Homework #4 Answers: Multivariate Analyses, alpha = .05 on all tests

For each question:

1. Choose the correct statistical technique

2. Write your hypotheses

3. Determine whether to reject or accept

4. Interpret results

1. Is there a relationship between how happy people are with their lives and their SEI level, controlling for age (ie, holding age constant)?

SEI is measured on a scale of 0-100.

Happiness is measured as very happy, pretty happy, and not too happy

Age ranges from 18-89.

very happy mean SEI = 52.04

pretty happy mean SEI = 48.43

not too happy mean SEI = 43.89

p = .000

statistical technique = ANCOVA

Ho (null): There is no relationship between how happy people are with their lives and their SEI level, controlling for age. f=0

H1 (research): There is a relationship between how happy people are with their lives and their SEI level, controlling for age. f≠0

Reject null hypotheses, p is less than alpha. There is a relationship between how happy people are with their lives and their SEI level, controlling for age. Very happy people have the highest SEI (average = 52.04). People who are not too happy have the lowest SEI (average = 43.89). Pretty happy people are in the middle with an average SEI of 48.43.

2. Is there a relationship between being unemployed during the last 10 years and owning a gun, controlling for education?

Unemployment is measured as yes or no.

Owning a gun is measured as yes or no.

Education is measured as less than HS, HS degree, and more than a HS degree.

less than HS	P = .37
	Unemployment
Own Gun	Yes	No
Yes	20%	25%
No	80%	75%
HS degree	P = .47
	Unemployment
Own Gun	Yes	No
Yes	35%	40%
No	65%	60%
More than HS	P = .56
	Unemployment
Own Gun	Yes	No
Yes	35%	34%
No	65%	66%

Statistical technique = elaboration

Ho (null): There is no relationship between being unemployed during the last 10 years and owning a gun, controlling for education. χ²=0

H1 (research): There is a relationship between being unemployed during the last 10 years and owning a gun, controlling for education. χ²≠0

Less than high school: Accept null, p is greater than alpha. For people with less than a high school degree there is no relationship between being unemployed during the last 10 years and owning a gun. Equal percentages of people with less than a high school degree who have and have not been unemployed in the last 10 years own a gun – about 20-25%.

High school degree: Accept null, p is greater than alpha. For people with a high school degree there is no relationship between being unemployed during the last 10 years and owning a gun. Equal percentages of people with a high school degree who have and have not been unemployed in the last 10 years own a gun – about 35-40%.

More than a high school degree: Accept null, p is greater than alpha. For people with more than a high school degree there is no relationship between being unemployed during the last 10 years and owning a gun. Equal percentages of people with more than a high school degree who have and have not been unemployed in the last 10 years own a gun – about 35%.

3. Do attitudes about teen sex influence attitudes about abortion, when controlling for religious preference?

RELIG RS RELIGIOUS PREFERENCE			TEENSEX SEX BEFORE MARRIAGE
			1 ALWAYS WRONG	2 ALMST ALWAYS WRG	3 SOMETIMES WRONG	4 NOT WRONG AT ALL
1 PROTESTANT p=.000	ABORTION FOR ANY REASON	1 YES	29.3%	45.3%	73.9%	44.4%
		2 NO	70.7%	54.7%	26.1%	55.6%
2 CATHOLIC p=.20	ABORTION FOR ANY REASON	1 YES	33.1%	50.0%	50.0%	50.0%
		2 NO	66.9%	50.0%	50.0%	50.0%
3 JEWISH p=.58	ABORTION FOR ANY REASON	1 YES	81.8%	66.7%	50.0%	0%
		2 NO	18.2%	33.3%	50.0%	0%
4 NONE p=.004	ABORTION FOR ANY REASON	1 YES	38.7%	57.7%	72.7%	83.3%
		2 NO	61.3%	42.3%	27.3%	16.7%

Statistical technique = elaboration

Ho (null): There is no relationship between attitudes about teen sex and attitudes about abortion, when controlling for religious preference. χ²=0

H1 (research): There is a relationship between attitudes about teen sex and attitudes about abortion, when controlling for religious preference. χ²≠0

Protestant: Reject null, p is less than alpha. For Protestants, attitudes about teen sex influence attitudes about abortion. Protestants who think teen sex is sometimes wrong are the most likely to think abortion for any reason is acceptable (74%). Protestants who think teen sex is always wrong are the least likely to think abortion for any reason is acceptable (29%).

Catholic: Accept null, p is greater than alpha. For Catholics attitudes about teen sex are not related to attitudes about abortion. Equal percentages of Catholics who think teen sex is always wrong, almost always wrong, sometimes wrong or not wrong at all think abortion for any reason is acceptable – about 30-50%.

Jewish: Accept null, p is greater than alpha. For Jews attitudes about teen sex are not related to attitudes about abortion. Equal percentages of Jews who think teen sex is always wrong, almost always wrong, or sometimes wrong think abortion for any reason is acceptable – about 50-80%.

No religious preference: Reject null, p is less than alpha. For people with no religious preference there is a relationship between about attitudes about teen sex and attitudes about abortion. People with no religious preference who think teen sex is sometimes wrong or not wrong at all are the most likely to think abortion for any reason is acceptable (73% and 83%). People with no religious preference who think teen sex is almost always wrong or always wrong are the least likely to think abortion for any reason is acceptable (39% and 58%).

4. Does social class influence the number of hours worked when controlling for years of education?

CLASS	Mean	Std. Deviation	N
1 LOWER CLASS	36.18	13.232	56
2 WORKING CLASS	42.00	13.240	919
3 MIDDLE CLASS	42.25	13.505	772
4 UPPER CLASS	40.47	14.618	57
Total	41.88	13.430	1804

p = .000

statistical technique = ANCOVA

Ho (null): There is no relationship between social class and the number of hours worked when controlling for years of education. f=0

H1 (research): There is a relationship between social class and the number of hours worked when controlling for years of education. f≠0

Reject null hypotheses, p is less than alpha. There is a relationship between how social class and the number of hours worked when controlling for years of education. Middle and working class people work the most (average = approximately 42 hours). Lower class people work the least (average = 36.18).

5. Is there a relationship between the number of hours worked and SEI, controlling for age in years?

r = .11, p = .000

statistical technique = partial correlation

Ho (null): There is no relationship between the number of hours worked and SEI, controlling for age in years. r=0

H1 (research): There is a relationship between the number of hours worked and SEI, controlling for age in years. r≠0

Reject null, p is less than alpha. There is a positive correlation between the number of hours worked and SEI, controlling for age in years. As the number of hours worked increases, SEI increases. As SEI increases, the number of hours worked increases.

r² = .11 * .11 = .0121

The number of hours worked explains 1.21% of the variation in SEI, controlling for age. SEI explains 1.21% of the variation in the number of hours worked, controlling for age.

6. Does education in years, how often people have sex, income, and age influence the number of children that people?

Coefficients(a)

	Unstandardized Coefficients		Standardized Coefficients	t	Sig.
	B	Std. Error	Beta
(Constant)	.926	.227		4.085	.000
EDUC	-.085	.012	-.146	-7.179	.000
SEXFREQ	.138	.018	.168	7.564	.000
AGE	.043	.002	.440	19.836	.000
INCOME	-.032	.014	-.046	-2.257	.024

R	R Square	Adjusted R Square	Std. Error of the Estimate	F	Sig.
.435(a)	.189	.188	1.475	125.285	.000(a)

statistical technique = regression

R² Test

Ho (null): Education, sex frequency, age, and income combined do not explain a significant amount of the variation in the number of children that people have. R²=0

H1 (research): Education, sex frequency, age, and income combined explain a significant amount of the variation in the number of children that people have. R²≠0

Reject null, p is less than alpha. Education, sex frequency, age, and income combined explain a significant amount (18.9%) of the variation in the number of children that people have.

Education

Ho (null): Education does not influence the number of children that people have, controlling for sex frequency, age, and income. b=0

H1 (research): Education influences the number of children that people have, controlling for sex frequency, age, and income. b≠0

Reject null, p is less than alpha. Education influences the number of children that people have, controlling for sex frequency, age, and income. As education increases one year, the number of children that people have decreases by .09 children.

Sex Frequency

Ho (null): Sex frequency does not influence the number of children that people have, controlling for education, age, and income. b=0

H1 (research): Sex frequency influences the number of children that people have, controlling for education, age, and income. b≠0

Reject null, p is less than alpha. Sex frequency does influence the number of children that people have, controlling for education, age, and income. As sex frequency increases, the number of children that people have increases by .14 children.

Age

Ho (null): Age does not influence the number of children that people have, controlling for education, sex frequency, and income. b=0

H1 (research): Age influences the number of children that people have, controlling for education, sex frequency, and income. b≠0

Reject null, p is less than alpha. Age influences the number of children that people have, controlling for education, sex frequency, and income. As age increases one year, the number of children that people have increases by .04 children.

Income

Ho (null): Income does not influence the number of children that people have, controlling for education, sex frequency, and age. b=0

H1 (research): Income influences the number of children that people have, controlling for education, sex frequency, and age. b≠0

Reject null, p is less than alpha. Income influences the number of children that people have, controlling for education, sex frequency, and age. As income increases, the number of children that people have decreases by .03 children.

Standardized Coefficients

Age has the largest influence on the number of children (B=.44), followed by education (B= -.15) and sex frequency (B= .17) which have about the same size effect. Of the variables in the model, income has the smallest impact (B= -.05) on the number of children that people have.