05.įortunately, we do not have to deal directly with the distribution of t scores. The red vertical lines represent the two-tailed critical values, and the green vertical lines the one-tailed critical values when α =. 14.įigure 13.1 Distribution of t Scores (With 24 Degrees of Freedom) When the Null Hypothesis Is True Thus the p value is the proportion of t scores that are +1.50 or above or that are −1.50 or below-a value that turns out to be. For now, let us define extreme as being far from zero in either direction. The probability of a t score at least this extreme is given by the proportion of t scores in the distribution that are at least this extreme. Consider, for example, a t score of +1.50 based on a sample of 25. (There are 24 degrees of freedom for the distribution shown in Figure 13.1 "Distribution of ".) The important point is that knowing this distribution makes it possible to find the p value for any t score. Its precise shape depends on a statistical concept called the degrees of freedom, which for a one-sample t test is N − 1. As shown in Figure 13.1 "Distribution of ", this distribution is unimodal and symmetrical, and it has a mean of 0. The reason the t statistic (or any test statistic) is useful is that we know how it is distributed when the null hypothesis is true.
SD is the sample standard deviation and N is the sample size. is a statistic that is computed only to help find the p value.) The formula for t is as follows:Īgain, M is the sample mean and µ 0 is the hypothetical population mean of interest. (A test statistic In null hypothesis testing, a statistic such as t or F that is computed only to help find the p value for the sample result. But finding this p value requires first computing a test statistic called t. To decide between these two hypotheses, we need to find the probability of obtaining the sample mean (or one more extreme) if the null hypothesis were true. The alternative hypothesis is that the mean for the population is different from the hypothetical population mean: μ ≠ μ 0. The null hypothesis is that the mean for the population (µ) is equal to the hypothetical population mean: μ = μ 0.
is used to compare a sample mean ( M) with a hypothetical population mean (μ 0) that provides some interesting standard of comparison. The one-sample t test A null hypothesis test used to compare one sample mean with a hypothetical population mean that provides an interesting standard of comparison.
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