An introduction to t-tests (includes Excel)

1. t-tests Dr Bryan Mills

2. Why?

5. The magnitude of the effect How Different?

6. The Spread of Data

7. n

9. Yes Significant 1 in 20 P < 0.05 No Not significant P > 0.05 Reject Null Hypothesis Alpha Level

10. Types of Error Correct Decision Type II Error Beta Null is False (true difference) Type I Error Alpha Correct Decision Null is True Reject Null (assume difference) Accept Null

15. Excel Output 2.006 t Critical two-tail 0.051 P(T<=t) two-tail 1.674 t Critical one-tail  You need this ! 0.026 P(T<=t) one-tail 1.995 t Stat 53.000 df 0.000 Hypothesised Mean Diff 30.000 30.000 Observations 156.742 83.381 Variance 17.597 23.241 Mean sample 2 sample 1 t-Test: Two-Sample Assuming Unequal Variances

17. 2.027 t Critical two-tail 2.02 t Critical two-tail 0.14 P(T<=t) two-tail 0.00 P(T<=t) two-tail not significant 1.69 t Critical one-tail significant difference 1.69 t Critical one-tail p>0.05 0.071 P(T<=t) one-tail p<0.05 0.001 P(T<=t) one-tail -1.50 t Stat 3.28 t Stat 37 df 38 df 0 Hypothesized Mean Difference 0 Hypothesized Mean Difference 20 20 Observations 20 20 Observations 89.34 63.78 Variance 3.84 4.77 Variance 64.53 60.38 Mean 60.12 62.27 Mean Women 2 Men 2 Men Women 60 65 60 62

18. The difference in [whatever the data represents] between sample 1 ( M = 23.241 , VAR = 83.381 ) and sample 2 ( M = 17.597, VAR = 156.742) was statistically significant, t (29) = 1.962, p < .05, one-tailed. 2.045 t Critical two-tail 0.059 P(T<=t) two-tail 1.699 t Critical one-tail 0.030 P(T<=t) one-tail 1.962 t Stat 29.000 df 0.000 Hypothesised Mean Difference -0.036 Pearson Correlation 30.000 30.000 Observations 156.742 83.381 Variance 17.597 23.241 Mean sample 2 sample 1 t-Test: Paired Two Sample for Means