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Class Evaluation

Problem

Of 33 students who took a statistics course, 24 took the course in person (live) and 9 took the course by watching a TV feed. At course end, when these students were asked whether they would recommend the course to a friend, 20 (83%) of the "live" students said they would recommend it, and 6 (67%) of the "TV" students said they would recommend it. Is the difference (16%) between the opinions of the two groups of students significant enough to warrant changing teaching arrangements to offer the statistics course only live in the future (see Simon, 1992)?

Null hypothesis (H₀): "Live" and "TV" students are equally likely to recommend the course. Alternative hypothesis (H₁): "Live" students are more likely to recommend the course.

Resampling Procedure

According to the real-world data, a higher proportion of the live group (N = 24) said they would recommend the course than of the TV group (N = 9); the difference in proportions was .16. To determine whether a difference this big or bigger could occur if both groups of students came from the same population, we will create a single, hypothetical universe and draw samples of sizes 24 and 9 from it. As our universe, we will use both groups combined: 26 recommend and 7 do not.

1. Take 33 pieces of paper. Write "yes" (to represent recommend) on 26 pieces and "no" (would not recommend) on 7 pieces.
2. Shuffle the papers, then draw out 24 pieces to represent the live group and 9 pieces to represent the TV group. Count the proportion of "yes" answers in the two groups. Subtract the two proportions to obtain a simulated difference.
3. Repeat (2) 1,000 times, recording the differences on a scoreboard.
4. Count how often the simulated groups differed by more than .16 in their opinions.

Computer Implementation in Resampling Stats

URN 26#1 7#0 students

"students" is a vector with "1" signifying approval ("yes") and "0" signifying "no".

REPEAT 1000
  SAMPLE 24 students live$
  SAMPLE 9 students tv$

simulate the two groups of students, 24 taking the course live lectures and 9 via TV.

  COUNT live$ = 1 liveyes$

how many of the live students would recommend the class?

  DIVIDE liveyes$ 24  prlive$

calculate the yes recommendations of live students as a proportion of the 24 in that group

  COUNT tv$ =1 tvyes$

how many of those watching TV would recommend the class?

  DIVIDE tvyes$ 9 prtv$

calculate the yes recommendations of TV students as a proportion of the 9 in this group

  SUBTRACT prlive$ prtv$ diff$

what's the difference between the proportion of recommendations from live versus TV students?

  SCORE diff$ scrboard

record this result

END
COUNT scrboard >=.16 more

how often did the proportions of yes recommendations exceed .16 -- the real-world value?

HISTOGRAM scrboard
DIVIDE more 1000 prob

divide by the number of repetitions to convert the proportions to a probability.

PRINT prob

Results

Frequency histogram of difference in proportions

prob = 0.184

Conclusion

According to the real-world data, 16% more of students taking a statistics course live said they would recommend the course (compared to those taking it via TV). The probability of getting a difference this big in resamples drawn from a single universe is estimated at .184, so we cannot rule out the possibility that students in live and TV sections are equally likely to recommend the course.

References

Simon, J.L. (1992, Fall). [Student evaluations for introductory business statistics]. Unpublished data, University of Maryland, School of Business.