# Question

A non-experimental study was done to assess the impact of the accident at the Three Mile Island (TMI) nuclear power plant on nearby residents (Baum, Gatchel, and Schaeffer, 1983). Data were collected from residents of the following four areas:

Group 1: Three Mile Island, where a nuclear accident occurred (n = 38)

Group 2: Frederick, with no nuclear power plant nearby (n = 27

Group 3: Dickerson, with an undamaged coal power plant nearby (n = 24)

Group 4: Oyster Creek, with an undamaged nuclear power plant nearby (n = 32)

Several different measures of stress were taken for people in these four groups. The researchers hypothesized that residents who lived near TMI (group 1) would score higher on a wide variety of stress measures than people who lived in the other three areas included as comparisons. One way ANOVA was performed to assess differences among these four groups on each outcome. Selected results are reported below for you to discuss and interpret. Here are results for two of their outcome measures (each cell lists the mean, followed by the standard deviation in parentheses)..

Outcome Variable

TMI nuclear plant with accident

No nuclear

plant

Undamaged coal plant

Undamaged nuclear plant

F(3, 117)

Total reported stress symptoms

25.97

(21.0)

14.54

(11.5)

16.63

(11.8)

16.16

(13.5)

3.827

Beck Depression Inventory

6.00

(6.5)

3.64

(3.3)

3.54

(3.6)

3.50

(4.2)

2.104

a. Write a Results section in which you report whether or not these overall differences were statistically significant for each of these two outcome variables (using α = .05). You will need to look up the critical value for F, and in this instance, you will not be able to include an exact p value. Include an 2 effect size index for each of the F ratios (you can calculate this by hand from the information given in the table). Be sure to state the nature of the differences: did the TMI group score higher or lower on these stress measures relative to the other groups?

b. Would your conclusions change if you used α = .01 instead of α = .05 as your criterion for statistical significance?

c. Name a follow-up test that could be done to assess whether all possible pair wise comparisons of group means were significant.

d. Write out the contrast coefficients to test whether the mean for group 1 (people who lived near TMI) differed from the average for the other three comparison groups.

e. Here is some additional information about scores on the Beck Depression Inventory. For purpose of clinical diagnosis, Beck (1996) suggested the following cut-offs.

0-13…………………………. minimal depression

14-19…………………………. mild depression

20-28…………………………. moderate depression

29-63…………………………. severe depression

In light of this additional information, what would you add to your discussion of the outcomes for depression in the TMI versus other regions? (Did the TMI accident make people severely depressed?)

Group 1: Three Mile Island, where a nuclear accident occurred (n = 38)

Group 2: Frederick, with no nuclear power plant nearby (n = 27

Group 3: Dickerson, with an undamaged coal power plant nearby (n = 24)

Group 4: Oyster Creek, with an undamaged nuclear power plant nearby (n = 32)

Several different measures of stress were taken for people in these four groups. The researchers hypothesized that residents who lived near TMI (group 1) would score higher on a wide variety of stress measures than people who lived in the other three areas included as comparisons. One way ANOVA was performed to assess differences among these four groups on each outcome. Selected results are reported below for you to discuss and interpret. Here are results for two of their outcome measures (each cell lists the mean, followed by the standard deviation in parentheses)..

Outcome Variable

TMI nuclear plant with accident

No nuclear

plant

Undamaged coal plant

Undamaged nuclear plant

F(3, 117)

Total reported stress symptoms

25.97

(21.0)

14.54

(11.5)

16.63

(11.8)

16.16

(13.5)

3.827

Beck Depression Inventory

6.00

(6.5)

3.64

(3.3)

3.54

(3.6)

3.50

(4.2)

2.104

a. Write a Results section in which you report whether or not these overall differences were statistically significant for each of these two outcome variables (using α = .05). You will need to look up the critical value for F, and in this instance, you will not be able to include an exact p value. Include an 2 effect size index for each of the F ratios (you can calculate this by hand from the information given in the table). Be sure to state the nature of the differences: did the TMI group score higher or lower on these stress measures relative to the other groups?

b. Would your conclusions change if you used α = .01 instead of α = .05 as your criterion for statistical significance?

c. Name a follow-up test that could be done to assess whether all possible pair wise comparisons of group means were significant.

d. Write out the contrast coefficients to test whether the mean for group 1 (people who lived near TMI) differed from the average for the other three comparison groups.

e. Here is some additional information about scores on the Beck Depression Inventory. For purpose of clinical diagnosis, Beck (1996) suggested the following cut-offs.

0-13…………………………. minimal depression

14-19…………………………. mild depression

20-28…………………………. moderate depression

29-63…………………………. severe depression

In light of this additional information, what would you add to your discussion of the outcomes for depression in the TMI versus other regions? (Did the TMI accident make people severely depressed?)

## Answer to relevant Questions

If there is an overall significant F in a one way ANOVA, can we conclude that the group membership or treatment variable caused the observed differences in the group means? Why or why not? Assuming that a researcher hopes to demonstrate that a treatment or group membership variable makes a significant difference in outcomes: which term does the researcher hope will be larger: MSbetween or MSwithin? Why? A review from Chapter 5 and 6: what other analyses could you do with the variables in the SPSS data set love.sav (variables described in Table 7.1)? Give examples of pairs of variables for which you could do t tests or one ...How are point biserial r (rpb) and the coefficient different from Pearson r? What is a multiple R? How is multiple R2 interpreted?Post your question

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