Question

19.14 In a classic study, Milgram et al. "lost" stamped envelopes with fictitious addresses (Medical Research Association, Personal Address, Friends of Communist Party, and Friends of Nazi Party). One hundred letters with each address were distributed among four locations (shops, cars, streets, and phone booths) in New Haven Connecticut, with the following results: ADDRESS RETURNED NOT RETURNED TOTAL Medical Research Association 28 100 Personal Address 100 Friends of Communist Party 25 100 Friends of Nazi Party 100 Total 193 207 400 *Milgram, S., Mann, L, & Harter, L. (1965). The Lost Letter Technique: A Tool of Social Research. Public Opinion Quarterly, 29, 437-438. 72

Answer 1

The research problem is:

The address does not matter in the underlying population.

The hypothesis being tested is:

H₀: Address does not matter in the underlying population

H_a: Address matters in the underlying population

		Col 1	Col 2	Total
Row 1	Observed	72	28	100
	Expected	48.25	51.75	100.00
	O - E	23.75	-23.75	0.00
	(O - E)² / E	11.69	10.90	22.59
Row 2	Observed	71	29	100
	Expected	48.25	51.75	100.00
	O - E	22.75	-22.75	0.00
	(O - E)² / E	10.73	10.00	20.73
Row 3	Observed	25	75	100
	Expected	48.25	51.75	100.00
	O - E	-23.25	23.25	0.00
	(O - E)² / E	11.20	10.45	21.65
Row 4	Observed	25	75	100
	Expected	48.25	51.75	100.00
	O - E	-23.25	23.25	0.00
	(O - E)² / E	11.20	10.45	21.65
Total	Observed	193	207	400
	Expected	193.00	207.00	400.00
	O - E	0.00	0.00	0.00
	(O - E)² / E	44.82	41.79	86.62
		86.62	chi-square
		3	df
		1.17E-18	p-value
		7.815	critical value

The df is 3.

The critical value is 7.815.

The value of X² is 86.62.

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that address matters in the underlying population.

Effect size = √X²/nt = √86.62/400*1 = 0.465

This is a very large effect size.

Odds ratio = [143/(143+57)]/(50/(50+150)] = 2.86

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