Final

Question 1

ANOVA

Answer 1

analysis of variance, measures differences in sample means accross 2 or more groups

Question 2

In ANOVA if H0 is false, there should be…

Answer 2

…a substatnial difference between categories between categories but not within

Question 3

F ratio =

Answer 3

mean square between / mean square within

Question 4

F ratio is bigger when…

Answer 4

categories are more distinct and tightly clustered

Question 5

[ . [ ] . ]

[ . ]

Answer 5

F ratio = smaller/larger = smaller

Question 6

[ . ] [ . ]

[ . ]

Answer 6

F ratio = larger/smaller = larger

Question 7

The assumptions of a ANOVA test

Answer 7

independent random samples, interval/ratio measurement, normal distribution, population variances are equal

Question 8

Limitations of ANOVA

Answer 8

• requires interval/ratio dependent , nominal independent
• just bc its significant doesn’t been its substantive
• the alternate hypothesis is not specific

Question 9

the alternate hypothesis of ANOVA test

Answer 9

At least one of the population means differs from the others

Question 10

synonyms of mean square between/mean square within

Answer 10

sum of square between/degrees of freedom between

sum of square within/degrees of freedom within

Question 11

Is ANOVA one-tailed or two-tailed?

Answer 11

one-tailed

Question 12

the main question of ANOVA

Answer 12

is there more variance between categories or within?

Question 13

strengths of chi-square test

Answer 13

allows use of nominal (and ordinal) variables for dependent instead of just interval/ratio like ANOVA

Question 14

in a bivariate table, is the independent variable in the columns or rows?

Answer 14

independent = columns, dependent = rows

Question 15

chi-square test

Answer 15

a test of independence/significance based on bivariate, crosstabulation tables.

Question 16

the H0 of chi-square test

Answer 16

the variables are completely random and independent, Fo = Fe

Question 17

what does Fe stand for and how is it calculated?

Answer 17

expected frequencies = row marginal x column marginal/n

Question 18

assumptions of chi-square test

Answer 18

independent random sample, nominal level of measurement, no assumption of sampling distribution

Question 19

why is there no assumption of sampling distribution in chi-square test?

Answer 19

bc chi-square test is non-parametric, i.e. it does not deal with distribution patterns

Question 20

degrees of freedom in chi-square

Answer 20

(rows - 1)(columns - 1)
degrees of freedom is like Sudoku –> how many cells can be missing while still being able to figure out all of the blanks

Question 21

limitations of chi-square

Answer 21

• tells us that categories are independent, but it doesn’t tell us about patterns/nature of the relationship
• difficult to interpret when variables have many categories
• with a small sample size, it cannot be assumed that chi-square sampling distribution is accurate
• very sensitive to sample size

Question 22

how does chi-square test react to large sample sizes?

Answer 22

as the sample size increases, chi-square obtained increases. With large samples, trivial relationships may be significant (i.e. things can be erroneously said to be significantly different)

Question 23

three questions of bivariate association

Answer 23

(1) does an association exist?
(2) how strong is the association?
(3) what is the pattern/direction of association?

Question 24

when do we want to use Lambda?

Answer 24

for nominal variables with large sample sizes that can’t be properly assessed with chi-square.

Question 25

PRE measures

Answer 25

Proportional Reduction in Error 1st prediction: ignore information about the independent variable and make many errors E in predicting the value of the dependent variable 2nd prediction: take into account information about the independent variable in predicting the value of the dependent. If variables are associated, we should make fewer errors

Question 26

is Lambda PRE?

Answer 26

yes | lambda = (E1 - E2)/E1

Question 27

interpreting Lambda statistic

Answer 27

e.g. lambda = .33 means that the ability to predict something increased by 33%. in other words, the likelihood of making a mistake is reduced by 66% 0.00–0.10 = weak .011–0.30 = moderate 0.31–1.00 = strong

Question 28

Limitations of Lambda

Answer 28

- asymmetric (value will vary dependening on which variable is independent, so care is needed in designating independent variable) - when row totals are very unequal, Lambda can be zero even when there is an association between the variables

Question 29

when row marginals are very unequal, what test should be used?

Answer 29

chi-square

Question 30

analyzing association between variables at ordinal elvel

Answer 30

to detect association within bivariate, use ch-square, then use Somer's d to detect the strength of the association (uses same scale as Lambda to determine strength)

Question 31

scattergrams

Answer 31

display relationships between two interval/ratio variables

Question 32

describe the axes of a scattergram

Answer 32

X = independent, y = vertical

Question 33

regression line

Answer 33

aka line of best fit, a line that gets as close to all cases as possible.

Question 34

assessing the strength of regression lines

Answer 34

clustering around the lines indicates strength of the linear relationship between two variables

Question 35

formula of regression line

Answer 35

``` Y = a +bX where, Y = score on the dependent variable a = the Y intercept b = the slope i.e. amount change produced in Y by unit change in X X = score on the independent variable ```

Question 36

Pearson's r

Answer 36

measure of association for two interval-ratio variables 0.00–0.10 = weak .011–0.30 = moderate 0.31–1.00 = strong

Question 37

r squared

Answer 37

aka coefficient of determination, provides PRE interpretation

Question 38

multivariate regression

Answer 38

looks at the part of y that x can explain that z can't explain i.e. the effect of x on y while controlling for z

Question 39

formula for multivariate regression line

Answer 39

y = z + (b1)(X1) + (b2)(x2) | the partial slope controls for the other relationship

Question 40

the ANOVA test is designed for independent variables measured at the ____ level.

Answer 40

nominal

Question 41

In the ANOVA test, when the sample means should be roughly equal in value...

Answer 41

... if the null hypothesis is true.

Question 42

The ANOVA test uses means and standard deviations to compare the amount of variation _____ with the amount of variation _____.

Answer 42

within categories, between categories

Question 43

In the ANOVA test, if the null hypothesis is false, the means of the different sample should be _____ and the standard deviation of the different samples should be _____.

Answer 43

very different in value, low in value

Question 44

In the ANOVA test, if the null hypothesis is true, then... (a) SSB should b at least twice as much as dfb (b) SSB should be much greater than SSW (c) the mean square between should be roughly equal to or smaller than the mean square within (d) the combined dfb and dfw should be much greater than the SST

Answer 44

(c) the mean square should be roughly equal to or smaller than the mean square within.

Question 45

ANOVA is a one tailed test and we are concerned only with those outcomes in which there is more variance...

Answer 45

...between categories than within categories.

Question 46

To conduct a chi square test, the variables must first be organized into a ______.

Answer 46

bivariate table

Question 47

The subtotals calculated for bivariate tables are also known as ____.

Answer 47

marginals

Question 48

In the context of chi square, variables are independent if... (a) they are related. (b) cause and effect can be proved. (c) the obtained chi square falls in the critical region. (d) the score of a case on one variable has no effect on the score of the case on the other variable.

Answer 48

(d) the score of a case on one variable has no effect on the score of the case on the other variable.

Question 49

In a 2x2 table, all cell frequencies are exactly the same. This is consistent with which of the following conditions?

Answer 49

The variables are independent.

Question 50

When the null hypothesis in the chi square test for independence is true, there should be...

Answer 50

....little difference between the observed frequencies and the expected frequencies.

Question 51

A Chi square test has been conducted to assess the relationship between marital status and church attendance. The obtained Chi square is 23.45 and the critical Chi square is 9.488. What may be concluded?

Answer 51

Reject the null hypothesis, church attendance and marital status are dependent

Question 52

In a research study conducted to determine if arrests were related to the socioeconomic class of the offender, the chi square critical score was 9.488 and the chi square test statistic was 12.2. We can conclude that the variables are ____.

Answer 52

dependent.

Question 53

If variables are arranged in a bivariate table, we can see if they are associated by... (a) adding their scores vertically. (b) subtracting their scores horizontally. (c) computing percentages in the direction of the independent variable. (d) computing percentages in the direction of the dependent variable.

Answer 53

(c) computing percentages in the direction of the independent variable.

Question 54

In the case of a perfect association, predictions from one variable to another can be made (with/without) error.

Answer 54

without

Question 55

"As education increases, income rises." This is an example of a ______ relationship.

Answer 55

positive

Question 56

If a researcher is looking to perform an analysis based upon the relationship between the number of arrests as an adult and number of encounters with police as a juvenile, they would use which measure of association? (a) Somers d. (b) Lambda. (c) Chi-Square. (d) none of these would be appropriate.

Answer 56

(d) none of these would be appropriate.

Question 57

Proportional reduction in error (PRE) measures of association are based on the logic of ______.

Answer 57

prediction

Question 58

If there is no association between two variables, knowledge of the independent variable does what to the number of errors of prediction?

Answer 58

Does not change the number of errors of prediction.

Question 59

A bivariate table shows the association between gender and whether or not a person ever attends formal religious services. Lambda was .34. What may be concluded? (a) Women are more likely to attend church. (b) Men are more likely to attend church. (c) Knowing a person's gender improves our ability to predict whether or not they attend religious services by 34%. (d) Knowing whether a person attends religious services improves our ability to predict their gender by 34%.

Answer 59

(c) Knowing a person's gender improves our ability to predict whether or not they attend religious services by 34%.

Question 60

A researcher has computed a Somers’s d of −0.75 between marital happiness and number of children. What can be concluded from this result?

Answer 60

that there is a strong, negative relationship between number of children and marital happiness

Question 61

On a scatterplot, the regression line...

Answer 61

...comes as close as possible to touching every score.

Question 62

There is no linear relationship between two interval-ratio variables when the regression line on a scatterplot...

Answer 62

is parallel to the horizontal axis.

Question 63

The Y intercept is the point where...

Answer 63

...the regression line crosses the vertical axis of the scattergram.

Question 64

If a regression line is parallel to the horizontal axis of the scattergram, the slope (b) will be ___.

Answer 64

0.00

Question 65

If the regression line showing the effect of education on income has a slope of 1000...

Answer 65

...every year of education increases income by 1000

Question 66

A researcher wants to measure the strength of the association between income (measured in dollars per year) and education (measured in number of years of formal schooling). Which of the following would be the most appropriate measure? (a) the slope (b) (b) y-intercept (c) chi-square (d) pearson's r

Answer 66

(d) pearson's r

Question 67

In a study of the relationship between geographical mobility (number of times a person has changed residences) and number of friends, Pearson’s r is reported as .40. Which of the following would be the most correct interpretation?

Answer 67

Mobility explains 16% of the variation in number of friends.

Question 68

mean square between groups

Answer 68

since we will simultaneously consider many groups, and evaluate whether their sample means differ more than we would expect from natural variation

Question 69

Null hypthesis for mean square between groups

Answer 69

If the null hypothesis is true, any variation in the sample means is due to chance and shouldn’t be too large.

Question 70

what is the statistic for ANOVA

Answer 70

f-statistic