Section 48-50 Computations for a One-Way ANOVA; Tukey’s HSD Test; Scheffé’s Test

Question 1

Computation for a One-Way ANOVA

Answer 1

_ANALYSIS of VARIANCE (ANOVA) (*F* -Test)_ is used to compare multiple sample means.

The calculation of ANOVA is multi-step. Please refer to the “ANOVA (1-Way)” tab on the “Quant Psych Tool” Spreadsheet.

• Essentially, the ANOVA 1-Way tests Multiple Means for STATISTICAL SIGNIFICANCE across a single measure.
• It looks at relationships “Between Groups”, “Within Groups”, and across the TOTALITY of the data and then compares these.
• THE DECISION RULE: If the OBSERVED VALUE of F is greater than the CRITICAL VALUE of F , then REJECT the NULL HYPOTHESIS and DECLARE STATISTICAL SIGNIFICANCE at the chosen ALPHA LEVEL (.05, .01, .001). Otherwise, do not reject it.
  
  • If you CANNOT REJECT the NULL HYPOTHESIS, then you are DONE.
  • If you CAN REJECT the NULL HYPOTHESIS, then you have to DETERMINE which of the means is SIGNIFICANT.
    
    • Until we learn a computational way to determine that, you can simply find the 95% Confidence interval around each of the SAMPLE means and see if there are any intervals that do NOT overlap the others. The one that does NOT overlap the other is the one that is SIGNIFICANT.
      
      • To calculate the 95% Confidence Interval, use the Standard Error of the Means (SEm) calculation and multiply by 1.96.
      • More specifically:
        
        • Top = m + SEm * 1.96
        • Bottom = m - SEm * 1.96

Question 2

Tukey’s HSD Test

Answer 2

TUKEY’s HSD Test (Tukey’s Honestly Significant Difference (HSD) test) – is a test for DETERMINING the SIGNIFICANCE of the DIFFERENCES among PAIRS of MEANS AFTER obtaining an OVERALL SIGNIFICANT RESULT using ANOVA.

• Once the one-way ANOVA indicates that there is at least one significant difference in an entire set of differences, then we move on to Tukey’s HSD Test to see which specific difference is the SIGNIFICANT one.
• See the “Tukey q Test” Tab on the “Quant Psych Tool” Spreadsheet for calculations (That feeds off of the “ANOVA 1-Way” Tab).

Question 3

Sheffe’s Test

Answer 3

SHEFFE’S TEST – Tests the individual relationships among groups AFTER an ANOVA has found statistical Significance among the entire group.

• This is MORE CONSERVATIVE than the Tukey HSD – meaning the Scheffe’s Test is LESS LIKELY to lead to a REJECTION of the NULL HYPOTHESIS than the Tukey’s Test.
• See “Sheffe’s Test” tab in the “Quant Psych Tool” Spreadsheet for steps, formulas, and interpretations.