Tests of Differences between Means, Independent Groups, Standard Deviation Estimated (7 of 8)

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SSE = SSE₁ + SSE₂ = 16 + 10 = 26
df = n₁ - 1 + n₂ - 1 = 7
MSE = SSE/df = 26/7 = 3.71





The p value associated with a t of 0.77 with 7 df is 0.47. Therefore, the difference between groups is not significant.

Summary of Computations

1. Specify the null hypothesis and an alternative hypothesis.
   
   
2. Compute M_d = M₁ - M₂
   
   
3. Compute SSE₁ = Σ(X - M₁)² for Group 1 and SSE₂ = Σ(X -M₂)² for Group 2
   
   
4. Compute SSE = SSE₁ + SSE₂
   
   
5. Compute df = N - 2 where N = n₁ + n₂
   
   
6. Compute MSE = SSE/df
   
   
7. Compute:
   
   
   (If the sample sizes are equal then n_h = n₁ = n₂).
   
   
8. Compute:
   
   
   
9. Compute:
   
   where µ₁ - µ₂ is the difference between population means specified by the null hypothesis (and is usually 0).
   
   
10. Use a t table to compute p from t (step 9) and df (step 5).