RES 710 Week 2 Descriptive Statistics Example

Describing Waits and Satisfaction: Descriptive Statistics for a Credit Union Member Survey

[Student Name]

University of Phoenix

RES/710: Statistical Research Methods and Design I

Week 2 Assignment

[Instructor Name]

[Date]

The learner, the credit union, its members and all data are composites written for a model paper.

Week 1 defined the variables for a composite operations director's study at a Grand Rapids, Michigan, credit union with 24 branches: wait time, service channel, satisfaction, net promoter likelihood and controls such as tenure, age and branch size. Over six weeks, 4,100 members were invited to a short survey within 48 hours of a transaction, and 1,240 responded, a response rate of about 30 percent. Each response was linked to the queue system's wait time for that transaction. This paper describes the data.

Why Describe Before Testing

Field (2018) advises researchers to explore data before any inferential analysis: to examine distributions, spot errors and outliers and check whether data meet the assumptions of planned tests. Descriptive statistics also communicate the basic facts of a study to readers, such as how long members typically wait, which a test statistic alone cannot do.

Service Channel and Member Characteristics

Channel is nominal, so it is described with counts and percentages: 645 branch transactions, 52 percent; 347 phone, 28 percent; and 248 app, 20 percent. Respondents' median age was 46, with app users younger, a median of 34. Median tenure was 11 years. Compared with all members invited, respondents were slightly older and longer-tenured, a pattern to keep in mind when generalizing.

Wait Time

Wait time is ratio-level and applies to branch and phone transactions only, since app transactions have no wait; 992 responses have a wait time. The mean wait was 7.9 minutes, but the median was 5.2 minutes, and the distribution is strongly right-skewed, with a skewness of 2.4. Most members waited under 10 minutes, but a tail of waits stretched beyond 40 minutes, almost all at lunchtime on Fridays at four high-volume branches. The interquartile range was 2.6 to 9.8 minutes.

Micceri (1989) examined 440 real data sets in psychology and education and found that very few were normally distributed; most showed skew, heavy tails or other departures, so assumptions of normality should be checked rather than assumed. The credit union's wait times are a clear case.

Screening the File

Before computing summaries, the learner checked every variable's minimum and maximum against its possible range. Two ages of 112 and one tenure of 64 years were traced to typing errors in member records and corrected from the source system. Duplicate responses from the same member within one week were reduced to the first one.

Spread Beyond the Standard Deviation

For wait time, the standard deviation of 7.1 minutes is almost as large as the mean, which signals heavy skew rather than wide spread in the usual sense. Reporting it alone would suggest that negative waits are plausible, which is impossible. The interquartile range of 7.2 minutes, the 90th percentile of 16.5 minutes and the maximum of 58 minutes together give readers a clearer sense of what a typical member experiences and how bad the worst waits become. For management, the 90th percentile may matter most, since it shows how long one member in ten waits.

Actual Versus Perceived Wait

Week 1 also added a survey question on each member's sense of how long the wait lasted. Perceived waits had a median of 7 minutes, almost two minutes longer than the recorded median, and members who waited more than 10 minutes overestimated by a wider margin. The correlation between recorded and perceived wait, computed with Spearman's rho because both are skewed, was .58, a moderate association. This gap suggests that perception adds information beyond the clock, which later regression models can test.

Missing Data

Of the 1,240 responses, 31 left one or more satisfaction items blank and 18 skipped the net promoter item. Scale scores were computed when at least three of four items were answered, which kept all but nine cases. No wait times were missing for branch or phone transactions, since they came from system records. Missing responses were slightly more common among members over 70, a pattern to report but too small to change the descriptive results.

Outliers

Twelve waits exceeded 40 minutes. Checking queue logs showed they were real, not errors: members who took a ticket and then waited through a system outage on two Fridays. They are not deleted, since they reflect actual member experience, but analyses will be run with and without them to see whether they change conclusions.

Satisfaction

Satisfaction is the mean of four items rated 1 to 7. Across all 1,240 respondents, the mean was 5.4 (SD 1.2) and the median 5.5. The distribution is mildly left-skewed, with most members satisfied and a smaller group very dissatisfied. Internal consistency was high, with Cronbach's alpha of .89, supporting the use of the average as a single score.

By channel, mean satisfaction was 5.3 for branch, 5.2 for phone and 6.0 for app users. These are descriptive differences that Week 5's t tests and later analyses will test.

Net Promoter Likelihood

The 0-to-10 item had a median of 8, with 41 percent scoring 9 or 10, 37 percent scoring 7 or 8 and 22 percent scoring 6 or lower. Because the item is ordinal, the median and the category percentages describe it better than the mean.

Members who used the app scored about three-quarters of a point higher on satisfaction, but they also never stood in a line.

Branch Differences

Branch medians for wait time ranged from 2.1 to 11.4 minutes. A box plot by branch shows that the four branches with the longest waits also have the widest spread and the lowest median satisfaction. This pattern suggests that branch-level factors, such as staffing, may matter and that later analyses should account for members being clustered in branches.

Displaying the Data

Weissgerber et al. (2015) reviewed published figures and found that bar graphs of means were widely used for continuous data even though they hide the distribution, sample size and outliers, and they recommended showing individual data points, box plots or histograms instead. The learner's report will use a histogram for wait time, box plots of wait time and satisfaction by branch and a dot plot of satisfaction by channel, rather than bar charts of means.

Implications for Later Analyses

Wait time's skew suggests a log transformation or rank-based tests when it is a variable in comparisons; regression with wait time as a predictor is less affected, but residuals must be checked. Satisfaction is close enough to normal, given the sample size, for t tests and regression. Clustering by branch should be addressed in later models. App users differ from others in age as well as channel, so comparisons should control for age.

Conclusion

The descriptive picture is clear: most members wait about five minutes, a few wait much longer at busy times, satisfaction is generally high but lower for branch and phone users and branches differ substantially. Choosing medians for skewed waits, frequencies for categories and distribution-revealing graphs gives an honest summary and sets up the inferential tests of Weeks 4 through 6.

References

Field, A. (2018). Discovering statistics using IBM SPSS statistics (5th ed.). Sage.

Micceri, T. (1989). The unicorn, the normal curve, and other improbable creatures. Psychological Bulletin, 105(1), 156-166. https://doi.org/10.1037/0033-2909.105.1.156

Weissgerber, T. L., Milic, N. M., Winham, S. J., & Garovic, V. D. (2015). Beyond bar and line graphs: Time for a new data presentation paradigm. PLoS Biology, 13(4), e1002128. https://doi.org/10.1371/journal.pbio.1002128