Two_samples_t_test_different_n

Two_samples_t_test_different_n - t Stat-0.05 P(T<=t...

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J. M. Cimbala, February 2007 Given: Two data sets, A and B of the same variable. Goal: Determine whether there is a statistically significant change in the variable. data point # 1 25.6 26.2 2 27.3 27.1 3 24.2 24.1 4 28.7 29.2 5 23.6 24.5 6 25.1 24.9 7 25.1 8 25.3 6 8 degrees of freedom (df): 5 7 25.75 25.8 1.93 1.67 3.72 2.79 Null hypothesis: There is no effect (no difference between test A and test B) t = -0.05 degrees of freedom (real number): 9.96 [Welch's equation - see class notes] degrees of freedom (nearest integer): df = 10 p = 0.96 Conclusions: There is a 96.05 % probability that the null hypothesis is correct. There is a 3.95 % probability that the null hypothesis is not correct. We are confident to 3.95 % that there is a change in the variable. Now let's repeat the analysis using Excel's built-in t-test: t-Test: Two-Sample Assuming Unequal Variances Variable 1 Variable 2 Mean 25.75 25.8 Variance 3.72 2.79 Observations 6 8 Hypothesized Mean Difference 0 df 10 This comes from Welch's equation
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Unformatted text preview: t Stat-0.05 P(T<=t) one-tail 0.48 Ignore these values - for a one-tail test t Critical one-tail 1.81 Ignore these values - for a one-tail test P(T<=t) two-tail 0.96 t Critical two-tail 2.23 Verify: 2.23 Two Samples - Using Excel's t-test for Two Independent Samples - Case with different values of n x A x B Sample numbers of data points ( n ): Sample means ( x _bar): Sample standard deviations ( S ): Sample variances ( S 2 ): OR, mathematically, μ A = B Calculate the t-statistic and the p-value: t-statistic: [ t = ( x _bar A- x _bar B ) / SQRT( S A 2 / n A + S B 2 / n B ) df real = [ df = ROUND(df real ,0) ] p-value: [ p = TDIST(ABS( t ),df,2) ] (Tools-Data Analysis-t-Test: Two-Sample Assuming Unequal Variances ) 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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