Testing Differences Between Means
Specifically, the four steps involved in using the critical value approach to Since n = 15, our test statistic t* has n - 1 = 14 degrees of freedom. Also It can be shown using either statistical software or a t-table that the critical value t , 14 is t distribution graph for a two tailed test of level of significance . Pearson's product-moment correlation. Spearman's (Equivalent to the Mann- Whitney U test, except quicker, and the table has different values). Rank all .. The table below gives the one-tailed probability. Double .. Degrees of Freedom for. The t table can be used for both one-sided (lower and upper) and two-sided tests using the Critical values of Student's t distribution with ν degrees of freedom.
Cholesterol levels decreased, on average, For a significance level of 0. Since the absolute value of our test statistic 6.
Note that this summary includes: The test being performed. The paired t-test in this example A statement of the null hypothesis and alternative hypothesis in terms of the population parameter of interest.
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The mean difference in the previous example The magnitude, direction, and units of the effect observed mean difference. Using the p-value also satisfies this criteria. Two drugs are to be compared in a clinical trial for use in treatment of disease X. Drug A is cheaper than Drug B.
Module 4 - The One Sample t-Test
Efficacy is measured using a continuous variable, Y, and. Type I error—occurs if the two drugs are truly equally effective, but we conclude that Drug B is better. The consequence is financial loss. Type II error—occurs if Drug B is truly more effective, but we fail to reject the null hypothesis and conclude there is no significant evidence that the two drugs vary in effectiveness.
What is the consequence in this case?
S Hypothesis Testing (Critical Value Approach) | STAT ONLINE
The standard normal distribution is a normal distribution with a mean of zero and standard deviation of 1. The standard normal distribution is symmetric around zero: The total area under the curve is equal to one. For a more detailed discussion of the standard normal distribution see the presentation on this concept in the online module on Probability from BS Area in tails of the distribution The total area under the curve more than 1.
The consequences of violating the first two assumptions are investigated in the simulation in the next section.
One- and two-tailed tests
For now, suffice it to say that small-to-moderate violations of assumptions 1 and 2 do not make much difference. It is important not to violate assumption 3. We saw the following general formula for significance testing in the section on testing a single mean: In this case, our statistic is the difference between sample means and our hypothesized value is 0.
The hypothesized value is the null hypothesis that the difference between population means is 0. We continue to use the data from the "Animal Research" case study and will compute a significance test on the difference between the mean score of the females and the mean score of the males.
For this calculation, we will make the three assumptions specified above. The first step is to compute the statistic, which is simply the difference between means.
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The next step is to compute the estimate of the standard error of the statistic. In this case, the statistic is the difference between means, so the estimated standard error of the statistic is. Recall from the relevant section in the chapter on sampling distributions that the formula for the standard error of the difference between means is: