Assign #4 - Quant by Cat

Question 1

3 things you can compare between a categorical and quantitative variable

Answer 1

1. central tendencies (means or medians),
2. dispersions (standard deviations or
   interquartile ranges)
3. shapes (histograms or boxplots)

for the distributions of Y by each value of X.

Question 2

provides an indication of the

strength of the association between a categorical X and quantitative Y

Answer 2

R2 in a regression

Question 3

the test of significance for the

comparison of two or more means.

Answer 3

The oneway Analysis of Variance (or oneway ANOVA)

Question 4

What are the hypotheses for the Oneway ANOVA test of significance?

Answer 4

Ho: the population means are the same

Ha: at least two of the means are different
or, not all of the means are the same

Question 5

Shorthand notation for hypotheses for Oneway ANOVA

Answer 5

Ho: μ1 = μ2 = μ3 = …

Ha: not all of μ1, μ2, μ3 are the same

Question 6

For Oneway ANOVA, which scenarios satisfy Ha (2)

Answer 6

• one mean differs from the other two

- all three means differ from one another

Question 7

What does the Oneway ANOVA mathematically look at to estimate variability (2)

Answer 7

1. between-group variation

2. within-group variation

Question 8

the variability of the group means (how spread out the group means are)

Answer 8

between-group variation

Question 9

the variability of the group observations about their separate means (how spread out the scores in the groups are, on average)

Answer 9

within-group variation

Question 10

What is the test statistic for the oneway ANOVA

Answer 10

F statistic

F = between-group variation / within-group variation

Question 11

What does more between-group variation mean

Answer 11

more evidence against the null

hypothesis.

Question 12

What does less within-group variation mean?

Answer 12

more evidence against the null

hypothesis.

Question 13

When Ho is true, what happens to F

Answer 13

F is small

Question 14

What does a small F mean?

Answer 14

little between-group variation and/or lots of within-group variation).

Question 15

When Ho is false, what happens to F

Answer 15

F is large

Question 16

What does a large F mean

Answer 16

lots of between-group variation and/or little within-group variation

Question 17

What is the relationship between F value and p-value

Answer 17

Inversely proportionate

Question 18

Data assumptions for the oneway ANOVA (2)

Answer 18

1. The population distributions on
   the quantitative variable for the groups are roughly normal.
2. The standard deviations of the
   population distributions for the groups are roughly equal.

Question 19

Guiding rule for Oneway ANOVA sample size

Answer 19

The sample size for each group is large (i.e., >= 50).

Question 20

Guiding rule for the Oneway ANOVA standard deviations

Answer 20

The largest standard deviation is no larger than twice the smallest one.

Question 21

Equation for multiple regression lines

Answer 21

Y = b1X1 + b2X2 + a

Question 22

In Y = b1X1 + b2X2 + a, b1 and b2 are

Answer 22

partial regression coefficients.

b1 represents the change in Y for a unit change in X1, holding X2 constant.

b2 represents the change in Y for a unit change in X2, holding X1 constant.

Question 23

Standardized versions of b1 and b2

Answer 23

beta1 and beta2

Question 24

the change in Y in standard

deviations for a one standard deviation change in X1, holding X2 constant.

Answer 24

beta1

Question 25

the change in Y in standard | deviations for a one standard deviation change in X2, holding X1 constant.

Answer 25

beta2

Question 26

the proportion of total variability in Y that is explained by X1 and X2 together.

Answer 26

R2

Question 27

What does multiple regression tell us?

Answer 27

whether X1 and X2 explain the same pot or different pots of variability in Y (or both).