🧠 MindStat

⚠️ Example not found

This example does not exist or may have been moved.

← Browse all examples
📊
ANOVA

One-Way ANOVA — Three Teaching Methods

Compare exam scores across Traditional, Blended, and Online teaching methods. Full SS decomposition, F-ratio, η²=.86, Tukey post-hoc.

📊 F(2,12) = 36.24, p < .001, η² = .86
← All Examples 📄 Full Examples Page ▶ Open in MindStat App
Step-by-step solution
View in context →

📊 3 · ANOVA

3a · One-Way ANOVA: Three Teaching Methods
ANOVA
Research Question: Do three teaching methods (Traditional, Blended, Online) produce different exam scores?
TraditionalBlendedOnline
708575
728878
688272
749080
718776
M=71M=86.4M=76.2
ANOVA Decomposition
S S T o t a l = S S B e t w e e n + S S W i t h i n S S B = ∑ j = 1 k n j ( x ¯ j − x ¯ . . ) 2 , S S W = ∑ j = 1 k ∑ i = 1 n j ( x i j − x ¯ j ) 2 F = M S B M S W = S S B / ( k − 1 ) S S W / ( N − k )
  1. 1
    Grand Mean:
    x ¯ . . = 71 ( 5 ) + 86.4 ( 5 ) + 76.2 ( 5 ) 15 = 1178 15 = 77.87
  2. 2
    SSBetween:
    S S B = 5 ( 71 − 77.87 ) 2 + 5 ( 86.4 − 77.87 ) 2 + 5 ( 76.2 − 77.87 ) 2 = 5 ( 47.20 ) + 5 ( 72.76 ) + 5 ( 2.79 ) = 236.0 + 363.8 + 13.9 = 613.7
  3. 3
    SSWithin:
    S S W = [ ( 70 − 71 ) 2 + ( 72 − 71 ) 2 + ⋯ ] + ⋯ = 20.0 + 38.8 + 42.8 = 101.6
  4. 4
    F-statistic:
    M S B = 613.7 3 − 1 = 306.85 , M S W = 101.6 15 − 3 = 8.467 F ( 2 , 12 ) = 306.85 8.467 = 36.24
  5. 5
    Effect size η²:
    η 2 = S S B S S T = 613.7 613.7 + 101.6 = 613.7 715.3 = 0.858 ( large,  η 2 > .14 )
36.24
F(2,12)
<.001
p
0.858
η²
306.85
MSB
8.467
MSW
🔴 Reject H₀ — Teaching method has a significant effect, F(2,12)=36.24, p<.001, η²=.86 (large). Post-hoc Tukey: B>C>A, all pairs significant.
APA-7
A one-way ANOVA revealed a significant effect of teaching method on exam scores, F(2, 12) = 36.24, p < .001, η² = .86. Post-hoc Tukey tests indicated that Blended (M = 86.40) outperformed Online (M = 76.20) and Traditional (M = 71.00), all ps < .001.

Related Examples