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1 Santa Fe Grill SPSS Results Tabulations Mean, Median and Mode The SPSS “click-through” sequence is ANALYZE DESCRIPTIVE STATISTICS FREQUENCIES. Let’s use X25 – Frequency of Patronage of Santa Fe Grill as a variable to examine. Click on X25 to highlight it and then on the arrow box for the Variables box to use in your analysis. Next open the Statistics box and click on Mean, Median, and Mode, and then Continue and OK. Recall that if you want to create charts open the Charts box. Your choices are Bar, Pie, and Histograms. For the Format box we will use the defaults, so click on OK to execute the program. Note: results for X25 and three other variables are shown below, after the range, standard deviation and variance results. Range, Standard Deviation and Variance The Santa Fe Grill database can be used with the SPSS software to calculate measures of dispersion, just as we did with the measures of central tendency. The SPSS clickthrough sequence is ANALYZE DESCRIPTIVE STATISTICS FREQUENCIES. Let’s use X22 – Satisfaction as a variable to examine. Click on X22 to highlight it and then on the arrow box to move X22 to the Variables box. Next open the Statistics box, go to the Dispersion box in the lower-left-hand corner, and click on Standard deviation, Variance, Range, Minimum and Maximum, and then Continue. If you would like to create charts, then open the Charts box – your choices are Bar, Pie, and Histograms. For the Format box we will use the defaults, so click on OK to execute the program. Below are SPSS results for question 22. Frequencies Statistics X22 -- Satis faction N Valid Missing Mean Median Mode Minimum Maximum 400 0 4.64 4.50 4 3 6 2 X22 -- Satisfaction Valid 3 4 5 6 Total Frequency 39 161 103 97 400 Percent 9.8 40.3 25.8 24.3 100.0 Valid Percent 9.8 40.3 25.8 24.3 100.0 Cumulative Percent 9.8 50.0 75.8 100.0 X22 -- Satisfaction 200 Frequency 100 0 3 X22 -- Satisfaction 4 5 6 3 Below are tabulations for survey questions 25, 30, 32 and 34. Frequencies Statistics N Valid Missing Mean Median Mode Minimum Maximum X25 -Frequency of Patronage of Santa Fe Grill 400 0 2.17 2.00 3 1 3 x30 -Distance Driven 400 0 1.84 2.00 1 1 3 X32 -- Gender 400 0 .41 .00 0 0 1 X34 -- Age 400 0 3.05 3.00 3 1 5 Note: Technically speaking, researchers should not calculate means for questions 25, 30 and 34, because they are ordinal measures. Practically speaking, it is often done. The median and mode are the proper statistics for ordinal data. The mean can be calculated for question 32 because it is dummy coded (0 – 1). 25. How often do you patronize the Santa Fe Grill? 1 = Occasionally (Less than once a month) 2 = Frequently (1 – 3 times a month) 3 = Very Frequently (4 or more times a month) The mean of question 25 is 2.17, as shown in the above table. Using the coding above for this question, this means the customers of Santa Fe Grill on average patronize the restaurant “Frequently”, which is defined as 1 – 3 times a month. The median frequency of patronage is 2.0 and the mode is 3, so the Santa Fe customers who responded are relatively frequent customers. 30. Distance Driven 1 2 3 Less than 1 mile 1 – 3 miles More than 3 Miles The mean of question 30 is 1.84, as shown in the above table. Using the coding above for this question, this means the customers of Santa Fe Grill on average drive somewhere in the range of 1 – 3 miles to eat at the restaurant. The median distance driven is 2.0 and the mode is 1, so the Santa Fe customers who responded most often drove less than one mile (N=183 out of 400). 32. Your Gender 0 1 Male Female 4 The mean of question 32 is 0.41, as shown in the above table. Using the coding above for this question, this means the customers of Santa Fe Grill who completed the questionnaire are predominantly more males than females, because the mean is below 0.5 which would be one-half males and one-half females. Indeed, looking at the frequencies below, we see there are 236 males and 164 females in the sample. 34. Your Age in Years 1 2 3 4 5 18 - 25 26 - 34 35 - 49 50 - 59 60 and Older The mean of question 34 is 3.05, as shown in the above table. Using the coding above for this question, this indicates the customers of Santa Fe Grill on average are somewhere between 35 and 49 years old. The median age is 3.0 and the mode is 3, so the Santa Fe customers who responded are typically 35 – 49 years old. Frequency Table X25 -- Fre que ncy of Patronage of Sa nta Fe Gril l Valid Frequency Oc cas ionally 111 Frequently 111 Very Frequently 178 Total 400 Percent 27.8 27.8 44.5 100.0 Valid Perc ent 27.8 27.8 44.5 100.0 Cumulative Percent 27.8 55.5 100.0 The above tabulation shows of those who responded to the questionnaire, most are frequent patrons. x30 -- Distance Driven Valid Frequency Less than 1 mile 183 1 -- 3 miles 98 More t han 3 miles 119 Total 400 Percent 45.8 24.5 29.8 100.0 Valid Percent 45.8 24.5 29.8 100.0 Cumulative Percent 45.8 70.3 100.0 The above tabulation shows of those who responded to the questionnaire, most (45.8%) drive less than one mile and another 24.5% drive 1-3 miles. Thus, the primary market for patrons is within three miles of the restaurant. 5 X32 -- Gender Valid Males Females Total Frequency 236 164 400 Percent 59.0 41.0 100.0 Valid Percent 59.0 41.0 100.0 Cumulative Percent 59.0 100.0 The above tabulation shows that the patrons of the restaurant who responded to the questionnaire were 59% males and 41% females. X34 -- Age Valid 18 - 25 26 - 34 35 - 49 50 - 59 60 and Over Total Frequency 39 37 207 100 17 400 Percent 9.8 9.3 51.8 25.0 4.3 100.0 Valid Percent 9.8 9.3 51.8 25.0 4.3 100.0 Cumulative Percent 9.8 19.0 70.8 95.8 100.0 The above tabulation shows that the patrons of the restaurant who responded to the questionnaire were mostly in the range of 35 – 49 (51.8%) and second most often in the age range of 50 – 59 (25.0%). Thus, the current customer mix is somewhat older. Cross-Tabulations Note: this first example not only shows cross-tabulations, but tests them using the Chi-Square statistic. Chi-Square The click-through sequence for Chi-Square is ANALYZE DESCRIPTIVE STATISTICS CROSSTABS. Click on X30 – Distance Traveled for the Row variable and on X32 – Gender for the Column variable. Click on the Statistics button and the Chi-square box, and then Continue. Next click on the Cells button, and in that dialog box click on Expected and Observed frequencies. Then click Continue and OK to execute the program. 6 Crosstabs Case Processing Summary Valid N x30 -- Distance Driven * X32 -- Gender Percent 400 Cases Missing N Percent 100.0% 0 Total N .0% Percent 400 100.0% x30 -- Distance Driven * X32 -- Ge nder Crossta bul ation x30 -- Distance Driven Less than 1 mile 1 -- 3 miles More t han 3 miles Total Count Ex pec ted Count Count Ex pec ted Count Count Ex pec ted Count Count Ex pec ted Count X32 -- Gender Males Females 88 95 108.0 75.0 58 40 57.8 40.2 90 29 70.2 48.8 236 164 236.0 164.0 Total 183 183.0 98 98.0 119 119.0 400 400.0 Chi-Square Te sts Pearson Chi-Square Lik elihood Ratio Linear-by-Linear As soc iation N of Valid Cases Value 22.616 a 23.368 22.343 2 2 As ymp. Sig. (2-sided) .000 .000 1 .000 df 400 a. 0 c ells (.0% ) have expected count less than 5. The minimum expected count is 40. 18. The above cross-tabulations shows that when we examine the distance driven by males vs. females, in general females are driving less than expected and males more than expected. For example, comparing the observed count for females with the expected count, we note that 95 females actually drove “less than 1 mile”, but we would have expected only 75 females. Similarly, only 88 males drove “less than 1 mile” and we expected 108 to drive this amount. For the distance of 1 – 3 miles the results are about as expected, with observed and actual frequencies about equal (40 vs. 40.2 for females and 58 vs. 57.8 for males). For the distance “more than 3 miles” males are driving longer distances than expected. For example, the expected number of males driving more than three miles to patronize the restaurant was 70.2, but in reality 90 males drove more than 3 miles. For females, we expected 48.8 females to drive more than 3 miles but only 29 indicated they drove less than 3 miles. Overall conclusion is males are willing to drive further than females to eat at the restaurant, and the Chisquare statistic demonstrates this conclusion is statistically valid. 7 Cross-Tabulation of Satisfaction (X22) and Gender (X32) Note: this second example not only shows cross-tabulations, but tests them using the Chi-Square statistic. We later show an ANOVA comparing the means of males and females. Crosstabs Case Processing Summary Cases Missing N Percent Valid N X22 -- Satis faction * X32 -- Gender Percent 400 100.0% 0 Total N .0% Percent 400 100.0% X22 -- Satisfaction * X32 -- Gender Crosstabulation X22 -Satisfaction 3 4 5 6 Total X32 -- Gender Males Females 21 18 23.0 16.0 70 91 95.0 66.0 73 30 60.8 42.2 72 25 57.2 39.8 236 164 236.0 164.0 Count Expected Count Count Expected Count Count Expected Count Count Expected Count Count Expected Count Total 39 39.0 161 161.0 103 103.0 97 97.0 400 400.0 Chi-Square Te sts Pearson Chi-Square Lik elihood Ratio Linear-by-Linear As soc iation N of Valid Cases Value 31.764 a 32.220 21.738 3 3 As ymp. Sig. (2-sided) .000 .000 1 .000 df 400 a. 0 c ells (.0% ) have expected count less than 5. The minimum expected count is 15. 99. The above tables show that in general males are more satisfied than females. This is based on the fact that the observed count for males is higher than the expected count for the higher (more satisfied) responses (5 and 6). Similarly, the observed count for females is higher than the expected count for the lower (less satisfied) responses (3 8 and particularly 4). The Chi-Square statistic indicates these differences are statistically significant, as do the results below for the test of differences in means. Compare Means for Satisfaction of Males vs. Females The click-through sequence is ANALYZE COMPARE MEANS ONE-WAY ANOVA. Highlight the dependent variable X22 – Satisfaction by clicking on it and move it to the Dependent List box. Next, highlight X32 – Gender and move it to the Factor box. Then click on the Options button on the lower right side and then on Descriptive and Continue. Finally, click OK to run the program. Results are shown below. Oneway Descriptives X22 -- Satis faction N Males Females Total 236 164 400 Mean 4.83 4.38 4.64 Std. Deviation .966 .874 .955 Std. Error .063 .068 .048 95% Confidence Interval for Mean Lower Bound Upper Bound 4.71 4.95 4.24 4.51 4.55 4.74 Minimum 3 3 3 ANOVA X22 -- Satis fact ion Between Groups W ithin Groups Total Sum of Squares 19.809 343.781 363.590 df 1 398 399 Mean Square 19.809 .864 F 22.933 Sig. .000 The results indicate that on average males are more satisfied with the Santa Fe Grill than are females. The mean satisfaction level for males is 4.83 and the mean satisfaction for females is 4.38. Of course, recall that satisfaction is measured using a 7-point scale so in reality there is a lot or room for improvement. That is, satisfaction ratings are a mean of 4.64 for the total sample and they could be as high as 7.00 (unlikely to be that high, but certainly realistic that they would be in the 5 – 6 range). Maximum 6 6 6