1. Rotate the Organization List.
(a) Why is it important for the interviewer to rotate the list of organizations?
Section 24.2 Investigation 5.1A: Newspaper Credibility Decline
Exercises The Study
With the proliferation of the Internet and 24-hour cable news outlets, it has become much easier for people to hear much more information, much more quickly. This has raised concerns that some news organizations may try to report information before it has been properly verified. A media believability survey has been conducted since 1985 (under the direction of the Pew Research Center for the People and the Press since 1996) to examine whether different news organizations have been losing credibility over time.
The survey is based on telephone interviews among a national sample of adults 18 years or older living in the continental United States. One question asked respondents to rate believability on a 4-to-1 scale, where 4 means they believe all or most of what the organization says and 1 means they believe almost nothing.
2. Include Cell Phone Interviews.
(b) Since 2010, cell phone interviewing has been included. Why is that an important consideration?
When asked about "The daily newspaper you are most familiar with," the percentage distribution of 1,004 responses in June 2006 was:
| Believe all or almost all (4) | 3 | 2 | Believe almost nothing (1) | Cannot rate |
|---|---|---|---|---|
| 18% | 37% | 26% | 12% | 7.1% |
3. Convert Percentages to Counts.
(c) Convert these percentages into observed counts among those who felt they could rate their daily newspaper. In other words, eliminate the "cannot rate" responses.
4. Compare Response Variable Types.
(d) How does the response variable in this study differ from the response variable in Investigation 5.1?
A similar study was also done in 1998 (922 respondents able to rate) and in 2012 (922 able to rate). A corresponding two-way table of counts across the three years is shown below.
5. Complete 2006 Column.
Enter your 2006 values from part (c) in the table:
| 1998 | 2006 | 2012 | |
|---|---|---|---|
| Believe almost all (4) | 265 | 181 | 183 |
| 3 | 353 | 371 | 342 |
| 2 | 235 | 261 | 268 |
| Believe almost nothing (1) | 69 | 120 | 129 |
| Total | 922 | 933 | 922 |
6. Track Category 4 Over Time.
(e) How has the percentage who believe "all or almost all" (among those who can rate) changed over time?
7. Overall Proportion for Rating 4.
(f) What percentage of individuals across these three studies rated the believability of their daily paper as a 4?
8. Expected Count for 2006 Rating 4.
(g) If the proportion who believe all or almost all of what they read was the same in all three populations, how many in the 2006 sample would you expect to give rating 4?
9. Expected Count for 2012 Rating 1.
(h) What is the expected number of rating-1 responses in 2012?
Definition: Expected Count.
In general, the expected count for each cell is:
\(\text{Expected count} = \frac{(\text{row total})(\text{column total})}{\text{table total}}\)
This preserves the null-model condition that the response distribution is the same in each category of the explanatory variable.
10. State Hypotheses.
(i) State null and alternative hypotheses for assessing whether the distribution of responses differs among the three years. State with symbols and in words.
We use the same chi-squared statistic, now with more than two categories for the response variable:
\(\chi^2 = \sum \frac{(O-E)^2}{E}\text{,}\) where \(r\) is the number of rows and \(c\) is the number of columns.
Degrees of freedom are \((r-1)(c-1)\text{.}\)
This model is considered appropriate if at least 80% of expected counts are at least 5 and all expected counts are at least 1.
11. Check Technical Conditions.
(j) Are the technical conditions met for using the chi-squared distribution with this table?
Technology Detour: Chi-squared Tests.
In R: Use
chisq.test() with either a matrix of counts or a two-way table from raw data. You can inspect expected counts with chisq.test(data)$expected and residuals with chisq.test(data)$residuals.
In Minitab: Use Stat > Tables > Chi-Square Test for Association with either summarized counts or raw data columns.
In JMP: Use Analyze > Fit Y by X, with response as Y and year as X. For tallied data, supply a frequency column.
In the applet: Use Analyzing Two-way Tables and paste either raw data or a two-way table.
12. Compute Test Statistic and p-value.
(k) Use technology to calculate the chi-squared statistic, verify the degrees of freedom, and find the p-value. Do you reject or fail to reject the null hypothesis?
Comparison to Two-sample z-test.
If we collapse categories to "largely believable" (3 or 4) versus "not largely believable" (1 or 2), we obtain:
| 2012 sample | 1998 sample | Total | |
|---|---|---|---|
| Largely believable | 525 | 618 | 1209 |
| Not largely believable | 397 | 304 | 701 |
| Total | 922 | 922 | 1844 |
13. Chi-squared Test on 2x2 Table.
(l) Use technology to carry out a chi-squared test for whether the population proportion giving a largely believable rating differs between 1998 and 2012. Report the statistic, degrees of freedom, and p-value.
14. Two-proportion z-test Comparison.
(m) Carry out a two-sided two-proportion \(z\)-test for the same 2x2 table. Report the standardized statistic and p-value. How do the p-values compare? What relationship do you observe between the standardized statistics?
Discussion: The chi-squared procedure can compare two or more proportions. For two proportions, chi-squared and the two-sided two-proportion \(z\)-test are equivalent: the chi-squared statistic equals \(z^2\text{,}\) and the p-values agree for a two-sided test. For one-sided alternatives, use the two-proportion \(z\)-test. With more than two proportions, use chi-squared.
For a 2x2 table, Fisher’s Exact Test is another option and is always valid when conditioning on margins.
Also remember that chi-squared tests detect evidence of association in general; they do not directly test a specific directional trend unless that is built into a different model.
15. Practice Problem 5.1A.
In 1992, NBC News admitted that it staged part of the General Motors truck explosion footage aired on Dateline NBC. Compare believability ratings from two polls:
August 1989 (1507 respondents): 4 = 32%, 3 = 47%, 2 = 14%, 1 = 2%, cannot rate = 5%.
February 1993 (2001 respondents): 4 = 31%, 3 = 42%, 2 = 18%, 1 = 6%, cannot rate = 3%.
(a) Is the difference in the distribution of believability ratings statistically significant between these two years?
(b) Is this convincing evidence that the GM explosion segment caused a decrease in NBC News believability?
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