![]() Z critical value is a point that cuts off an area under the standard normal distribution. The critical value of t helps to decide if a null hypothesis should be supported or rejected. T value is used in a hypothesis test to compare against a calculated t score. In all reality, you will probably never have heard of these adjustments because SPSS Statistics hides this information and simply labels the two options as "Equal variances assumed" and "Equal variances not assumed" without explicitly stating the underlying tests used.T critical value is a point that cuts off the student t distribution. If the Levene's Test for Equality of Variances is statistically significant, which indicates that the group variances are unequal in the population, you can correct for this violation by not using the pooled estimate for the error term for the t-statistic, but instead using an adjustment to the degrees of freedom using the Welch-Satterthwaite method. Overcoming a violation of the assumption of homogeneity of variance However, if p < 0.05, we have unequal variances and we have violated the assumption of homogeneity of variances. 05), our group variances can be treated as equal. We are primarily concerned with the significance value – if it is greater than 0.05 (i.e., p >. This test for homogeneity of variance provides an F-statistic and a significance value ( p-value). If you have run Levene's Test of Equality of Variances in SPSS Statistics, you will get a result similar to that below: The assumption of homogeneity of variance can be tested using Levene's Test of Equality of Variances, which is produced in SPSS Statistics when running the independent t-test procedure. If your variances are unequal, this can affect the Type I error rate. The independent t-test assumes the variances of the two groups you are measuring are equal in the population. If you find that either one or both of your group's data is not approximately normally distributed and groups sizes differ greatly, you have two options: (1) transform your data so that the data becomes normally distributed (to do this in SPSS Statistics see our guide on Transforming Data), or (2) run the Mann-Whitney U test which is a non-parametric test that does not require the assumption of normality (to run this test in SPSS Statistics see our guide on the Mann-Whitney U Test). What to do when you violate the normality assumption The exception to this is if the ratio of the smallest to largest group size is greater than 1.5 (largest compared to smallest). ![]() This means that some deviation away from normality does not have a large influence on Type I error rates. However, the t-test is described as a robust test with respect to the assumption of normality. You can run these tests using SPSS Statistics, the procedure for which can be found in our Testing for Normality guide. You can test for this using a number of different tests, but the Shapiro-Wilks test of normality or a graphical method, such as a Q-Q Plot, are very common. Note: Technically, it is the residuals that need to be normally distributed, but for an independent t-test, both will give you the same result. The independent t-test requires that the dependent variable is approximately normally distributed within each group. An example would be gender - an individual would have to be classified as either male or female – not both.Īssumption of normality of the dependent variable Often we are investigating differences in individuals, which means that when comparing two groups, an individual in one group cannot also be a member of the other group and vice versa. Unrelated groups, also called unpaired groups or independent groups, are groups in which the cases (e.g., participants) in each group are different. One independent, categorical variable that has two levels/groups.In order to run an independent t-test, you need the following: What do you need to run an independent t-test? Most commonly, this value is set at 0.05. ![]() To do this, we need to set a significance level (also called alpha) that allows us to either reject or accept the alternative hypothesis. In most cases, we are looking to see if we can show that we can reject the null hypothesis and accept the alternative hypothesis, which is that the population means are not equal: The null hypothesis for the independent t-test is that the population means from the two unrelated groups are equal: Null and alternative hypotheses for the independent t-test The independent t-test, also called the two sample t-test, independent-samples t-test or student's t-test, is an inferential statistical test that determines whether there is a statistically significant difference between the means in two unrelated groups. Independent t-test for two samples Introduction
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