Understanding Inferential Statistics with SPSS: A Practical Guide

1. SPSS (the Statistical Package for the Social Sciences) PART 2

2. Lesson objectives • Recap SPSS • Data entry • Data view • Variable view • Descriptive analysis • Determining reliability • Inferential Statistics with SPSS

3. Inferential Statistics • Based on the assumption that the sample is random • Types of tests • Chi Squared • Correlation • T test

4. Example research Purpose : To determine if a certain method of teaching will lead to higher achievement among visual learners

5. Design Independent Variable INTERVENTION Teaching method Dependent Variable Learning styles Achievement Satisfaction • Population: EDU 540 students (154) • Sample ( chosen at random, 3 lessons taught by the same person using the ‘method’) • Class 1 (30) • Class 2 (45) • Class 3 (38)

6. Instruments • Learning style inventory • Scores will determine learning styles • Can categorize as visual, tactile or auditory • Questionnaire • Satisfaction regarding the teaching method • higher score – higher lesson satisfaction • Test • Scores will determine achievement

7. What to describe? • Descriptive stats • Age • Gender • Program • Learning styles • Cross tabulate? • Gender and learning styles

8. Significance • If significant, unlikely to have occurred by chance • there is statistical evidence that there is a difference, a correlation, an association between etc….

9. Significance level • Significance levels show you how likely a result is due to chance. • The most common level, used to mean something is good enough to be believed, is .95. • The finding has a 95% chance of being true. • No statistical package will show you "95%" or ".95" to indicate this level. Instead it will show you ".05," meaning that the finding has a five percent (.05) chance of not being true, which is the converse of a 95% chance of being true. • To find the significance level, subtract the number shown from one. For example, a value of ".01" means that there is a 99% (1-.01=.99) chance of it being true

10. Hypothesis testing • The Null hypothesis states there is no true difference/no relationship between parameters in the population • We reject or accept the null hypothesis • It is rejected only when it becomes evidently false, that is, when the researcher has a certain degree of confidence, usually 95% to 99%, that the data do not support the null hypothesis • Example • There is no significant difference between the mean test scores of visual and tactile learners

11. Hypothesis testing YOU ALWAYS TEST THE NULL HYPOTHESIS!

12. Significance • Test of significance • To decide whether to accept or reject the null hypothesis • Select probability • 5 out of 100 times the difference did not occur by chance ( Significance level: 0.05) • 1 out of 100 times the difference did not occur by chance ( Significance level: 0.01) • Confidence level? • 95% or 99%

13. Example • Null hypothesis • There is no relationship between variables.. • Significance level : 0.05 • Test statistic • Probability value 0.009 or Sig. 0.009 (smaller than 0.05) • What does that mean? • very unlikely that there’s no relationship between the variables • Variables not independent of each other • REJECT Null hypothesis

14. Example • Null hypothesis • There is no relationship between variables.. • Significance level : 0.01 • Test statistic • Probability value 0.12 or Sig. 0.12(greater than 0.01) • What does this mean? • Higher likelihood that there’s no relationship between the variables • Variables are independent of each other • ACCEPT Null hypothesis

15. Let’s get on with inferential statistics

16. Now.. What to infer? • Independence/ Association • Correlation • Differences

17. Independence test –Chi squared • Chi squared test is used in situations where you have two categorical variables • Gender and employment sector • Gender and learning styles • Chi-square test of independence tests the null hypothesis that there is no association between the two variables

18. Example: Test for independence • Gender • Female • Male • Learning styles • Visual • Tactile • Auditory • Null Hypothesis: No association between gender and learning styles

19. Using SPSS for chi squared • Click • Analyze • Descriptive • Crosstabs • Statistics

20. Using SPSS for chi squared • Low chi squared statistic • Sig.961 • Accept null hypothesis • There is no association… • Variables independent of each other

21. Correlation • Measure of the linear relationship between two variables. • A correlation coefficient has a value ranging from -1 to 1. • Values that are closer to the absolute value of 1 indicate that there is a strong relationship between the variables being correlated whereas values closer to 0 indicate that there is little or no linear relationship. • The sign of a correlation coefficient describes the type of relationship between the variables being correlated. • A positive correlation coefficient indicates that there is a positive linear relationship between the variables: as one variable increases in value, so does the other. • A negative value indicates a negative linear relationship between variables: as one variable increases in value, the other variable decreases in value.

22. Example: Correlation • Correlation between learning styles and test scores • Correlation between learning styles and satisfaction

23. Correlation in SPSS • Start at the Analyze menu. • Select the Correlate option from this menu. You will see three options for correlating variables: • Bivariate • Partial • Distances. • The bivariate correlation is for situations where you are interested only in the relationship between two variables

25. Correlation in SPSS • Then, consider is the type of correlation coefficient. • Pearson's is appropriate for continuous data • Kendall's tau-b and Spearman's, are designed for ranked data. • The choice between a one and two-tailed significance test in the Test of Significance box should be determined by the hypothesis you are testing • if you are making a prediction that there is a negative or positive relationship between the variables, then the one-tailed test is appropriate • if you are not making a directional prediction, you should use the two-tailed test (there is not a specific prediction about the direction of the relationship between the variables)

26. Output

27. Output • Correlation is not statistically significant

28. Let’s check for significant difference Differences between test scores of the groups of learners

29. Differences: Using t test • The t test is a useful technique for comparing mean values of two sets of numbers. • Statistic for evaluating whether the difference between two means is statistically significant. • t tests can be used either • to compare two independent groups (independent-samples t test) • to compare observations from two measurement occasions for the same group (paired-samples t test).

30. Remember t test - tests the null hypothesis / that there is no difference …

31. t test • If you are using the t test to compare two groups, the groups should be randomly drawn from normally distributed and independent populations. • Using SPSS • Analyze • Compare Means            One-Sample T test...            Independent-Samples T test...            Paired-Samples T test...

32. Types of t-test • The one-sample t test is used compare a single sample with a population value. • Example, a test could be conducted to compare the average test scores of U5C with a value that was known to represent the whole EDU 540 population. • The independent-sample t test is used to compare two groups' scores on the same variable. • Example : Compare the test scores of U5C and PKPG to evaluate whether there is a difference in their scores. • The paired-sample t test is used to compare the means of two variables within a single group. • Example, it could be used to see if there is a statistically significant difference between test 1 and test 2 among the members of U5C

33. Using SPSS : t test

34. Output • Notice the two parts of the output • Equal variances assumed • Equal variance not assumed • Which to use? • Look at Levene’s test for equality of variance • If small Sig. - groups have unequal variances

35. Output • t-statistics is -6.024 • Sig. level : .000 • The significance level tells us that the probability that (there is no difference between visual and tactile learners) – the “NULL” is very small • Hence, there is a significant difference in the test scores between visual and tactile learners

36. Have fun with SPSS! Proceed to Qualitative Analysis and Ethics in Research