How to use SPSS software in studies .pptx

SPSS software widely is used for data collection in conducting research.

1. Using SPSS for Hypothesis Testing Comparing Means One sample Two samples ANOVA

2. Hypothesis and Hypothesis Testing HYPOTHESIS A statement about the value of a population parameter developed for the purpose of testing. HYPOTHESIS TESTING A procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement. TEST STATISTIC A value, determined from sample information, used to determine whether to reject the null hypothesis. CRITICAL VALUE The dividing point between the region where the null hypothesis is rejected and the region where it is not rejected. 10- 2

3. Taking Decision Reject H if Z > Z  OR Reject H if p-value <  We Use P-value to make decision in SPSS p -VALUE is the probability of observing a sample value as extreme as, or more extreme than, the value observed, given that the null hypothesis is true. In testing a hypothesis, we can also compare the p -value to the significance level ( ) . Decision rule using the p-value: Reject H if p -value < significance level 10- 3

4. One Sample Test for Mean: Using SPSS Open file: Bodyfat.sav and test whether the body fat level in an typical American is 23%. Step 1: Make Hypothesis E.g. H : Mu is equal to 23 H 1 : Mu is not equal to 23 ( Bodyfat file) Step 2: Run Command Analyze> Compare Means>One-Sample T-Test… Add Test Value and Click Ok Make Decision Compare “Sig. value (two-tailed)” with Alpha of your choice.

5. Reading Output

6. Interpreting p-value for One Tailed Test For Example Ho: Mu is not less than 23, H1: Mu is less than 23 OR Ho: Mu is not greater than 23, H 1 : Mu is greater than 23 Calculate p-value as follows: Divide the Sig. Value in half if the alternative hypothesis and test value are consistent in direction. I.e. P-value = Sig./2 If the alternative hypothesis and test value are at odds then calculate by: P-value= 1 – (Sig./2)

7. Small Sample Test If the sample is small i.e. less than 30 the procedure is sample but check the normality graphically. The distribution should be symmetrical at least around one mode. Use chart builder and to draw histogram in this case.

8. Comparing Two Means Two Different Cases Independent Samples When samples are drawn from two different groups e.g. comparing output of male and female employees. Dependent Samples or Paired Observations When the second sample is based on the selection of first sample. E.g. comparing output of employees before and after a training.

9. Comparing Two Population Means: Independent Samples No assumptions about the shape of the populations are required. The samples are from independent populations. The formula for computing the test statistic ( z ) is: EXAMPLE The U-Scan facility was recently installed at the Byrne Road Food-Town location. The store manager would like to know if the mean checkout time using the standard checkout method is longer than using the U-Scan. She gathered the following sample information. The time is measured from when the customer enters the line until their bags are in the cart. Hence the time includes both waiting in line and checking out. Step 1 : State the null and alternate hypotheses. (keyword: “longer than”) H : µ S ≤ µ U H 1 : µ S > µ U Step 2: Select the level of significance. The .01 significance level is stated in the problem. 11- 10

10. Example 1 continued Step 3: Determine the appropriate test statistic. Because both population standard deviations are known, we can use z-distribution as the test statistic Step 4: Formulate a decision rule. Reject H if Z > Z  Z > 2.33 Step 5: Compute the value of z and make a decision The computed value of 3.13 is larger than the critical value of 2.33. Our decision is to reject the null hypothesis. The difference of .20 minutes between the mean checkout time using the standard method is too large to have occurred by chance. We conclude the U-Scan method is faster. LO1 11- 11

11. Hypothesis Testing Involving Paired Observations - Example Step 1: State the null and alternate hypotheses. H :  d = 0 H 1 :  d ≠ Step 2: State the level of significance. The .05 significance level is stated in the problem. Step 3: Find the appropriate test statistic. We will use the t -test Step 4: State the decision rule. Reject H if t > t /2, n-1 or t < - t /2,n-1 t > t .025,9 or t < - t . 025, 9 t > 2.262 or t < -2.262 11- 12

12. Comparing Means Two Independent Samples Using SPSS Step 0: Check Assumptions Step 1: Formulate Hypothesis Step 2: Analyze> Compare Means> Independent-Sample T-Test… Select Variable and enter grouping variables Step 3: Make Decision Compare “Sig. value (two-tailed)” with Alpha of your choice. Note: calculate p-value if test is one tailed.

13. Comparing Means Two Independent Samples Using SPSS T-test for independent samples need to satisfy three assumptions: Samples should be independent Both populations should be normal Variances of both populations should be equal (for small sample sizes) Example: Open file Student.sav Test whether the height of male students is larger than the height of female students.

14. Checking Normality Assumption Use Chart Builder

15. Checking Equality of Variances The sampling distribution of variance follows the F-distribution. F distribution is a positively skewed distribution with positive values. We need to test: H0: Variances are equal, H1: Variances are different

16. Making Decision about equality of Means Choose the first row values of t test if your variances proved to be equal otherwise choose the second row values.

17. Comparing Means: Dependent Samples/Paired Observations Example: Open file swimmers2 The coach wants to see whether the team has improved in 100 meter free style race?

18. Comparing Means: Dependent Samples/Paired Observations Step 1: Formulate Hypothesis Step 2: Analyze> Compare Means> Paired-Sample T-Test… Select Variable and enter grouping variables Step 3: Make Decision Compare “Sig. value (two-tailed)” with Alpha of your choice. Note: calculate p-value if test is one tailed.

19. ANOVA

20. Analysis of Variance (ANOVA) Variance follows F-distribution, which is a positively skewed distribution. Applications: Comparing Standard Deviations Comparing m ore than two means Assumptions Independent Samples Normal Populations Homogeneity of population variances

21. Comparing more than two means Open file Student.sav The variable WorkCat shows the amount of work students do outside of school in three categories. Does the students working outside have their grades/GPAs suffering.

22. The ANOVA procedure Check Assumptions Formulate Hypothesis Ho: There is no difference in average grades of students At least one population mean is different from others. Run ANOVA test: Analyze>Compare Means>One-way ANOVA

23. Testing for Normality: Kolmogorov- Smimov Test Analyze>Descriptive Statistics>Explore Choose: Plots > normality plots with tests Reading Output: Ho: the distribution is normal As .200 is greater than alpha so we can’t reject Ho

24. Testing equality of variances This statistic will be found in the ANOVA test. So choose Analyze>Compare Means>One way ANOVA Choose: Options>Homogeneity of variances test Reading Output Ho: Variances are Homogeneous As p-value is greater than alpha so we do not reject Ho

25. ANOVA Output Reading ANOVA table As p-value is less than alpha so we reject Ho. This means that at least one mean is difference. Hence can be concluded that outside work affects GPA of students.

26. Which mean is different? To check which of the means is different we use Post-Hoc tests. One commonly used test is “ Tuckey’s Honestly Significant Difference Test”. Analyze>Compare Means>One way ANOVA Choose: Post-Hoc > Tekey Reading Output Ho: I and J Means are equal

27. Correlation and Regression Analysis

28. Coefficient of Correlation A measure of the Direction of the linear relationship between x and y. If x and y are directly related, r > 0. If x and y are inversely related, r < 0. Strength of the linear relationship between x and y. The larger the absolute value of r , the more the value of y depends in a linear way on the value of x . © 2002 The Wadsworth Group

29. Coefficient of Determination A measure of the Strength of the linear relationship between x and y. The larger the value of r 2 , the more the value of y depends in a linear way on the value of x . Amount of variation in y that is related to variation in x . Ratio of variation in y that is explained by the regression model divided by the total variation in y . © 2002 The Wadsworth Group

30. Measuring Correlation: Using SPSS Open file US.sav Is there any relationship between aggregate income and consumption? Graphical Method Graphs>Chart Builder > choose scatter plot

31. Regression Analysis Regression analysis generates a “best-fit” mathematical equation that can be used in predicting the values of the dependent variable as a function of the independent variable. © 2002 The Wadsworth Group

32. Direct vs Inverse Relationships Direct relationship: As x increases, y increases. The graph of the model rises from left to right. The slope of the linear model is positive. Inverse relationship: As x increases, y decreases. The graph of the model falls from left to right. The slope of the linear model is negative. © 2002 The Wadsworth Group

33. Simple Linear Regression Model Probabilistic Model: y i = b + b 1 x i + e i where y i = a value of the dependent variable, y x i = a value of the independent variable, x b = the y -intercept of the regression line b 1 = the slope of the regression line e i = random error, the residual Deterministic Model: = b + b 1 x i where and is the predicted value of y in contrast to the actual value of y . © 2002 The Wadsworth Group