
- 0.35 = large
- Number of predictors: Enter the number of independent variables
- α level: Commonly 0.05
- Power (1 – β): Typically 0.80 or 0.90
For example:
Effect size = 0.15
Predictors = 4
α = 0.05
Power = 0.80
🔹 Step 4: Run the Analysis
Click OK. SPSS will output:
- Required sample size
- Effect size and power curves (if requested)
- A summary table with all inputs and computed results
🧾 Interpreting SPSS Output
The output will show:
- Required N (sample size)
- Achieved power (if computing power instead of N)
- Graph (optional) showing the relationship between power and sample size
💡 Tip: Use Charts for Reports
Click the Plots tab before running the analysis to generate:
- Power vs. sample size graphs
- Helpful visuals for presentations or publications
🧠 Bonus: Effect Size Estimator Tool in SPSS
SPSS also includes an Effect Size Calculator under:
Analyze > Power Analysis > Effect Size Estimator
Use it to convert between:
- R² and f²
- Cohen’s d and η²
- t-values and effect sizes
✅ Final Thoughts
With SPSS’s new Power Analysis module, you no longer need to switch between tools like G*Power or Excel. You can now plan, analyze, and report everything from within SPSS — all using a consistent interface.
✅ Summary
| Component | Description |
|---|---|
| Effect Size | f² based on expected R² |
| Tool to Use | G*Power (recommended), SPSS |
| Ideal Power | ≥ 0.80 |
| Main Use | Plan sample size for detecting effects |