The smaller the p-value, the stronger the evidence against the null hypothesis.įollowing these steps, you should be able to find the test statistic and p-value in StatCrunch for your hypothesis test. Generally, the test statistic is used to assess the strength of evidence against the null hypothesis, while the p-value indicates the probability of obtaining the observed result (or one more extreme) given the null hypothesis is true. You can interpret the test statistic and p-value in accordance with your specific hypothesis and research question. The value in this column represents the calculated p-value.ħ. Similarly, look for the column labeled \"P-Value\" or something similar. The value in this column represents the test statistic.Ħ. Look for the column labeled \"Test Statistic\" or something similar, depending on the specific test you conducted. The results will be displayed in a table. Once you have entered the data, click on the \"Compute!\" button to perform the analysis.ĥ. Make sure to specify the necessary details such as sample sizes, observed values, population means, or proportions.Ĥ. Enter your data in the provided input fields. Click on \"Stat\" in the top menu and select the appropriate analysis based on the type of test you are conducting (e.g., \"2-Proportion Stats\" for a two-proportion hypothesis test or \"T Stats\" for a t-test).ģ. Open StatCrunch and log into your account.Ģ. You may notice that the F-test of an overall significance is a particular form of the F-test for comparing two nested models: it tests whether our model does significantly better than the model with no predictors (i.e., the intercept-only model).To find the test statistic and p-value on StatCrunch, follow these steps:ġ. The test statistic follows the F-distribution with (k 2 - k 1, n - k 2)-degrees of freedom, where k 1 and k 2 are the numbers of variables in the smaller and bigger models, respectively, and n is the sample size. You can do it by hand or use our coefficient of determination calculator.Ī test to compare two nested regression models. With the presence of the linear relationship having been established in your data sample with the above test, you can calculate the coefficient of determination, R 2, which indicates the strength of this relationship. The test statistic has an F-distribution with (k - 1, n - k)-degrees of freedom, where n is the sample size, and k is the number of variables (including the intercept). We arrive at the F-distribution with (k - 1, n - k)-degrees of freedom, where k is the number of groups, and n is the total sample size (in all groups together).Ī test for overall significance of regression analysis. Its test statistic follows the F-distribution with (n - 1, m - 1)-degrees of freedom, where n and m are the respective sample sizes.ĪNOVA is used to test the equality of means in three or more groups that come from normally distributed populations with equal variances. All of them are right-tailed tests.Ī test for the equality of variances in two normally distributed populations. P-value = 2 × min, we denote the smaller of the numbers a and b.)īelow we list the most important tests that produce F-scores. Right-tailed test: p-value = Pr(S ≥ x | H 0) Left-tailed test: p-value = Pr(S ≤ x | H 0) In the formulas below, S stands for a test statistic, x for the value it produced for a given sample, and Pr(event | H 0) is the probability of an event, calculated under the assumption that H 0 is true: It is the alternative hypothesis that determines what "extreme" actually means, so the p-value depends on the alternative hypothesis that you state: left-tailed, right-tailed, or two-tailed. More intuitively, p-value answers the question:Īssuming that I live in a world where the null hypothesis holds, how probable is it that, for another sample, the test I'm performing will generate a value at least as extreme as the one I observed for the sample I already have? It is crucial to remember that this probability is calculated under the assumption that the null hypothesis H 0 is true! Formally, the p-value is the probability that the test statistic will produce values at least as extreme as the value it produced for your sample.
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