Test of Difference Between Means.pptx Test of Difference Between Means.pptx

Stat

1. TEST OF DIFFERENCE BETWEEN MEANS REPORTER: ANGEL G. ELARAN – MPA 2

2. WHAT IS A T-TEST? A t-test is a statistical test that is used to compare the means of two groups. It is often used in hypothesis testing to determine whether a process or treatment has an effect on the population of interest, or whether two groups are different from one another. Mathematically, the t-test takes a sample from each of the two sets and establishes the problem statement. It assumes a null hypothesis that the two means are equal.

3. T-TEST FORMULA: Calculating a t-test requires three fundamental data values. They include: 1. The difference between the mean values from each data set, or the mean difference. 2. The standard deviation of each group, and; 3. The number of data values of each group. This comparison helps to determine the effects of chance on the difference, and whether the difference is outside that chance range. The t-test questions whether the difference between the groups represents a true difference in the study or merely a random difference.

4. T-TEST FORMULA: The t-test produces two values as its output: t-value and  degrees of freedom . The t-value, or t-score , is a ratio of the difference between the mean of the two sample sets and the variation that exists within the sample sets. Degrees of freedom refer to the values in a study that has the freedom to vary and are essential for assessing the importance and the validity of the null hypothesis. Computation of these values usually depends upon the number of data records available in the sample set.

5. PAIRED SAMPLE T-TEST The correlated t-test, or paired t-test, is a dependent type of test and is performed when the samples consist of  matched pairs  of similar units, or when there are cases of repeated measures. For example, there may be instances where the same patients are repeatedly tested before and after receiving a particular treatment. Each patient is being used as a control sample against themselves. This method also applies to cases where the samples are related or have matching characteristics, like a comparative analysis involving children, parents, or siblings.

6. The formula for computing the t-value and degrees of freedom for a paired t-test is: where: mean 1 and  mean 2 = The average values of each of the sample sets s (diff) = The standard deviation of the differences of the paired data values n = The sample size (the number of paired differences) n −1 = The degrees of freedom​

7. EQUAL VARIANCE OR POOLED T-TEST The equal variance t-tes t is an independent t-test and is used when the number of samples in each group is the same, or the variance of the two data sets is similar.

8. The formula used for calculating t-value and degrees of freedom for equal variance t-test is: and

9. UNEQUAL VARIANCE T-TEST The unequal variance t-test is an independent t-test and is used when the number of samples in each group is different, and the variance of the two data sets is also different. This test is also called Welch's t-test.

10. The formula used for calculating t-value and degrees of freedom for an unequal variance t-test is: and

11. WHICH T-TEST TO USE? The following flowchart can be used to determine which t-test to use based on the characteristics of the sample sets. The key items to consider include the similarity of the sample records, the number of data records in each sample set, and the variance of each sample set.

12. ANALYSIS OF VARIANCE (ANOVA) ANOVA is to test for differences among the means of the population by examining the amount of variation within each sample, relative to the amount of variation between the samples. Analyzing variance tests the hypothesis that the means of two or more populations are equal.

13. TWO TYPES OF ANOVA: ONE-WAY ANOVA - is a type of statistical test that compares the variance in the group means within a sample whilst considering only one independent variable or factor. It is a hypothesis-based test, meaning that it aims to evaluate multiple mutually exclusive theories about our data. In a one-way ANOVA there are two possible hypotheses: 1. The null hypothesis (H0) is that there is no difference between the groups and equality between means (walruses weigh the same in different months). 2. The alternative hypothesis (H1) is that there is a difference between the means and groups (walruses have different weights in different months) .

14. TWO TYPES OF ANOVA: TWO-WAY ANOVA - A two-way ANOVA is, like a one-way ANOVA, a hypothesis-based test. However, in the two-way ANOVA each sample is defined in two ways, and result. The two-way ANOVA therefore examines the effect of two factors (month and sex) on a dependent variable – in this case weight, and also examines whether the two factors affect each other to influence the continuous variable.  

15. ONE-WAY VS. TWO-WAY ANOVA DIFFERENCES CHART: ONE-WAY ANOVA TWO-WAY ANOVA DEFINITION A test that allows one to make comparisons between the means of three or more groups of data. A test that allows one to make comparisons between the means of three or more groups of data, where two independent variables are considered.  NUMBER OF INDEPENDENT VARIABLES One Two WHAT IS BEING COMPARED The means of three or more groups of an independent variable on a dependent variable. The effect of multiple groups of two independent variables on a dependent variable and on each other.  NUMBER OF GROUP OF SAMPLES Three or more. Each variable should have multiple samples.

16. PREPARED BY: ANGEL G. ELARAN – MPA 2