IBM SPSS 19 manual

1 Using IBM SPSS 19* Descriptive Statistics SPSS Help. SPSS has a good online help system. Once SPSS is up and running, you can nd it by going to Help>T opics in the menu bar , i.e., click Help in the menu bar and then click T opics in the drop window that opens. Y ou will now be in the help contents window . Click T utorial . _______________[...]

2 Y ou can then open any of the books comprising the tutorial by clicking on the + to get to the various subtopics. Once in a subtopic is open, you can just keep clicking on the right and left arrows to move through it page by page. I suggest going through the entire Overview booklet. Once you are working with a data set, and have an idea of what y[...]

3 Sorting the Data . From the menu, choose Data>Sort Cases… , click the right arrow to move protein to the Sort by box, make sure Ascending is chosen, and click OK . Our data column is now in ascending order . However , the rst thing that come up is an output page telling you what has happened. Click the table with the Star on it to get bac[...]

4 Click the Statistics... button, then make sure Descriptives and Percentiles are checked. W e will use 95% for Condence Interv al for Mean . Click Continue . Then click Plots... . Under Bo xplots , select F actor levels together , and under Descriptiv e , choose both Stem-and-leaf and Histogr am . Then click Continue .[...]

5 Then click OK . This opens an output window with two frames. The frame on the left contains an outline of the data on the right.[...]

6 The Standard Error of the Mean is a measure of how much the value of the mean may vary from repeated samples of the same size taken from the same distribution. The 95% Condence Interv al for Mean are two numbers that we would expect 95% of the means from repeated samples of the same size to fall between. The 5% T rimmed Mean is the mean after [...]

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8 Now click on a number on the horizontal axis and then click on Number Format . In the diagram to the left below , we see that we have 2 decimal places. The values in this window can be changed as desired. Next, click on one of the bars and then Binning in the Properties window . Suppose we want bars of width 20 beginning at 30. Check Custom , Int[...]

9 Next choose P ercentiles from either output frame. The following comes up. Obviously , there are two dif ferent methods at work here. The formulas are given in the SPSS Algorithms Manual . T ypically , use the W eighed A verage . T ukey’ s Hinges was designed by T ukey for use with the boxplot. The box covers the Interquartile range (IQR) = Q 7[...]

10 Then click back to Data View . From the menu, choose T ransform>Compute V ariable... . When the Compute V ariable window comes up, click Reset , and type cum_bin in the box labeled T arget V ariable . Scroll down the Function group: window to CDF & Noncentral CDF to select it, then scroll to and select Cdf .Binom in the Functions and Spec[...]

1 1 Poisson Distribution. Let us assume that l =.5. W e will rst nd P(X ≤ x | .5)for x = 0, ..., 15, i.e., the cumula- tive probabilities. First put the numbers 0 through 15 in a column of a worksheet. (W e have already done this above. Again, you only need to enter the numbers whose cumulative probability you desire.) Then click V ari- abl[...]

12 cumulative Poisson probabilities are now found in the column cum_pois. Now we want to put the individual Poisson probabilities into the column pois_pro . Do basically the same as above, except make the T arget V ariable “ pois_pro ,” and the Numeric Expression “ CDF . POISSON(number ,.5) - CDF .POISSON(number-1,.5) .” The Data View now l[...]

13 The probability is now found in the column cum_norm . Staying with the normal distribution with mean 100 and standard deviation 20, suppose we with to nd P(90 ≤ X ≤135). Do as above except make the T arget V ariable “ int_norm ,” and the Numeric Expression “ CDF . NORMAL(135,100,20) - CDF .NORMAL(90,100,20) .” The probability is n[...]

14 Condence Intervals and Hypothesis T esting Using t A Single Population Mean . W e found earlier that the sample mean of the data given on page 2, which you may have saved under the name protein.sav , is 73.3292 to four decimal places. W e wish to test whether the mean of the population from which the sample came is 70 as opposed to a true mea[...]

15 SPSS gives us the basic descriptives in the rst table. In the second table, we are given that the t -value for our test is 1.110 . The p -value (or Sig. (2-tailed) ) is given as .272 . Thus the p -value for our one-tailed test is one- half of that or .136 . Based on this test statistic, we would not reject the null hypothesis, for instance, f[...]

16 and again press Add . Then hit OK and complete the V ariable View as follows. Returning to Data View gives a window whose beginning looks like that below . Now we wish to test the hypotheses H 0 : m 1 - m 2 = 0 H a : m 1 - m 2 ≠ 0 where m 1 refers to the population mean for the non-smokers and m 2 refers to the population mean for the smokers.[...]

17 Then click Continue . As before, click Options... , enter 95 (or any other number) for Condence Inter- val , and again click Continue followed by OK . The rst table of output gives the descriptives. T o get the second table as it appears here, I rst double-clicked on the Independent Samples T est table, giving it a fuzzy border and brin[...]

18 discount this hypothesis, so we will take our results from the Equal V ariances Assumed column. W e see that, with 30 degrees of freedom, we have t =-2.468 and p =.020, so we reject the null hypothesis H 0 : m 1 - m 2 = 0 at the a =.05 level of signicance. That we would reject this null hypothesis can also be seen in that the 95% Con- denc[...]

19 The rst output table gives the descriptives and a second (not shown here) gives a correlation coefcient. From the third table, which has been pivoted to interchange rows and columns, we see that we have a t -score of 12.740. The fact that Sig.(2-tailed) is given as .000 really means that it is less than .001. Thus, for our one-sided test, [...]

20 H 0 : m N = m F = m C H a : Not all of m N , m F , and m C are equal. From the menu we choose Analyze>Compare Means>One- W ay ANOV A... . In the window that opens, place volume under Dependent List and Smok er[smoking] u nder F actor . Then click P ost Hoc... For a post-hoc test, we will only choose T ukey (T ukey's HSD test) with Sig[...]

21 Then we click options and choose Descriptive , Homogeneity of variance test , and Means plot . The Homogeneity of v ariance test calculates the Levene statistic to test for the equality of group variances. This test is not dependent on the assumption of normality . The Brown-Forsythe and W elch statistics are better than the F statistic if the a[...]

22 The results of the T est of Homogeneity of V ariances is nonsignicant since we have a p value of .974 , showing that there is no reason to believe that the variances of the three groups are different from one another . This is reassuring since both ANOV A and T ukey's HSD have equal variance assumptions. W ithout this reassur- ance, inte[...]

23 Simple Linear Regression and Corr elation W e will use the following 109 x-y data pairs for simple linear regression and correlation. The x 's are waist circumferences (cm) and the y 's are measurements of deep abdominal adipose tissue gathered by CA T scans. Since CA T scans are expensive, the goal is to nd a predictive equation. F[...]

24 Then click OK to get the following scatter plot, which leads us to suspect that there is a signicant linear relation- ship. Regression. T o explore this relationship, choose Analyze>R egression>Linear ... from the menu, select and move y under Dependent and x under Independent(s) .[...]

25 Then click Statistics... , and in the window that opens with Estimates and Model t already checked, also check Condence interv als and Descriptives . Then click Continue . Next click Plots... . In the window that opens, enter *ZRESID for Y and *ZPRED for X to get a graph of the standardized residuals as a function of the standardized predi[...]

26 Then click Continue followed by OK to get the output. W e rst see the mean and the standard deviation for the two variables in the Descriptive Statistics . In the Model Summary , we see that the bivariate correlation coefcient r ( R ) is .819, indicating a strong positive linear relationship between the two variables. The coefcient of d[...]

27 reject the null hypothesis of b =0. W e now return to the scatter plot. Double click on the plot to bring up the Chart Editor and choose Options>Y Axis R eference Line from the menu. In the window that opens, select Refernce Line and, from the drop- down menue for Set to: , choose Mean and then click Apply . Next, from the Chart Editor menu, [...]

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29 for the mean value m y|74.5 is ( 32.41572, 52.72078) , corresponding to the limits of the inner bands at x=74.5 in the scatter plot, and the 95% condence interval for the individual value y I (74.5)is (-23.7607,108.8972), correspond- ing to the limits of the outer bands at x =74.5. The rst pair of acronyms lmci and umci stand for “lower [...]

30 W e see again that the Pearson Correlation r is .819, and from the Sig. of .000, we know that the p -value is less than .001 and so we would reject a null hypothesis of r =0. Multiple Regr ession W e will use the following data set for multiple linear regression. In this data set, required ram , amount of input , and amount of output , all in ki[...]

31 Choose Analyze>R egression>Linear ... from the menu, select and move minutes under Dependent and ram , input , and output , in that order , under Independent(s) . Then ll in the options for Statistics , Plots , and Save exactly as you did for simple linear regression. Finally , click OK to get the output. W e rst see the mean and the[...]

32 1.049x 3 . From the last two rows of numbers in the table, one gets that 95% condence intervals are (-.694,2.645) for a , (.061,.138) for b 1 , (.000,.487) for b 2 , and (.692,1.407) for b 3 . The t test is used for testing the various null hypotheses b i =0. It can be used similarly to test the null hypothesis a =0, but this is of much less [...]

33 Finally , consider the residual plot below . On the horizontal axis are the standardized y values from the data points, and on the vertical axis are the standardized residuals for each such y . If all the regression assumptions were met for our data set, we would expect to see random scattering about the horizontal line at level 0 with no notica[...]

34 Then click back to Data View . From the menu, choose T ransform>Compute V ariable... . When the Compute V ariable window comes up, click R eset , then type lny in the box labeled T arget V ariable . Then scroll down the Function Group window to Arithmetic and then down the Functions and Special V ariables window to Ln to select it and press t[...]

35 Choosing a Model using Curve Estimation. T o nd an appropriate model for a given data set, such as the one in the previous section, choose Analyz e>Regression>Curve Estimation... . In the Curve Estimation window that opens, enter y under Dependent(s) , x under Independent with V ariable selected, and make sure Include constant in equati[...]

36 Finally , click OK . W e show below the output for the Quadratic model. The regression equation is ŷ=336.790- 693.691x+295.521x 2 . The other data, although arranged differently , is similar to that for linear and multiple regression. W e do note that the Standard Error is 1 1 1.856. Although they are not shown here, the regression equation for[...]

37 Chi-Squar e T est of Independence For data, we will use a survey of a sample of 300 adults in a certain metropolitan area where they indicated which of three policies they favored with respect to smoking in public places. W e wish to test if there is a relationship between education level and attitude to- ward smoking in public places. W e test [...]

38 This is not very well documented, but the rst thing we need to do for c 2 is to tell SPSS which column contains the frequency counts. Choose Data>W eight Cases... from the menu, and in the window that opens, choose W eight cases by and move the variable count under Frequency V ariable . Then click OK . Now choose Analyze>Descriptive Sta[...]

39 Check Observed and Expected under Counts , followed by Continue and OK . The rst table of output simply provides a table of the Counts and the Expected Counts if the variables are independent. From the second table, the Pearson Chi-Square statistic is 22.502 with a p -value ( Asymp . Sig. (2-sid- ed) ) of .001. Thus, for instance, we would re[...]

40 From the menu, choose Analyze>Nonpar ametric T ests>Legacy Dialogs>2 Related Samples... . In the window that opens, rst click output followed by the arrow to make it V ariable 1 for Pair 1 , then con- stant followed by the arrow to make it V ariable 2 . Make sure Wilcoxon is checked. If you want descriptive statistics and/or quartile[...]

41 The Z in the second table is the standardized normal approximation to the test statistic, and the Asymp. Sig (2-tailed) of .140, which we will use as our p -value, is estimated from the normal approximation. Because of the size of this p -value, we will not reject the null hypothesis at any of the usual levels of signicance. The Mann-Whitney [...]

42 Put 1 in the box for Group 1 and 2 in the box for Group 2 . Then click Continue . Y ou may click Options... if you want the output to include descriptive statistics and/or quartiles. Finally , click OK to get the output. W e see from the rst table, after ranking the hemoglob values from least to greatest, the Mean R ank and Sum of R anks for [...]

43 T o create the control chart(s), click Analyze>Quality Control>Control Charts... from the menu bar , and in the window that opens, select X -Bar , R, s under V ariable Charts and make sure Cases are units is checked under Data Organization . Then click Dene , and in the new window that opens, move g_per_l under Process Measurement and d[...]

44 Click Options , and enter 2 for Number of Sigmas . After clicking Continue, since we have specications for the mean, we click Statistics... , and in the window that opens, based on our specied mean and standard deviation, enter 50.756 for Upper and 49.244, Lower for Specication Limits , and 50 for T arget . Then select Estimate using S-[...]

45 Control Charts for the Proportion. T o illustrate control charts for the proportion, we use the number of defec- tives in samples of size 100 from a production process for twenty days in August. August: 6 7 8 9 10 1 1 12 13 14 15 Defectives: 8 15 12 19 7 12 3 9 14 10 August: 16 17 18 19 20 21 22 23 24 25 Defectives: 22 13 10 15 18 1 1 7 15 24 2 [...]

46 Now click Options, and enter 3 for Number of Sigmas . Then click Continue followed by OK to get the control chart, which is again pretty much self-explanatory . W e see that the process is out of control on August 24 and 25, although it is hard to call too few defectives out of control.[...]