Lau X B Assi X B Disc X 4 My X x Trac X x Trac X Pro X WH X DIS X G hov X Star X SHOV X + V X C @ File | file:///C:/Users/Owner/Downloads/WHEN%2015%20IT%20SAFE%20TO%20USE%20THE%20CHI%20SQUARE%20TEST%20(1).PDF Apps Traductor de Google B Elena's CCEL Classes @ Homepage - Langa... email langara Class MARK 4820 in... DEEPL Creator Studio PLE > Other bookmarks Reading list E WHEN IS IT SAFE TO USE THE CHI SQUARE TEST 1 /2 77% + WHEN IS IT SAFE TO USE THE CHI SQUARE TEST? - AN EXAMPLE Background A random sample of 107 Langara students was selected. Students were asked to report their primary method of transportation traveling to (and from) Langara to their residence. A 'term project team' of students was interested in exploring whether there was an association between gender and method of transportation. Using Statgraphics, they produced the following contingency table and chi-square test results. 1 Drive Car Pool Transit Walk Bicycle Row Total Alone Male 19 10 25 10 47 17.76% 0.009 23.36% 2.80% 0.00% 43.93% 40.439 0.00% 53.19% 6.38% 0.009 46.34% 0.00% 50.00% 37.50% 0.00% 18.01 2.64 21.96 3.51 10.88 10.05 2.64 0.42 10.08 10.88 Female 22 25 5 2 60 20.56% 5.61% 23.36% 4.67% 1.87% 56.07% 36.67% 10.00% 41.67% 8.33% 3.33% 53.66% 100.00% 50.00% 62.50% 100.00% 22.99 3.36 28.04 4.49 1.12 2 0.04 2.06 10.33 0.06 0.69 Column Total 41 50 8 2 107 38.32% 5.61% 46.73% 7.48% 1.87% 100.00% Cell contents: Observed frequency Percentage of table Percentage of row Percentage of column Expected frequency Contribution to chi-square Tests of Independence Test Statistic Df P-Value Chi-Square 7.247 4 0.1234 Warning: some expected cell counts Other bookmarks Reading list E WHEN IS IT SAFE TO USE THE CHI SQUARE TEST 2 /2 83% + WHEN IS IT SAFE TO USE THE CHI SQUARE TEST? - AN EXAMPLE Since 6 of the 10 cells (60%) in the contingency table had expected frequencies less than 5, the chi-square test was not valid. The 'term project team' decided to re-analyze these data. To do this, they selected the methods of transportation with the smallest frequencies, and combined them into one category called 'other'. Revised Contingency Table Drive Transit Other Row Total Alone Male 19 25 47 17.76% 23.36% 2.80% 43.93% 40.43% 53.19% 6.38% 46.34% 50.00% 18.75% 18.01 21.96 7.03 0.05 10.42 2.31 Female 22 25 13 60 20.56% 23.36% 12.15% 56.07% 36.67% 41.67% 21.67% $3.66% 50.00% 81.25% 22.99 28.04 18.97 0.04 10.33 1.81 Column Total 41 50 16 107 2 38.32% 46.73% 14.95% 100.00% Cell contents: Observed frequency Percentage of table Percentage of row Percentage of column Expected frequency Contribution to chi-square Tests of Independence Test Statistic Df P-Value Chi-Square 4.963 10.0836 Question 3: How many cells had an expected frequency less than 5? Question 4: Is the chi-square test valid in this situation? O w P ES A 4:11 PM ESP 2021-11-16 FA