Statistical Test Interpretation and SPSS Decision Rules

Posted on Dec 12, 2025 in Statistics

Statistical Significance: The Main Rule

The decision rule for hypothesis testing is based on the p-value:

  • p < 0.05: Significant → Reject H0 (Null Hypothesis)
  • p ≥ 0.05: Not significant → Fail to reject H0

Choosing the Appropriate Test:

  • 1 group vs known value → One-Sample T-Test
  • 2 groups (different people) → Independent Samples T-Test
  • 2 groups (same people before/after) → Paired Samples T-Test
  • 3+ groups → ANOVA (+ Tukey Post-Hoc if significant)
  • Numeric ↔ Numeric relationship → Correlation
  • Predict Y from X → Regression
  • Categorical ↔ Categorical relationship → Chi-Square Test

1. One-Sample T-Test

  • Use Case: Comparing one group’s mean against a known target number.
  • Core Question: “Is my sample average equal to this known value?”
  • SPSS Output: Check Sig (2-tailed).
  • Interpretation: If p < 0.05, the mean is significantly different.
  • Interpretation Template: “p = __. Mean is (significantly/not significantly) different from the known value.”

2. Independent Samples T-Test

  • Use Case: Comparing means of two separate groups.
  • Core Question: “Do two groups have different averages?”
  • SPSS Output: Group Statistics + Independent Samples Test.
  • Interpretation: If p < 0.05, the groups differ significantly.
  • Interpretation Template: “p = __. Groups differ. Group __ mean is higher.”

3. Paired Samples T-Test

  • Use Case: Comparing the same people before & after an intervention.
  • Core Question: “Did the group improve or change?”
  • SPSS Output: Paired Samples Test.
  • Interpretation: If p < 0.05, there is a significant change.
  • Interpretation Template: “p = __. Before ≠ After.”

4. Analysis of Variance (ANOVA)

  • Use Case: Comparing means of 3 or more groups.
  • Core Question: “Do at least one of these groups differ?”
  • SPSS Output: ANOVA → Sig.
  • Interpretation: If p < 0.05, at least one group mean differs significantly.
  • Interpretation Template: “ANOVA p = __. At least one group differs. Highest mean: __.”

5. Tukey Post-Hoc Test

  • Use Case: Used after a significant ANOVA result.
  • Core Question: “Which specific groups are actually different from each other?”
  • SPSS Output: Compare each pair; check Sig.
  • Interpretation: If p < 0.05, the specific pair differs significantly.
  • Interpretation Template: “__ vs __ differs (p < 0.05).”

6. Chi-Square Test

  • Use Case: Analyzing the relationship between categorical vs. categorical variables.
  • Core Question: “Are these two categories related or associated?”
  • SPSS Output: Chi-Square Tests → Asymp. Sig.
  • Interpretation: If p < 0.05, the categories are related (associated).
  • Interpretation Template: “Chi-square p = __. Variables are associated.”

7. Pearson Correlation

  • Use Case: Analyzing the relationship between two numeric variables.
  • Core Question: “Do X and Y move together?”
  • SPSS Output: Pearson r, Sig.
  • Interpretation:
    • r > 0 → Positive relationship
    • r < 0 → Negative relationship
    • |r| near 1 → Strong relationship
    • p < 0.05 → Significant relationship
  • Interpretation Template: “r = __, p = __. There is a significant (positive/negative) correlation.”

8. Linear Regression Analysis

  • Use Case: Predicting Y from X.
  • Core Question: “If X increases by 1 unit, how does Y change?”
  • SPSS Output: Coefficients (B, Sig) and Model Summary (R²).
  • Interpretation:
    • p < 0.05 → Predictor is significant
    • B > 0 → Y increases as X increases
    • B < 0 → Y decreases as X increases
    • R² = Percentage of variance explained
  • Interpretation Template: “B = __, p = __. The predictor is significant. R² = __.”

Statistical Test Assumptions

Levene’s Test for Variance Equality

  • Rule:
    • p ≥ 0.05 → Equal variances assumed → Use top row of output.
    • p < 0.05 → Variances are not equal → Use bottom row of output.
  • Template: “Levene p = __ → (equal/not equal) variances.”

Assessing Normality

Normality is typically assessed using visual checks:

  • Histogram: Look for a bell-shaped distribution.
  • Q-Q Plot: Points should lie approximately on the diagonal line.

Template: “Data is approximately normal.”

Regression Residual Analysis

  • Rule: A random scatter of residuals indicates assumptions are met.
  • Template: “Residuals are random → model assumptions are valid.”

Interpreting Effect Sizes

Effect sizes quantify the magnitude of the findings, independent of sample size.

  • Correlation Strength (r):
    • r = 0.1: Weak
    • r = 0.3: Moderate
    • r = 0.5: Strong
  • ANOVA (Eta Squared, η²):
    • η² = 0.01: Small effect
    • η² = 0.06: Medium effect
    • η² = 0.14: Large effect
  • Regression (R²): R² represents the percentage of variation in the dependent variable explained by the model.

Null and Alternative Hypotheses (H0 / H1)

  • One-Sample T-Test: H0: μ = value
  • Independent T-Test: H0: μ1 = μ2
  • Paired T-Test: H0: μ_before = μ_after
  • ANOVA: H0: μ1 = μ2 = μ3… (All group means are equal)
  • Correlation: H0: ρ = 0 (No linear relationship)
  • Regression: H0: β = 0 (Predictor has no effect)
  • Chi-Square: H0: Variables are independent (No association)

3-Step SPSS Interpretation Method

  1. Find the Sig. value (p-value).
  2. Compare the p-value with 0.05.
  3. Use the template, incorporating means, r, or B for directionality.

General Template: “p = __ (< or ≥ 0.05), so we (reject/fail to reject) H0. The result is (significant/not significant). Direction: __ has a higher mean / positive relation / predictor increases Y.”

Choosing the Right Statistical Test

  • One-Sample T-Test: 1 group vs a known value. “Is my group’s average equal to this number?”
  • Independent T-Test: 2 different groups. “Do Group A and Group B differ?”
  • Paired T-Test: Same group measured twice. “Did people change after training/treatment?”
  • ANOVA: 3+ groups. “Is at least one group different?”
  • Tukey (Post-Hoc): Used after ANOVA. “Which specific groups differ?”
  • Correlation: Numeric ↔ Numeric relationship. “As X increases, does Y increase?”
  • Regression: Predict Y from X. “How much does Y change when X increases?”
  • Chi-Square: Categorical ↔ Categorical. “Are two categories related?”

Interpreting Statistical Graphs

Boxplot Interpretation

  • Median line = Typical value
  • Higher median → Higher group average
  • Box length = Variation; tall box → High variability
  • Outliers = Dots
  • Overlapping boxes = Similar groups

Template: “Group __ has a higher median; outliers: yes/no.”

Histogram Interpretation

  • Bell-shaped = Normal distribution
  • Right/left skew = Non-normal distribution
  • Multiple peaks = Potential subgroups

Template: “Distribution is approximately normal / skewed.”

Q-Q Plot Interpretation

  • Points on the diagonal line = Normal distribution
  • S-curve = Non-normal distribution
  • Far points = Outliers

Template: “Points follow the diagonal line → Data is normal.”

Scatterplot Interpretation

  • Upward trend = Positive correlation
  • Downward trend = Negative correlation
  • Random cloud = No correlation
  • Tight points = Strong correlation; spread points = Weak correlation
  • Curved pattern = Non-linear relationship

Template: “There is a (positive/negative/weak/strong) relation; outliers yes/no.”

Residual Plot Interpretation

  • Random scatter = Assumptions are met (Homoscedasticity, Linearity)
  • Funnel shape = Heteroscedasticity (unequal variance)
  • Curve pattern = Non-linearity

Template: “Residuals are random → model assumptions are acceptable.”

Error Bar Interpretation

  • Non-overlapping error bars = Likely significant difference between means.

Template: “Error bars overlap / do not overlap.”

Crosstab and Mosaic Plot Interpretation

  • Uneven rectangle sizes (in Mosaic plots) or differing counts (in Crosstabs) suggest an association.

Template: “Counts differ → categories are related.”