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Applause

Problem

[To study] the effects of media-transmitted behavior on individual preferences, an experiment was designed in which an audience would show approval (by applause) of a speaker's presentation in a large-group discussion [Stocker-Kreichgauer & von Rosentiel, 1982]. The topic of discussion was whether members of radical political parties should or should not be refused public employment. There were two speakers, one on each side of the issue. There were two conditions -- in one, the audience showed strong approval of one argument (pro) and in the other, the audience showed strong approval of the other argument (con). Subjects who viewed the debate and the audience reactions were asked to indicate their own preference for one of the two speakers. The researchers hypothesized that the audience's approval would affect the subject's preference; specifically, the applauded speaker would be more favored and the nonapplauded speaker would become less favored. Subjects rated their own position on the issue before and after debate.

The data consisted of the change in these ratings. The magnitude of the change was ignored, and only the direction of the change was coded. . . . The researchers wished to determine the strength of the relation between the audience behavior and the change in preference by observers. (Siegel & Castellan, 1988, Example 9.2, pp. 233-234)

People who had not changed their opinion were apparently not included in the analysis. The data for the experiment are summarized as follows.

Applause Table. Number of People Changing Preference for Speakers After Audience Reaction

# of people changing preference
	Con	Pro	Total
Before	21	37	58
After	26	14	40
Total	47	51	98

Note. Adapted from Siegel & Castellan, 1988, Table 9.2, p. 234

Null hypothesis (H₀): People do not change their opinions toward the side that is apparently supported by members of the audience. Alternative hypothesis (H₁): People tend to change their opinion toward the side that is apparently supported by the audience.

Resampling Procedure

Compute the number of preference changes toward the audience opinion (26+37=63) and the number of preference changes against the audience opinion (21+14=35). The difference (63-35 = 28) is the observed value of our test statistic. This test statistic will yield higher values if the alternative hypothesis is correct, that is, if people tend to change their preference toward the speaker applauded by the audience.

1. Prepare 98 paper cards. Mark 58 of them as "audience is con" and 40 as "audience is pro".
2. Split at random the 98 cards into two groups of 47 and 51 cards, respectively. The first group corresponds to the people who changed preference toward the pro side; the second group represents people who changed preference toward the con side.
3. Compute the value of our test statistic in the same way as it was done for the observed data: Compute the number of preference changes toward the audience opinion and the number of preference changes against the audience opinion. The difference is the resampled value of our test statistic.
4. Repeat (2) and (3) 1,000 times. Determine the proportion of the trials in which the value of our test statistic was at least as great as the observed value (28).

Computer Implementation in Resampling Stats

URN 58#7 40#8 applaud

There are 98 cards; "7" indicates the audience that supported con, and "8" indicates the audience that supported pro.

REPEAT 1000
  SHUFFLE applaud applaud$

Randomize the data, then split them into two groups.

TAKE applaud$ 1,47  topro$

A simulated group of people who shifted opinion to the pro side,

TAKE applaud$ 48,98 tocon$       

and the rest are the simulated who went to the con side

COUNT topro$ =8 pro2pro$ 

An "8" says the audience supported the "pro" side, so this is the number of people who shifted to pro after watching the audience supporting pro.

COUNT tocon$ =7 con2con$ 

A "7" says the audience supported the "con" side, so these are people who shifted to con after watching an audience supporting con.

ADD pro2pro$ con2con$ agreed$

The total in vector "agreed$" where the people shifted in accordance with the apparent audience opinion.

COUNT topro$ =7 con2pro$

Independent-minded people who shifted to pro despite exposure to a con audience

COUNT tocon$ =8 pro2con$

and their counterparts in the opposite side

ADD con2pro$ pro2con$ anti$

Vector "anti$" holds the number of people who shifted opposite to the audience approval.

SUBTRACT agreed$ anti$ stat$           

Compute the value of our test statistic.

SCORE stat$ scrboard

Retain this simulated statistic.

END

HISTOGRAM scrboard
COUNT scrboard >= 28 more

How frequently did the simulation's statistic equal or better the observed statistic?

DIVIDE more 1000 prob  

Convert this to a proportion of the total number of runs.

PRINT prob

Results

Frequence histogram of changes in preference toward audience minus changes in preference against audience

Outcome of 5 runs of the program:

prob =  0.006

prob     =  0.004

prob     =  0.005

prob     =  0.002

prob     =  0.008

Conclusion

The test data's statistic was 28. We simulated a situation corresponding to the null hypothesis --that the change in preference has no relation to the attitude of the audience. Only about 0.5% of the simulation runs yielded a statistic at least as high as 28. Therefore, the null hypothesis is rejected, and we conclude that people tended to change their preference toward whichever side was (apparently) supported by the audience.

References

Siegel, S., & Castellan, N. J., Jr.. (1988). Nonparametric statistics for the behavioral sciences (2nd ed.). New York: McGraw-Hill.

Stocker-Kreichgauer, G., & von Rosenstiel, L. (1982). Attitude change as a function of the observation of vicarious reinforcement and friendliness/hostility in a debate. In B. Brandstatter, J.H. Davis, & G. Stocker-Kreichgauer (Eds.), Group decision making (pp. 241-255). New York: Academic Press.