- We have samples for each of two conditions. We provide an answer for “Are the two sample means significantly different from each other, or could both.

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- We have samples for each of two conditions. We provide an answer for “Are the two sample means significantly different from each other, or could both plausibly come from the same population?” Statistical Inference for the Mean: t-test Comparison of sample means using unpaired samples:

Statistical Inference for the Mean: t-test Comparison of sample means using unpaired samples:

Sample 1 Statistical Inference for the Mean: t-test Comparison of sample means using unpaired samples: Sample 2 Sample mean: Sample standard deviation: Combined estimate of variance: Sample size: n1n1 n2n2 Variance of the difference between the two means: S 1 and S 2 must be compatible. Pooled or combined variance

Statistical Inference for the Mean: t-test Comparison of sample means using unpaired samples: Combined estimate of variance: S 1 and S 2 must be compatible: - If the variances are not significantly different at the 10% level of significance, they can be combined to give a better estimate of variance to use in the t-test. (p.255, DeCoursey) - Larger departures from equality of the variances can be tolerated if the two samples are of equal size. n 1 =n 2 (p.234, DeCoursey)

The test statistics t is or Normal Distribution: Statistical Inference for the Mean: t-test Comparison of sample means using unpaired samples When comparing the sample mean to a population mean:

The degrees of freedom are Normal Distribution: no such a parameter. Statistical Inference for the Mean: t-test Comparison of sample means using unpaired samples When comparing the sample mean to a population mean: n (sample size) df = n 1 -1+n 2 -1

Test of Significance: Comparing the sample means using unpaired samples - State the null hypothesis in terms of means, such as - State the alternative hypothesis in terms of the same population parameters. - Determine the combined variance and the variance of the difference of the sample means. - Calculate the test statistic t of the observation using the means and variance. - Determine the degrees of freedom: - State the level of significance – rejection limit. - If probability falls outside of the rejection limit, we reject the Null Hypothesis, which means the sample mean is significantly different from the other one. Assume the sample means are normally distributed. Statistical Inference for the Mean: t-test df = n 1 -1+n 2 -1