Comparing Two Samples Part 5

T-test types and conditions of use What is a T-test: It is one of the most important and most widely used statistical tests in research and studies that aim to reveal the significance of statistical differences between the averages of two samples. Example: (When the researcher tries to test the differences between the averages of two groups of students, each of them studied in a different way of teaching to know the extent of statistically significant differences that tell us the preference of one method over the other). There are a set of general conditions in the parametric tests, including the T-test. The level of measurement of the dependent variable (the laboratory) should be quantitative, whether it is relative or categorical. Random sampling means using the random method in selecting samples. Independence of measurement or observations. The mean distribution of scores for the dependent variable. The homogeneity of the variance is the same as the dispersion of the scores of the groups around their mean. Types of Test (T) The idea of the t-test is based on calculating the ratio of the deviation of any two averages from the mean of the statistical distribution to the associated standard error. One-Sample T Test. Independent Samples T test. Paired Samples t-test. First: One-Sample T Test: This test is used to compare the mean of a sample with an assumed value of the population. for example: Comparing the average achievement of students in a school in the subject of geography with the average achievement of general students in the schools of the governorate as a whole. It is an answer to the question: Does the average sample in the school differ from the general average in the governorate? The test can be performed through the following steps: Formulate the null hypothesis and the alternative hypothesis. Determine the highest error rate allowed by the researcher (significant level @). Gathering information and data through various measurement tools. Perform the test on the data. Make a decision in light of the results. There are a set of conditions for using a one-sample t-test, which are: The dependent variable must be measured at the quantitative level. That the dependent variable follows the equilibrium distribution. Viewing independence. The sample is randomly selected. Independent Samples T test: This test is used to compare the mean of two independent samples (ie, the people in group 1 are not the same as the people in group 2). Conditions for using an independent t-test: The independent variable should be a two-level categorical variable (male - female or student in one group and student in another group). Group independence in case this condition is not met, such as when a person is measured twice, then we need tests for related samples). The distribution of the dependent variable is equilibrium. The variances of the dependent variable for groups are homogeneous (we can use another method to calculate the t-value) Samples are selected at random. Steps to take a two-sample independent t-test: Formulate the null hypothesis and the alternative hypothesis. Determine the appropriate test to test the null hypothesis. Determine the highest error rate allowed by the researcher (significant level @). Gather information and take the test. Make decision. Third: Paired Samples t-test: This test is used to compare the mean of two related samples (eg the people in group 1 are the same as the people in group 2). Conditions for using the unlearned two-sample correlated t-test: That the independent variable be a two-level taxonomic variable (male - teacher and uneducated ... and this) That the distribution of differences follows the average distribution. The dependent variable is measured at the quantitative level. The sample is randomly selected Steps for using a two-sample t-test: Formulate the null hypothesis and the alternative hypothesis. Determine the highest error rate allowed by the researcher (significant level @). Data collection. and take the test. Make decision. T-Test The “T” test is one of the most common tests of significance in psychological, social and educational research, and its first origin goes back to the research of the world “Student.” That is why the test was called the most frequent letter in its name, which is the letter Taa, and one of the most important areas in which this test is used is to reveal the differences between Males and females in a subject by calculating the significance of the difference in the average achievement of males from the average achievement of females, and it can be said that the “t” test is used to measure the significance of the differences of the unrelated and correlated averages of equal and unequal samples. Conditions for using the t-test to indicate mean differences The researcher is not entitled to use the t-test before studying the characteristics of the research variables in the following respects:- size of each sample. The difference between the size of the two research samples. The homogeneity of the sample. The moderation of the frequency distribution for each of the two research samples. 1- The size of each sample The size of each of the two samples should be more than “5” and preferably more than “30”, but if the size of any of the two samples is less than “5”, the “t” test cannot be used. 2- The difference between the size of the two research samples: the convergence condition The size of the two research samples must be close, so that, for example, the size of one of the two samples is "500" and the size of the other "30" because the size has its effect on the level of significance of "T". 3- Homogeneity of the two samples The homogeneity of samples means the extent to which they belong to a single or multiple origins. If the samples are related to one origin, they are homogeneous, and if the samples do not belong to one origin, they are heterogeneous. 4- The moderation of the frequency distribution for each of the two research samples The moderation of the distribution means that the data is free from outliers or randomness and that the data curve is moderate and resembles the shape of a bell. There are several tests to measure the moderation of the distribution, including the K-S test and others. Uses of the t-test 1 - The t-test is used in the case of a single sample, by taking the differences between the sample mean and the population average imposed by the researcher 2- The t-test is used in the case of two independent samples, by measuring the differences between the mean of two independent populations, meaning that the data in the first community are not related to the data in the second community, and the previous conditions must be taken into account. 3. The t-test is used in pairs if there are two treatments and the experimental units in each pair have a strong correlation between them or it is the same experimental unit, but it was treated with two treatments such as the treatments before and after taking a particular drug or measuring a trait on the experimental units before or after performing an exercise Specific or a particular treatment. It is also required in this test that the individuals are randomly taken and that the trait under the measurement follows a normal distribution. Levene's Test In statistics, the Levine Test of Equality of Difference is an inferential statistic used to assess the equality of the variances of a computed variable for two or more groups. Some common statistical procedures assume that the differences in the different sampled populations are equal. The Levine test for equality of difference evaluates this assumption. Tests the null hypothesis that population variances are equal (called homogeneity of variance or homozygosity). If the resulting p-value of the Levine test is less than some level of significance (typically 0.05), then the obtained differences in sample variances based on random sampling from a group of equal variances are unlikely to occur. Thus, the null hypothesis for equal variances is rejected and it is concluded that there is a difference between the differences in the population. Some of the procedures that assume that one can use the Levine test for equality of variances include analysis of variance and the T-test, often using the Levine test for equality of difference before comparing means. When the Levine test shows significance, one should turn to more general tests devoid of assumptions of homosexuality (sometimes even non-parametric tests). The Welch test, or unequal variance test, is a more conservative test. The Levine Test for Equality of Difference can also be used as a key test to answer a stand-alone question about whether two subsamples in a population have equal or different variances. The Levine test for equality of difference is equivalent to the one-way analysis of variance between groups (ANOVA), where the dependent variable is the absolute value of the difference between the score and the mean of the group to which the score belongs (as noted in the image below). Levine test for equality of difference Levine test for equality of difference The w-statistic test is equivalent to the f-statistic that will be produced by ANOVA, and is defined as: Levine test for equality of difference Levine test for equality of difference whereas: K is the number of different groups to which the sampled cases belong Ni is the number of states in i of the groups N is the total number of cases in all groups Yij is the value of the measured variable for j of states in i of the groups. Levine test for equality of difference Levine test for equality of difference As for the mean and median of a group of groups (i of groups for example), the calculation is done as follows: