PRR 475 Math refresher and summary of basic SPSS stat proceduresReview these if you are having trouble with SPSS exercise.1. Exponential or scientific notation:5.3 * E -02 is .053 - stands for 5.3 * 10-2 Simply move decimal point n places to left if E -n and n places to right if E +n. 2. Mean of a variable measured as 0-1. Many variables are dichotomous or binary taking on only two values, e.g true-false, yes-no, male-female,participate-don't. These are usually coded as 0 for no and 1 for yes. Such variables can be treated as any measurement scale so you can run frequencies, crosstabs or means on them. The mean of a 0-1 variable is simply the percent with the 1 response (yes).Run both FREQ and DESC on a binary variable such as GENDER or MVP, or any activity variable (participate or not). Make sure you understand what each is telling you.Example : GENDERFREQ PctMale (0) .55Female (1) .45MEAN for GENDER .45Mean is the percentage of 1's in sample. In above example female was coded 1, so it is percentage of females.3. Selected SPSS Statistical Procedures - runs on HCMA95.SAV file. You should try to replicate these results yourself and make sure you understand the interpretations. I've put those statistics you normally should report in bold on output tables. Also wrote brief interpretation. a. FREQ - freq table b. DESCRIPTIVES - means for interval scale variablesc. CORRELATION d. CROSSTAB - income vs MVP95e. MEANS HCMATOT (total visits for year) by MVP95 (annual permit)f. Same run WEIGHTEDg. Independent Sample T-TESTh. Another weighting example - FREQ on MVP95i. SPSS Chart to show distribution of HCMATOTStatistics in bold are usually the best ones to report.a. FREQUENCIES ON INCOMETOTAL HOUSEHOLD INCOME BEFORE TAXES Frequency Percent ValidPercentCum Percent Valid UNDER $25,000 346 8.6 11.2 11.2 $25,000 TO $49,999 940 23.3 30.5 41.7 $50,000 TO $74,999 955 23.7 31.0 72.7 $75,000 OR MORE 843 20.9 27.3 100.0 Total 3084 76.5 100.0 Missing CHOOSE NOT TO ANSWER 592 14.7 System 355 8.8 Total 947 23.5 Total 4031 100.0 Interpretation: Focus on the Valid pct column as the population estimates. In above case 11% have incomes under $25K, 27% $75K or more. Might report these four valid pcts in a simple pie chart to show income distribution. Should know how to do this in Excel or could try SPSS charts.Raw freq are number in sample - not that useful. Can simply report sample size is 4,031 and 23% of sampledidn't give income or checked "choose not to answer". Distribution is based on 3,084 subjects who gave their income. b. DESCRIPTIVES ON AGE - ask for SE MeanDescriptive Statistics N Minimum Maximum Mean Std.Deviation Statistic Statistic Statistic Statistic Std. Error Statistic AGE OFSUBJECT3650 16 89 44.01 .24 14.75 Valid N(listwise)3650 Interpretation: Average age of visitors is 44. If you want can note this is based on sample of 3,650 cases and 95% confidence interval is 44 + or - .48 (two standard errors) or roughly (43.5, 44.5).c. CORRELATIONS, PEARSON - ask for Pearson CorrCorrelations PURCHASEAN ANNUALMVP 95Total femalesin partyTotal males inpartyAGE OFSUBJECT MVP 95 Pearson Correlation 1.000 .312 -.150 .216 Sig. (2-tailed) . .000 .000 .000 N 3842 3176 3737 3524 Females Pearson Correlation .312 1.000 -.118 .132 Sig. (2-tailed) .000 . .000 .000N 3176 3329 3210 3020 Males Pearson Correlation -.150 -.118 1.000 -.129 Sig. (2-tailed) .000 .000 . .000 N 3737 3210 3893 3549 AGE OFSUBJECTPearson Correlation .216 .132 -.129 1.000 Sig. (2-tailed) .000 .000 .000 . N 3524 3020 3549 3650 ** Correlation is significant at the 0.01 level (2-tailed).Interpretation: The table shows all bivariate correlations for 4 variables. I've picked just the age vs MVP95 correlation. Correlation is .216 which is mild positive correlation, meaning those with annual permits (coded 1 vs 0 if not) tend to be older. Correlation is significant at the 95% confidence level (SIG <.000) - this means we can reject null hypothesis that correlation in the population is zero.d. CROSSTAB - ask for Row and Col Pcts and Chi squareTOTAL HOUSEHOLD INCOME BEFORE TAXES * DID YOU PURCHASE AN ANNUAL MOTOR VEHICLE PERMIT IN 1995? CrosstabulationTOTAL HOUSEHOLD INCOME BEFORE TAXES MVP95 NO YES < $25,000 Count 151 178 329 % within INCOME 45.9% 54.1% 100.0% % within MVP95 11.7% 10.6% 11.1% $25- 49.9K Count 405 510 915 % within INCOME 44.3% 55.7% 100.0% % within MVP95 31.4% 30.3% 30.8% $50KTO 74.9 Count 397 513 910 % within INCOME 43.6% 56.4% 100.0% % within MVP95 30.8% 30.5% 30.6% $75,000 + Count 337 481 818 % within INCOME 41.2% 58.8% 100.0% % within MVP95 26.1% 28.6% 27.5% Total Count 1290 1682 2972 % within INCOME 43.4% 56.6% 100.0% Chi-Square Tests Value df Asymp.Sig. (2-sided) Pearson Chi-Square 2.745 3 .433 Likelihood Ratio 2.749 3 .432 Linear-by-LinearAssociation2.547 1 .110 N of Valid Cases 2972 a 0 cells (.0%) have expected count less than 5. The minimum expected count is 142.80.Interpretation: First - stat test. Chi square statistic of table of income vs MVP95 is 2.745, not significant at 95% confidence level (SIG =.433 which is not less than .05). So conclusion is no relationship, MVP purchase not vary with income level. Note- a better stat is to run means as I do below. If there is a significant relationship, you should look for the pattern in the table by comparing row percentages with those at bottom in totals row. Issue is does each row look the same as totals? If so no difference in patterns across income levels.e. MEANS HCMATOT by MVP95 - ask for ANOVA table and SE Mean - First Unweighted (*wrong results)ReportMVP95 by hcmatot - Means on total HCMA Visits in 1995MVP95 Mean N Std.DeviationStd. Errorof Mean NO 17.39 1330 39.21 1.08 YES 69.00 1846 96.01 2.23 Total 47.39 3176 81.54 1.45 ANOVA Table Sum ofSquaresdf MeanSquareF Sig. MVP95 byHCMATOTBetweenGroups(Combined) 2059325.5261 2059325.526343.087 .000 WithinGroups 19051413.2393174 6002.336 Total 21110738.7653175 Interpretation: Visitors who did not purchase a MVP last year averaged 17 visitsto HCMA parks in 1995 compared to 69 days for visitors with annual permits. Based on F test, this difference is statistically significant at 99% level (SIG <.001). Overall visitors averaged 47 visits to HCMA parks in 1995. You can use standard errors above to compute 95% confidence levels for the subgroup means. I.e. NO group averages 17