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# T test, independant sample, paired sample and anova

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### T test, independant sample, paired sample and anova

1. 1. “Multivariate Analysis With SPSS”1Qasimraza555@gmail.com
2. 2. 2Qasimraza555@gmail.com
3. 3. “Multivariate Analysis With SPSS”Compare Means Analyses:1. T-test2. One-Sample T-test3. Independent Sample T-test( Levene’s Test)1. Paired Sample T-test2. ANOVA3. Q & A Session3Qasimraza555@gmail.com
4. 4. 1. What is meant by T-test?The t-test compares the actual difference between two meansin relation to the variation in the data (expressed as thestandard deviation of the difference between the means).4Qasimraza555@gmail.com
5. 5. 2. One-Sample T-test The one-sample t-test allows us to test whether a sample mean issignificantly different from a population mean. When only the samplestandard deviation is known. Simply, when to use the one-sample t-test,you should consider using this test when you have continuous datacollected from group that you want to compare that group’s averagescores to some known criterion value (probably a population mean). Often performed for testing the mean value of distribution. It can be used under the assumption that sample distribution is normal. For large samples, the procedure performs often well even for non-normal population.5Qasimraza555@gmail.com
6. 6. One-Sample T-test (Cont…)Example:To test whether the average weight of student population is differentfrom 140 lb.Data:A random sample of 22 students’ weights from student population.To perform One Sample t-Test for the data above:135 119 106 135 180 108 128 160 143 175 170205 195 185 182 150 175 190 180 195 220 2356Qasimraza555@gmail.com
7. 7. One-Sample T-test (Cont…)1. Create data file: Enter the data in SPSS, with the variable “weight” takesup one column as shown in the picture onthe right.7Qasimraza555@gmail.com
8. 8. One-Sample T-test (Cont…)2. To perform the one sample t-test, first click through the menu selectionsAnalyze / Compare Means / One Sample T Test… as in the followingpicture, and the One-Sample t-test dialog box will appear on the screen.8Qasimraza555@gmail.com
9. 9. One-Sample T-test (Cont…)Select the variable “weight” to be analyzed into the Test Variable box, and enterthe Test Value which the average value to be tested with (the mean valuespecified in the null hypothesis, that is 140 in this example). Click Continueand click OK for performing the test and estimation. The results will bedisplayed in the SPSS Output window.9Qasimraza555@gmail.com
10. 10. One-Sample T-test (Cont…)Interpret SPSS Output: The statistics for the test are in the following table.The one sample t-test statistic is 3.582 and the p-value from this statistic is .002and that is less than 0.05 (the level of significance usually used for the test)Such a p-value indicates that the average weight of the sampled population isstatistically significantly different from 140 lb. The 95% confidence intervalestimate for the difference between the population mean weight and 140 lb is(11.27, 42.46).10Qasimraza555@gmail.com
11. 11. 3. Independent Sample t-test Purpose: test whether or not the populations represented by the two sampleshave a different mean. Independent Sample t-test measures the significance difference in the meansof the Two categories /variables/Groups. Examples:o Whether there is a significant difference in the satisfaction level ofconsumers using Prepaid and Post Paid Packaging…Here we have Packagein two subcategories as a variable and Test Variable is Satisfaction Level.o Social work students have higher GPA’s than nursing studentso Social work students volunteer for more hours per week than educationmajors11Qasimraza555@gmail.com
12. 12. Assumptions Level Of Measurement:Independent sample t-test assume that grouping variable or categoricalvariable should be measured on Nominal Scale whereas Test variableshould be measured on interval or Ratio Scale. This is LOM for this Test. Normality:The test variable should be Normal or Homogeneous. In order tocheck the homogeneity, Independent Sample t-test has Levene’sTest.If Test variable is abnormal or Heterogeneous then we can notproceed to independent sample t-test rather we have to switch forNon-Parametric alternate to independent Sample t-test i.e. MannWhitney test etc. 12Qasimraza555@gmail.com
13. 13. Solving the problem with SPSS:Evaluating normality13Qasimraza555@gmail.com
14. 14. Solving the problem with SPSS:Evaluating normality (Cont…)14Qasimraza555@gmail.com
15. 15. Solving the problem with SPSS:Evaluating normality (Cont…)"Highest year of school completed" [educ] didnot satisfy the criteria for a normaldistribution. The skewness of the distribution(-.137) was between -1.0 and +1.0, but thekurtosis of the distribution (1.246) fell outsidethe range from -1.0 to +1.0.Having failed the normality requirement usingthis criteria, we will see if we can apply thecentral limit theorem.15Qasimraza555@gmail.com
16. 16. Solving the problem with SPSS:The independent-samples t-testSelect Compare Means> Independent-Samples T Test… fromthe Analyze menu.16Qasimraza555@gmail.com
17. 17. “Solving the problem with SPSS:The independent-samples t-test (Cont…)17Qasimraza555@gmail.com
18. 18. Solving the problem with SPSS:The independent-samples t-test (Cont..)18Qasimraza555@gmail.com
19. 19. Solving the problem with SPSS:The independent-samples t-test (Cont…)19Qasimraza555@gmail.com
20. 20. Solving the problem with SPSS:Evaluating equality of group variancesThe independent-samples t-test assumes that the variances ofthe dependent variable for both groups are equal in thepopulation. This assumption is evaluated with Levenes Test forEquality of Variances. The null hypothesis for this test states thatthe variance for both groups are equal. The desired outcome forthis test is to fail to reject the null hypothesis, whichdemonstrates equality.The probability associated with Levenes Test for Equality ofVariances (.161) is greater than alpha (.05), indicating that theEqual variances assumed formula for the independent samplest-test should be used for the analysis.20Qasimraza555@gmail.com
21. 21. 4. Paired Sample T-testA paired sample t test is used to test if an observed difference betweentwo means is statistically significant i.e. whether there is a significantdifference between the average values of the same measurement madeunder two different conditions.Assumptions for paired sample T-test:To run the paired sample T-test data Should have normal distribution Is a large data set Has no outliers21Qasimraza555@gmail.com
22. 22. Paired Sample T-test (Cont…)Research Questions for Paired Sample T-testIs there an instructional effect taking place in the computer class?Hypothesis for Paired Sample T-test:NULL HYPOTHESIS (H0): H0 specifies that the value for the populationparameters are the same. H0 always includes an equality.H0: there is no influence of using internet on academic achievement forthis class.ALTERNATE HYPOTHESIS (H1): H1 always includes a non-equalityH1: there is an influence of using the internet on academic achievementfor this class. 22Qasimraza555@gmail.com
23. 23. Paired Sample T-test (Cont…)Steps for paired sample T-test:Click on Analyze/ Compare Means/Paired-Samples T-Test/ Click on Pretest andthen Posttest/ Click OK.SPSS Output23Qasimraza555@gmail.com
24. 24. Paired Sample T-test (Cont…)Paired Sample t-test Output:24Qasimraza555@gmail.com
25. 25. Paired Sample T-test (Cont…)Results:Given that the researcher is interested in assessing the results in onedirection, this is a one-tailed T-test. The Significance (p) value (2-tailed),located in the above table, must be divided by 2 before reporting the finalresults. In this case, it remained the same(p = .000/2 = .000).25Qasimraza555@gmail.com
26. 26. 5. Analysis of Variance (ANOVA) ANOVA measures significant difference among at-least three or morecategories . Purpose of ANOVA: In statistics, analysis of variance (ANOVA) is acollection of statistical models about comparing the mean values ofdifferent groups. There are a few types of ANOVA depending on thenumber of treatments and the way they are applied to the subjects in theexperiment. In SPSS, you can calculate One-way ANOVA in two different ways;o Analyze/Compare Means/ One-way ANOVAo Analyze/ General Linear Model/ Univariate26Qasimraza555@gmail.com
27. 27. “ Analysis of Variance (ANOVA)”Null and Alternate Hypothesis: The null hypothesis is that the mean are all equali. Ho: u1=u2=u3=…=ukii. For Example, with three groups: Ho: u1=u2=u3 The alternate hypothesis is that at least one of the mean is differentfrom another In other words, H1: u1=u2=u3=…=uk would not be an acceptable way towrite the alternate hypothesis (this slightly contradicts Gravettter &Wallnau, but technically there is no way to test this specific alternativehypothesis with a one-way ANOVA ).27Qasimraza555@gmail.com
28. 28. Assumptions Level of Measurement assumption: According to this assumption one variable should be categoricalhaving at least 3-subcategories or nominal scale and Test variable(dependent ) should be measured on interval or Ratio Scale. Normality: 2nd assumption is Normality or Homogeneity of the Testvariable. This means that the test variable should be normal and wetest this by means of Levene’s Test.The Hypothesis of ANOVA areNull : means across the categories are equalAlternate: means across the categories are not equal28Qasimraza555@gmail.com
29. 29. Normality Homogeneity is whether the variances in the populations are equal.When conducting an ANOVA, one of the options is to produce a test ofhomogeneity in the output, called Levene’s Test.If Levene’s test is significant (p < .05) then equal variances are NOT assumed,called heterogeneity.If Levene’s is not significant (p > .05) then equal variances are assumed, calledhomogeneity.29Qasimraza555@gmail.com
30. 30. What ifIf Test variable is not Normal ,then we switch to the NON-Parametricalternate to ANOVA i.e. Kruskal Wallis Test….30Qasimraza555@gmail.com
31. 31. Difference ANOVA is different than “t-test” in that the t-test is testing the meandifference between two groups; whereas ANOVA is testing the meandifference between three or more groups. Examples:T-test compares two means to each other(Who is happier: Republicans, Democrats?)ANOVA compares three or more means to each other(Happier: Republicans, Democrats, Independents, etc)31Qasimraza555@gmail.com
32. 32. Extension of ANOVA……Post Hoc ANOVA Sees only significant difference (Yes/No). In order to extend this analysis of measure of difference from onesubsection to another subsection, we proceed to Post Hoc test. With inPost Hoc test we have further sub-categories in terms of Homogeneity orHeterogeneity. If Normal we proceed asANOVA to Post Hoc to TukeyIf Not NormalANOVA to Post Hoc to Duuntt’s-332Qasimraza555@gmail.com
33. 33. “One-way ANOVA Results”33Qasimraza555@gmail.com
34. 34. “Multivariate Analysis With SPSS”hhhhyy34Qasimraza555@gmail.com
35. 35. “Question & Answer Session”35Qasimraza555@gmail.com
36. 36. 36Qasimraza555@gmail.com