PERSONALITY PROFILER STATISTICAL METHODS AND COMPUTING May 1 2006 Dan Ernst Shauna Blackwell Katie Lehmann 0 The Golden Personality Profiler is a magnificent way to understand one s personality The more a person knows about their personality the more they can understand why they act the way they do in certain situations such as in relationships or in a group setting It is also an extraordinary way of understanding one s peers and the way they act in those similar situations Over the course of 70 years psychologists have identified a number of traits to be tested on that are common among many people From these traits personality types were formed According to psychologists there are four component scales extraverting E vs introverting I sensing S vs intuiting N thinking T vs feeling F and organizing Z vs adapting A These four scales characterize 16 personality types eStZ eNFz iNTa iStA etc From these personality types there are four temperaments NT NF SZ and SA The personality chart below in Figure 1 indicates what percentage of the population is each of the 16 and Figure 2 shows the percentage of the four temperaments eNTa eNTz eNFa 5 5 5 iNTa iNTz 1 eSfZ 1 1 eStZ 13 iSfZ iNFa eSfA 13 13 iStZ 6 iSfA 6 6 Figure 1 16 Personality Types NT NF 12 12 SZ SA 38 38 Figure 2 Four Temperaments 1 eNFz 5 iNFz 1 eStA 13 iStA 6 Over the past several years the engineering and business departments have selected approximately 286 students the majority being engineering and business majors to take the Golden personality profiler After taking the test each student was categorized as one of the four temperaments described above The objective of the statistical analysis of the sample data is to determine its credibility In order to do this a test will be performed that will verify whether this sample data is an accurate representation of the population The first step in analyzing our data was to create a SAS file uploaded from the Excel file containing the sample data The objective was to find the frequency of each temperament NF NT SA and SZ The SAS code and output are shown below options linesize 75 proc freq data project tables temp run The SAS System 21 06 Sunday April 16 2006 The FREQ Procedure Temp Cumulative Cumulative Frequency Percent Frequency Percent NF 85 29 72 85 29 72 NT 87 30 42 172 60 14 SA 7 2 45 179 62 59 SZ 107 37 41 286 100 00 Temp From this data we have found that proportions of students are as follows NF 30 NT 30 5 SA 2 5 and SZ 37 In comparing these results with the population percentages we observed that the results differed greatly In order to confirm these observations we decided to perform a Chi Square test A Chi Square test is a statistical test that tells us whether the observed differences between the population and the sample data are statistically significant 1 This test compares the observed and expected counts of the sample data in order to obtain a Chi Square statistic The Chi Square statistic is a measure of how far away the observed counts are from the expected counts 1 The expected counts shown in Table 1 were calculated by applying the known population percentages for each temperament to a sample size of 286 Table 1 Observed vs Expected Counts Temperament Observed Expected NF 85 34 32 NT 87 34 32 SA 7 108 68 SZ 107 108 68 Total Number of Observations 286 286 In order to perform a Chi Square test a null and alternative hypothesis must be stated For this test the hypotheses are as follows 2 H o p NF p NF p NT p NT p SA p SA p SZ p SZ H a p NF p NF p NT p NT p SA p SA p SZ p SZ The null hypothesis for this test states that the sample proportions of temperaments NF NT SA and SZ are equal to the population proportions of the same temperaments The alternative hypothesis states that the two proportions are not equal After inputting the following SAS code into the SAS program editor a Chi Square statistic was generated and the test was performed SAS Code options linesize 75 data leave input categ count datalines NF 85 NT 87 SA 7 SZ 107 proc freq tables categ testp 12 12 38 38 weight count run The SAS System 14 45 Saturday April 29 2006 The FREQ Procedure Test Cumulative Cumulative Frequency Percent Percent Frequency Percent NF 85 29 72 12 00 85 29 72 NT 87 30 42 12 00 172 60 14 SA 7 2 45 38 00 179 62 59 SZ 107 37 41 38 00 286 100 00 categ Chi Square Test for Specified Proportions Chi Square 250 8574 DF 3 Pr ChiSq 0001 Sample Size 286 A Chi Square statistic X2 is evaluated using Equation 1 A large value for X2 is evidence against the null hypothesis because it implies that the observed counts are far from the expected counts 1 3 X 2 observedcount exp ectedcount 2 exp ectedcount Equation 1 Chi Square Statistic1 As shown above in the SAS output the Chi Square statistic is quite large at a value of 250 86 This value implies that the difference between the observed and expected counts for the four temperaments is not statistically significant It also provides overwhelming evidence that the sample proportions from the group of engineering and business students did not match the population proportion for the four personality temperaments The Chi Square test generated a P value less than 0 001 Because SAS output cannot produce numbers less than this it is assumed that the probability is so close to zero that the deviation is neglected Many factors may have contributed to the results of the test The sample data did not exactly resemble a random sample of students it was specifically targeted to engineering and business students This implies that students in similar majors will have similar personalities After analyzing the data produced from the Chi Square test it is concluded that the null hypothesis must be rejected on account of a high Chi Square statistic and a low P value It is assumed that a more random sample would be a more accurate representation of the population An enhanced understanding of the purpose and significance of a Chi Square test as well as a realization of the importance of statistics was achieved by the team during this research experiment 4 REFERENCES 1 Moore David S The Basic Practice of Statistics 3rd ed W H Freeman and Company New York 2004 5