Two_samples_t_test_same_n

# Two_samples_t_test_same_n - Variable 2 Mean 25.75 26...

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Paired Samples - Using Excel's t-test for Paired Samples J. M. Cimbala, February 2006 Given: Two data sets, A and B of the same variable. Goal: Determine whether there is a statistically significant change in the variable. data # 1 25.6 26.2 0.6 Calculate the sample mean and 2 27.3 27.1 -0.2 3 24.2 24.1 -0.1 4 28.7 29.2 0.5 0.25 5 23.6 24.5 0.9 0.48 6 25.1 24.9 -0.2 n = 6 Sample means: 25.75 26 0.25 df = 5 Sample standard deviations: 1.93 1.93 0.48 Null hypothesis: There is no effect (no difference between test A and test B) 0 (Note: I use absolute value here since it is a two-tailed test) t = 1.29 p = 0.26 Conclusions: There is a 25.5 % probability that the null hypothesis is correct. There is a 74.5 % probability that the null hypothesis is not correct. We are confident to 74.50 % that there is a change in the variable. Now let's repeat the analysis using Excel's built-in t-test: t-Test: Paired Two Sample for Means Variable 1
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Unformatted text preview: Variable 2 Mean 25.75 26 Variance 3.72 3.71 Observations 6 6 Pearson Correlation 0.97 Hypothesized Mean Difference df 5 t Stat-1.29 P(T<=t) one-tail 0.13 Ignore these values - for a one-tail test t Critical one-tail 2.02 Ignore these values - for a one-tail test P(T<=t) two-tail 0.26 t Critical two-tail 2.57 Verify: 2.57 x A x B δ = x B- x A sample standard deviation of : mean = S = OR, mathematically, μ = 0 (population mean of variable ) = Calculate the t-statistic and the p-value: t-statistic: [ t = ABS(( mean- ) * SQRT( n )/ S ) ] p-value: [ p = TDIST( t ,df,2) ] (Tools-Data Analysis-t-Test: Paired Two Sample for Means ) This is our t-statistic This is our p-value This is the critical value of t ( t α /2 ) for = 0.05 (95% confidence) t /2 = [ t /2 = TINV(0.05,df) ]...
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## This note was uploaded on 07/23/2008 for the course ME 345 taught by Professor Staff during the Spring '08 term at Penn State.

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