Missing Data with Correlation & Multiple Regression Missing Data Missing data have several sources, response refusal, coding error, data entry errors, and outliers are a few. SPSS allows you to identify specific data values as “missing” – those specific values will be recognized as “non data” and not used in statistical computations. Once the missing values are set, it is easy to use Frequencies to find the number of cases with missing data for each variable This data set of N = 103 cases has no more than 6 missing values for any variable – so, around 1-5% outliers, not bad. But remember that we are using at least 2 ( a single correlation) and maybe many more (several correlations or a multiple regression) variables in our analyses. The real problem with missing data is that the number of cases with incomplete data “adds up” across the multiple variables used in an analysis Statistics99 100 98 101 974 3 5 2 63.3051 1.5200 1.4796 3.6050 6.6959ValidMissingNMean1st yr gradgpa --criterionvariablegender prograting derivedfrom letters ofrecommendatonUndergraduate grade pointaverage on1-9 scale Correlation After selecting the variables for the analysis, the specific type of correlation and the type of NHST to be done, the Options window can be used to obtain univariate stats & select the type of Missing Values treatment. Pairwise -- each correlation is computed using data from all the participants who have non-missing values for those two variables -- “different samples” representing the population for each correlation but the most “inclusion” for each correlation Listwise -- all the correlations are computed using only data from participants who have non-missing values for all variables selected -- gives the “same sample” for each correlation, but smallest NCorrelation Pairwise Analysis Descriptive Statistics3.3051 .61783 991.5200 .50212 1001.4796 .50215 983.6050 .81183 1016.6959 .96436 971st yr grad gpa -- criterionvariablegenderprograting derived from lettersof recommendatonUndergraduate gradepoint average on 1-9scaleMeanStd.DeviationN Notice: The gender – ggpa correlation is based on the 96 folks with scores on both, but the gender mean & std are based on N=100 and the ggpa mean & std are based on N=99. Univariate & Bivariate stats are usually not computed from the same participants’ data. Correlations1 .071 .217 .616 .152.491 .036 .000 .07299 96 94 97 93.071 1 -.389 -.015 -.071.491 .000 .883 .49896 100 95 98 94.217 -.389 1 .212 .083.036 .000 .038 .21994 95 98 96 92.616 -.015 .212 1 .198.000 .883 .038 .02797 98 96 101 95.152 -.071 .083 .198 1.072 .498 .219 .02793 94 92 95 97Pearson CorrelationSig. (2-tailed)NPearson CorrelationSig. (2-tailed)NPearson CorrelationSig. (2-tailed)NPearson CorrelationSig. (2-tailed)NPearson CorrelationSig. (2-tailed)N1st yr grad gpa -- criterionvariablegenderprograting derived from lettersof recommendatonUndergraduate gradepoint average on 1-9scale1st yr gradgpa --criterionvariablegender prograting derivedfrom letters ofrecommendatonUndergraduate grade pointaverage on1-9 scale Different correlation results from the two procedures can be because of sample size/power differences, sampling/representation differences, or both. prog & ggpa Æ not much difference in r value, but NHST difference (less powerful . . . . . Listwise results are nonsignificant) . ggpa & ugpa Æ huge difference in r – which one represents the population? Listwise Deletion Descriptive Statistics3.2699 .61302 831.5542 .50007 831.4819 .50271 833.5771 .80157 836.6687 .97304 831st yr grad gpa -- criterionvariablegenderprograting derived from lettersof recommendatonUndergraduate gradepoint average on 1-9scaleMeanStd.DeviationN Notice: There were “only a few missing data”( 2-6 ) based on the initial univariate analysis. But if different participants are missing data for different variables, the number lost to Listwise deletion can be substantial. Correlationsa1 .035 .202 .614 .642.752 .067 .000 .000.035 1 -.445 .032 -.069.752 .000 .774 .534.202 -.445 1 .224 .330.067 .000 .041 .002.614 .032 .224 1 .559.000 .774 .041 .000.642 -.069 .330 .559 1.000 .534 .002 .000Pearson CorrelationSig. (2-tailed)Pearson CorrelationSig. (2-tailed)Pearson CorrelationSig. (2-tailed)Pearson CorrelationSig. (2-tailed)Pearson CorrelationSig. (2-tailed)1st yr grad gpa -- criterionvariablegenderprograting derived from lettersof recommendatonUndergraduate gradepoint average on 1-9scale1st yr gradgpa --criterionvariablegender prograting derivedfrom letters ofrecommendatonUndergraduate grade pointaverage on1-9 scaleListwise N=83a.Multiple Regression Using the Statistics window, you can get univariate statistics and Bivariate correlations. Remember that both of these are calculated as inferential (not descriptive) statistics. These statistics, as well as the regression model are computed based on the Missing Values procedure chosen from the Options window. Be sure that the univariate, correlation and multiple regression analyses you report “go together”. It is a good idea to carefully compare the results from separate analyses to be sure you’ve got the right values: • Compare the mean, stds & Ns obtained via Frequencies, Correlation and Multiple Regression • Compare the correlations and Ns via Correlation and Multiple RegressionCase wise Deletion Pairwise Analysis Descriptive Statistics3.2699 .61302 831.5542 .50007 831.4819 .50271 833.5771 .80157 836.6687 .97304 831st yr grad gpa -- criterionvariablegenderprograting derived from lettersof recommendatonUndergraduate gradepoint average on 1-9scaleMeanStd.DeviationN The univariate statistics will match those from both the Frequencies and Correlation procedures. Please Note: The mean, std & N from the Pairwise univariate analyses aren’t computed from the same participants as the correlations or the regression model. Descriptive Statistics3.3051 .61783 991.5200 .50212 1001.4796 .50215 983.6050 .81183 1016.6959 .96436 971st yr grad gpa -- criterionvariablegenderprograting derived from lettersof recommendatonUndergraduate gradepoint average on 1-9scaleMeanStd.DeviationN Note: You’ll get the same Casewise correlation matrix as from the Correlation procedure above Note: You’ll get the same Pairwise correlation matrix as from the Correlation procedure above Model Summary.714a.510 .485