Here's a clear, step-by-step guide for interpreting your two-way ANOVA (Analysis of Variance) results for understanding how factors like Gender and Time Intervals impact oxidative enzyme activity in response to UV radiation or similar experiments in your study:

Step 1: Identify Key Components

Your two-way ANOVA tests three main effects:

Step-by-Step Interpretation:

1. Check Assumptions:

• Normality: Residuals should be normally distributed (use Shapiro-Wilk test).
• Homogeneity of variance: Similar variance across groups (Levene’s test).

If these assumptions hold, move forward.

2. Look at the ANOVA Table:

A typical two-way ANOVA table provides these details:

| Source | df | Sum of Squares | Mean Square | F-value | p-value | |---------------------|---------------------|-------------|-----------|-----------| | Factor 1 (Gender) | | | | | Factor 2 (Time Interval) | | | | | Interaction (Gender × Time Interval)| | | | | Error | | | | | Total | | | |

Check the significance of each factor:

• If p-value < 0.05 → the effect is statistically significant.
• If p-value ≥ 0.05, no significant effect is detected.

2. Interpreting Main Effects:

Gender:

• If significant (p < 0.05): Indicates gender significantly affects enzyme activity overall.
• If not significant, enzyme activity doesn't differ significantly by gender overall.
• Time Interval:Significant: Enzyme activity changes significantly over time. Not significant: Enzyme activity does not significantly differ across different time intervals.

3. Interaction Interpretation (Gender × Time Interval):

• Significant Interaction:Indicates that the effect of one factor (time) depends on the level of the other (gender). This means gender groups respond differently over time. Example: Male and female enzyme activities differ in how they respond over time. You'd need follow-up tests (simple effects analysis or pairwise comparisons) to identify exactly where differences occur.
• Not Significant:No interaction indicates the effect of time interval is consistent across gender groups.

4. Post-hoc Tests (If Needed):

If you find a significant interaction or a significant main effect with multiple levels (e.g., multiple time intervals):

• Tukey HSD or Bonferroni-corrected tests are commonly used to identify exactly which groups differ significantly from each other.

5. Effect Size (Partial Eta squared, η²):

• Indicates the magnitude of differences (0.01 = small; 0.06 = medium; 0.14+ = large effect size).

Practical Example:

• Significant Gender effect: "Male and female enzymes differ significantly in oxidative activity overall (p < 0.05)."
• Significant Time effect: "Enzyme activity varied significantly over time (p < 0.05), with peak activity at 24 hours post-UV exposure."
• Significant Interaction: "Gender affects enzyme activity differently at specific time intervals after exposure (p < 0.05), suggesting follow-up comparisons are needed."

Example Reported Statement:

“A two-way ANOVA showed significant effects of Gender (F(1,28)=5.21, p=.02) and Time (F(3,84)=4.67, p=.005), with a significant Gender × Time interaction (F(3,84)=3.45, p=.02). Post-hoc analysis revealed significant differences at 24 and 48 hours for males compared to females.”