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# Two-Sample $t$ Test Calculator

• The two-sample $t$ procedures assume that both our samples come from an SRS and will give trustworthy conclusions only if this condition is met.

• If the sum of the sample size is less than 15, the $t$ procedures yield trustworthy conclusions only if you can reasonably assume that your data from both samples come from a normal distribution, that is, if the distribution appears to be symmetric with one peak and no outliers. If your data are obviously skewed or if there are any outliers, it is not advisable to use the $t$ procedures. Non-parametric methods may be more advisable: try the Wilcoxon Rank Sum Test.

• If the sum of the sample sizes is 15 or larger, the $t$ procedures can be trusted if there are no outliers and the distribution is not obviously skewed.

• If the sum of the sample sizes is 40 or larger, you may use $t$ procedures even if your distributions appear to be skewed.

• The two-sample $t$ procedures are more robust against non-normal data when the sample sizes of both samples are equal. Therefore, when planning a two-sample study, try to choose equal sample sizes.
 Sample 1 Sample 2 Sample data goes here (enter numbers in columns): Null Hypothesis: $H_0: \mu_1=\mu_2$ Alternative Hypothesis: $H_a:\mu_1$ $\neq$ $<$ $>$ $\mu_2$ Level of Significance: $\alpha=$ 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005

 Sample Sizes: $n_1=$ $n_2=$ Sample Means: $\overline{x}_1=$ $\overline{x}_2=$ Sample Standard Deviations: $s_1=$ $s_2=$ Degrees of Freedom: $df=$ Critical $t$ Value: $t^{*}=$ $t$ statistic: $t=$ $p\mbox{-value}$: $p\mbox{-value}=$