1 / 32

Testing Statistical Hypothesis Independent Sample t-Test

Testing Statistical Hypothesis Independent Sample t-Test. Heibatollah Baghi, and Mastee Badii. Research Design. Steps in Test of Hypothesis. Determine the appropriate test Establish the level of significance: α Determine whether to use a one tail or two tail test

slone
Download Presentation

Testing Statistical Hypothesis Independent Sample t-Test

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Testing Statistical HypothesisIndependent Sample t-Test Heibatollah Baghi, and Mastee Badii

  2. Research Design

  3. Steps in Test of Hypothesis • Determine the appropriate test • Establish the level of significance:α • Determine whether to use a one tail or two tail test • Calculate the test statistic • Determine the degree of freedom • Compare computed test statistic against a tabled value

  4. 1. Determine the Appropriate Test • If comparing a sample to a population, use one sample tests. • If comparing two samples in order to draw inferences about group differences in the population use two sample t-test. • Here the test statistic is based on a theoretical sampling distribution known as sampling distribution of the difference between two means. Mdiff = • The standard deviation of such a sampling distribution is referred to as the standard error of the difference.

  5. 1. Determine the Appropriate Test • Assumptions and Requirements for the two sample test (comparing groups means) are: • Independent variable consists of two levels of a nominal-level variable (when there are two and only two groups). • Dependent variable approximates interval-scale characteristics or higher. • Normal distribution or large enough sample size to assume normality due to the central limit theorem. • Equal variance: assumption of the homogeneity of variance 12 = 12

  6. 1. Determine the Appropriate Test • If the two groups are independent of each other uses independent group t-test. • If the two groups are not independent of each other use dependent group t-test also known as paired t-test. This lecture focuses on independent sample t-test which is a parametric test

  7. 2. Establish Level of Significance • α is a predetermined value • The convention • α = .05 • α = .01 • α = .001

  8. 3. Determine Whether to Use a One or Two Tailed Test • If testing for equality of means then two tailed test • If testing whether one mean greater/smaller than the other then one tailed test

  9. 4. Calculating Test Statistics • For the independent groups t-test the formula is: • The numerator is the difference in means between the two samples, and the denominator is the estimated standard error of the difference.

  10. 4. Calculating Test Statistics • The estimated standard error of the difference is estimated on the basis of variances of the two samples (Pooled Variance t-test). • Where S21= variance of Group 1 S22 = variance of Group 2 n 1= number of cases in Group 1 n 2= number of cases in Group 2

  11. 5. Determine Degrees of Freedom • Degrees of freedom, df, is value indicating the number of independent pieces of information a sample can provide for purposes of statistical inference. • Df = Sample size – Number of parameters estimated • Df is n1 +n2 -2 for two sample test of means because the population variance is estimated from the sample

  12. 6. Compare the Computed Test Statistic Against a Tabled Value If |tc| > |tα| Reject H0 If p value < α Reject H0

  13. Example of Independent Groups t-tests • Suppose that we plan to conduct a study to alleviate the distress of preschool children who are about to undergo the finger-stick procedure for a hematocrit (Hct) determination. • Note: Hct = % of volume of a blood sample occupied by cells.

  14. Example of Independent Groups t-tests, Continued • Twenty subjects will be used to examine the effectiveness of the special treatment. • 10 subjects randomly assigned to treatment group. • 10 assigned to a control group that receives no special preparation.

  15. 1. Determine the Appropriate Test • Testing hypothesis about two independent means (t-test) • Dependent variable = the child’s pulse rate just prior to the finger-stick • Independent variable or grouping variable = treatment conditions (2 levels)

  16. 1. Determine the Appropriate Test • Two samples are independent. • Two populations are normally distributed. • The assumption of homogeneity of variance. (Examine Levene’s Test) Ho: 12 = 12 Ha: 12  12 If sig. level or p-value is > .05, the assumption is met.

  17. 2. Establish Level of Significance • The convention • α = .05 • α = .01 • α = .001 • In this example, assume α = 0.05

  18. 3. Determine Whether to Use a One or Two Tailed Test • H0 : µ1 = µ2 • Ha : µ1 µ2 • Where • µ1 = population mean for the experimental group • µ2 = population mean for the control group

  19. 4. Calculating Test Statistics

  20. Experimental Group Control Group Rearrange the Data

  21. 4. Calculating Test Statistics (continued) Group 1 (Experimental) Group 2 (Control) -------------------------------------------------------------------------------------------------- X1 X2 ------------ --------------

  22. 4. Calculating Test Statistics (continued)

  23. 6. Compare the Computed Test Statistic Against a Tabled Value

  24. 6. Compare the Computed Test Statistic Against a Tabled Value • If we had chosen a one tail test: • H0 : µ1 = µ2 • Ha : µ1 <µ2 1.73 The null hypothesis can be rejected

  25. SPSS Output for Two Sample Independent t-test Example

  26. Nature & Magnitude of Relationship Going Beyond Test of Significance

  27. rpb (-1.85)2 rpb (-1.85)2 +18 Point Biserial Correlation Measures Strength of the relationship • Point biserial correlation is similar to Pearson r and can be calculated using the same formula or using the following formula:

  28. rpb (-1.85)2 rpb (-1.85)2 +18 Measures of Practical Significance • Point biserial correlation also provides information about the proportion of explained variation in the dependent variable. • In our example 16 % of the variation in the children’s pulse rates is explained by the group membership.

  29. Effect Size • Effect size, gamma () is a measure of the strength of the relationship between two variables in the population and an index of how wrong the null hypothesis is. • The higher the effect size the greater the power of the test.

  30. Effect Size • To evaluate the magnitude of the difference between two means, a mean difference is divided by a “pooled standard deviation.” • Since researches typically do not have the value of the population effect size, it is estimated from sample data.

  31. Most Statistical Tests Assume Randomness • Perfect randomness is often impossible and so researchers try to minimize the different forms of bias in their selection of subjects: • Selection bias • Attrition bias • Non-response bias • Cohort bias

  32. Take Home Lesson How to Compare Mean of Two Independent Samples

More Related