Question

Here is Exercise 25.2 for reference:

Peer Victimization and Depression. Exercise 25.2 describes a comparison of the distribution of the frequencies of having been bullied at age 13 for a sample of 18-year-olds in southwest England who suffer and don't suffer from depression. The null hypothesis "no relationship" says that in the population of all 18-vear-olds in southwest England, the proportions who have experienced each frequency of bullying at age 13 are the same for those who suffer and don't suffer from depression. n BULLYING (a) Find the expected cell counts if this hypothesis is true, and display 25.6 them in a two-way table. Add the row and column totals to youir table, and check that they agree with the totals for the observed counts. (b) Are there any large deviations between the observed counts and the expected counts? What kind of relationship between the two variables do these deviations point to? Peer Victimization and Depression. The Avon Longitudinal Study of Parents and Children (ALSPAC) included approximately 14,000 children born between 1991 and 1992 in southwest England, and was intended to investigate a wide range of influences on the health and development of children. The data reported here investigate the relationship between being bullied at age 13, which includes incidents such as the taking of personal belongings; being threatened, blackmailed, hit, or beat up; being called nasty names, having lies told about them, or the like; and depression at 18 years of age. From the original cohort, 3898 children had data on both the frequency of being bullied and later depression. Here are the results:3 BULLYING 25.2 Frequency of Being Bullied Never 97 1762 Occasionally 103 1343 Frequently 101 582 Depressed Not depressed (a) It appears that 18-year-olds suffering from depression were bullied more often than those who do not suffer from depression. Give percents to back up this claim. Make a bar graph that compares your percents for subjects who do and do not suffer from depression at age 18. (b) Association does not prove causation. Explain why you can't conclude from this study that being bullied causes depression.

Answer 1

Presenting the relevant 2-way frequency data and calculating the totals:

	Frequency of never being bullied			TOTAL
	Never	Occasionally	Frequently
Depressed	97	103	101	301
Not depressed	1762	1343	582	3687
TOTAL	1859	1446	683	3988

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(a) The expected cell counts are as follows:

EXPECTED TOTALS
	Frequency of never being bullied			TOTAL
	Never	Occasionally	Frequently
Depressed	140.31	109.14	51.55	301
Not depressed	1718.69	1336.86	631.45	3687
TOTAL	1859	1446	683	3988

Calculating the totals, we can see that we get the same totals as the above table.

The method for calculating the expected cell counts is:

Expected cell count for each cell = (Corresponding row total*Corresponding column total)/n

where, n = Overall total number in the population i.e. 3988

For ex: For the 1st cell - Depressed & Never - Expected value = 1859*301/3988 = 140.31

Similarly, we calculate the remaining 5 cells and then the totals to verify if we got the same totals as before or not.

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(b) There is no large differences or deviation in the expected (Table 2) and observed values (Table 1) for the sample of 18-year olds who are not depressed. The only major deviation that is seen is in those who are depressed and when we see their expected values, we find that for those who were never bullied as 13-year olds 140 of them were expected to be depressed but the observed number is just 97; while of those who were frequently bullied, 52 were expected to be depressed but 101 have been observed to be so. This gives us a hint that being frequently bullied leads to higher chances of depression later and never being bullied lowers the chances of being depressed later.

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Kindly let me know if you need any further clarifications. Thanks.

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