Question 503:

Asked on November 7, 2008

Tags: ANOVA , F-statistic

1

Answer:

No answer provided yet.

No one likes to wait for the doctor, but we also don't like to feel rushed when it's finally our turn.  At one doctor's office, four physician share the patients on a 1st come first serve basis. 

1. The purpose of the study is to see if there is a difference in time the doctors spend with each patient.  The dependent variable will be the amount of time each patient spends with the physician.
2. The population is all patients that attend the clinic and see these four physicians (approximately 400 patients in total).
3. Over a period of three months, 10 week days were randomly selected so as to gather a reasonable cross-section of days and weeks of the month that might cause changes in the type of patients that attend or the other unknown fluctuations in the physicians schedules. An equal number of Monday, Tuesdays and so forth were selected. Patient times were recorded from a randomly selected hour of the day until there were at least 28 total times.
4. We will suspect that there is a difference in patient times if the there is less than a 5% probability the difference was due to chance. This makes out alpha (a) .05.
5. The null hypothesis is that there is no difference between patient times spent with any of the four physicians. We will reject the Null Hypothesis if the p-value is less than our alpha of .05
6. The data appear in the table below:

Patient Times with each physician in minutes.

Physician 1	Physician 2	Physician 3	Physician 4
34 25 27 31 26 34 21	33 35 31 31 42 33	17 30 30 26 32 28 26 29	28 33 31 27 32 33 40

A 1-Way Analysis of Variance was conducted on the patient times which produced an F-statistic of F(3,24) = 3.4971. There are 3 degrees of freedom in the numerator and 24 in the denominator. An F-statistic with these degrees of freedom (based on the sample) and number of groups generates a p-value of .0309.

Since the p-value .0309 is less than our decision criteria of .05 we reject the null hypothesis and conclude that there is greater than chance evidence that some physicians spend more time with their patients.

In summary, the results of a 1-ANOVA the suggest the mean time spent with each physician is statistically different (p <.05). Further analysis would be necessary to determine which doctors are faster and which are slower. It would also be important to understand if there were other variables which might affect the times, such as some physicians have specialties which take less or more time. While an attempt was made to collect a random selection of days and times across a 3-month period, there might also likely be other nuisance variables affecting the fluctuations in times. This might be a topic for a future analysis.