# Understanding the Pearson Chi-Square Test

Pearson Chi-Square Test is used in the assessment of three types of comparison, which are homogeneity, the goodness of fit, and independence. Goodness of fit is used to establish whether an observed frequency is different from the theoretical one. On the other hand, homogeneity is used to compare the distribution of groups using similar categorical values.

## Overall, how satisfied are you with Virgin Atlantic?

 Frequency Percent Valid Percent Cumulative Percent Valid Completely Dissatisfied 3 0.9 0.9 0.9 Somewhat Dissatisfied 10 3.0 3.0 3.8 Somewhat Satisfied 66 19.5 19.5 23.4 Completely Satisfied 259 76.6 76.6 100.0 Total 338 100.0 100.0
The result above shows that 0.9% of respondents are completely dissatisfied while 3% are somewhat dissatisfied. 19.5% of respondents are somewhat satisfied and 76.6% are completely satisfied. We can conclude that the respondents are generally satisfied because 96.1% of the respondents are either completely or somewhat satisfied.

## Descriptive Statistics

 N Mean Rating: Delivers your luggage in good condition 338 8.5503 Rating: Gives you confidence your luggage will get there 338 8.4527 Rating: Gets your luggage there when it should 338 8.3817 Rating: Provides the service it promises 338 8.2633 Rating: Is a first-rate company 338 8.2219 Rating: Knows where your luggage is at all times 338 8.2160 Rating: Treats you as an important customer 338 7.6302 Rating: Gives customized service 338 7.3284 Rating: Helps you solve your business travel problems 338 7.2959 Rating: Works as part of your team 338 7.2160 Rating: Understands your business travel needs 338 7.1953 Rating: Is competitively priced 338 6.8846 Rating: Communicates with you regularly 338 6.2663 Valid N (listwise) 338
The result above shows that the airline gets the highest average ratings on delivering luggage in good conditions (8.55) followed by respondents having confidence that their luggage will get there (8.45) and then respondents getting their luggage when it should (8.38). However, regular communication is the least rated by respondents with a mean of 6.27 followed by competitive pricing with a mean of 6.88, and then the understanding of respondents need with a mean of 7.20. the result shows that in terms of taking care of the client's luggage, the airline is doing well. However, in the issue of communication, pricing, and understanding the client’s needs, the airline needs much improvement. I recommend that all measures that can improve communication and pricing should be implemented by the company.

## Respondents

The crosstab and chi-square result is presented below. The result shows that none of the respondents who are Owner/partner/proprietors none of them are completely dissatisfied or somewhat dissatisfied while 20.8% are somewhat satisfied and 79.2% are completely satisfied. From respondents who are Sr. management/CEO/President/Vice President/CFO, none are completely dissatisfied, 5.7% are somewhat dissatisfied, 28.6% are somewhat satisfied and 65.7% are completely satisfied. From respondents who are Manager/Supervisor – travel arrangements, 2.1% are completely dissatisfied, 3.5% are somewhat dissatisfied, 18.2% are somewhat satisfied and 76.2% are completely satisfied. From respondents who are Non-managerial personnel – travel arrangements, none are completely dissatisfied, 5% are somewhat dissatisfied, 25% are somewhat satisfied and 70% are completely satisfied. From respondents who are Analysts/planners/technicians/designers/other professionals, none are completely dissatisfied, none are somewhat dissatisfied, 17.5% are somewhat satisfied and 82.5% are completely satisfied. Finally, from respondents who are Security/receptionist/admin, none are completely dissatisfied, 1.8% are somewhat dissatisfied, 14% are somewhat satisfied and 84.2% are completely satisfied. The chi-square result shows that chi2(15)=11.530, p=0.714>0.05 which connotes non-rejection of the null hypothesis that there is an association between satisfaction and respondent’s occupation title. Therefore, we conclude that there is no significant relationship between satisfaction and occupation title.

## Chi-Square Tests

 Value df Asymp. Sig. (2-sided) Pearson Chi-Square 11.530a 15 .714 Likelihood Ratio 14.026 15 .524 Linear-by-Linear Association 2.764 1 .096 N of Valid Cases 319
a. 14 cells (58.3%) have an expected count of less than 5. The minimum expected count is .19.

## Descriptive statistics

Descriptive Statistics
 Overall, how satisfied are you with Virgin Atlantic? N Mean Completely Dissatisfied How would you rate the price 3 2.3333 How would you rate the quality 3 2.3333 Valid N (listwise) 3 Somewhat Dissatisfied How would you rate the price 10 5.1000 How would you rate the quality 10 5.4000 Valid N (listwise) 10 Somewhat Satisfied How would you rate the price 66 5.6515 How would you rate the quality 66 6.9848 Valid N (listwise) 66 Completely Satisfied How would you rate the price 259 7.2317 How would you rate the quality 259 8.3900 Valid N (listwise) 259
The result shows that price and quality rating progress as the level of satisfaction progresses. We observe that average ratings of the price for completely dissatisfied customers are 2.33 while the ratings for somewhat dissatisfied clients improve significantly to 5.1 and ratings for somewhat satisfied client increases to 5.65 and for completely satisfied clients, average price ratings are as high as 7.2. similarly, the average ratings of quality for completely dissatisfied customers are 2.33 while the quality ratings for somewhat dissatisfied clients improve significantly to 5.4 and ratings for somewhat satisfied client increases to 6.98, and for completely satisfied clients, average quality ratings are as high as 8.39. We can see from the result that there is a significant improvement in ratings as the level of satisfaction progresses. Thus, I recommend that the management should explore all means that will improve consumer satisfaction.
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