Chapters Beyond 9

Question 1

What does the mean squares represent?

Answer 1

The between group variability and the within group variability.

Between is on top
Within is on bottom

Question 2

When do we do in pairwise comparisons?

Answer 2

When we reject H_o in an ANOVA and want to see which means are different between groups.

Question 3

Why do we do pairwise comparisons?

Answer 3

To be able to see which groups have different means

Question 4

What does it mean if two variables measured on the same subject are associated?

Answer 4

Knowing one value of the variable tells us something about the value of the other variable.

Question 5

What do we use to show the correlation coefficient, and what are its units?

Answer 5

r.

r has no units

Question 6

What is the parameter for the correlation coefficient?

Answer 6

Rho (p)

Question 7

r = 1 corresponds to what correlation?

Answer 7

A perfect positive correlation.

Question 8

r = -1 corresponds to what correlation?

Answer 8

A perfect negative correlation.

Question 9

r = 0 signifies what?

Answer 9

No correlation. No linear association.

Question 10

What happens to the scatter plot when there is a strong linear association?

Answer 10

The points are tightly clustered around a line.

Question 11

What is the explanatory variable?

Answer 11

X

Question 12

Which is the response variable?

Answer 12

Y

Question 13

Does r change if we interchange the explanatory and response variables?

Answer 13

No

Question 14

When there is a strong linear association, what do we know?

Answer 14

That information about one variable helps in predicting the other.

Question 15

What happens in a weak association?

Answer 15

The points are scattered broadly

Question 16

What does a low r mean?

Answer 16

It means there is no linear association - however not necessarily that there is no association

Question 17

Correlation does not imply _______

Answer 17

Causation

Question 18

What is linear regression used for?

Answer 18

To find a line that summarizes the linear relationship between two variables.

With it we can make predictions about y, the response variable

Question 19

How do we notate the regression line?

Answer 19

y_i = beta_o + beta_1x_i + epsilon_i

beta_o = intercept
beta_1 = slope
epsilon_i = error term. Indicates how far y_i is from the line.

Question 20

What is beta_o?

Answer 20

Intercept

Represents the average value of y when x is zero.

Question 21

What is beta_1?

Answer 21

Slope

Represents the change in the average for y for every one unit increase in x

Question 22

What is epsilon_i?

Answer 22

error term. Indicates how far y_i is from the line.

Question 23

We estimate the slope and intercept of the regression line from the data to get:

Answer 23

y_hat i = beta_hat o + beta_hat i * x

Question 24

You don’t want to use a regression line to estimate values that are…

Answer 24

Outside of the range of data we got in our sample. (This is known as extrapolation)

Question 25

What is the least squares regression line?

Answer 25

The line that minimizes the total squares vertical error (i.e. The total of the squares residuals)

Question 26

What are residuals?

Answer 26

The vertical deviations between the points and the line y_i-B_o+B_ix_i = epsilon_i

Question 27

In the least squares line: | B_hati can be found by?

Answer 27

r *(sd_y / sd_x)

Question 28

In the least squares line : | B_hato can be found by?

Answer 28

y_bar - B_hat1*x_bar

Question 29

In ANOVA, what describes how much the observations vary around the sample mean?

Answer 29

the within group variance

Question 30

In ANOVA, what describes how much the sample means vary around a total mean?

Answer 30

the between group variance

Question 31

What does a Chi-squared Goodness of Fit Test measure?

Answer 31

it measures the discrepancy between observed cell counts and cell counts expected under the null hypothesis, to assess whether the hypothesized distribution is plausible

Question 32

What is H_o for the goodness of fit test?

Answer 32

H_o: p1=p1*, p2+p2*, ..., pk = pk*

Question 33

What is H_A for the goodness of fit test?

Answer 33

H_A: pi != pi*, for some i.

Question 34

What are the expected counts in a goodness of fit test?

Answer 34

The proportion given to us, multiplied by the total # of observations in our test. All the expected counts summed should equal our total observations in our test!

Question 35

What is the Pearson chi-square test statistic?

Answer 35

chi-squared = sum from i to k of [(x_i-e_i)^2]/e_i | or [(observed-expected)^2]/expected

Question 36

How is the p-value for a chi-squared goodness of fit test calculated?

Answer 36

We use the table for chi-square, and we always want a one-tailed right hand tail.

Question 37

What are the degrees of freedom for a chi-square test?

Answer 37

k-1, or the number of groups minus 1.

Question 38

What do we use a chi-square test of independence for?

Answer 38

To determine whether two variables, summarized in a 2-way contingency table, are independent.

Question 39

What is a two-way contingency table?

Answer 39

a set of frequencies that summarize how a set of objects is simultaneously classified under two different categorizations.

Question 40

What is H_o in a test for independence?

Answer 40

H_o: the two variables are independent

Question 41

What is H_A in a test for independence?

Answer 41

H_A: the two variables are not independent.

Question 42

How do we calculate the expected count in a test for independence? (e_ij)

Answer 42

e_ij = (row_i total * col_j total)/grand total

Question 43

What is the chi-square test statistic for a test for independence?

Answer 43

chi^2 = sum from i to r of, sum from j to c of (x_ij - e_ij)^2/e_ij

Question 44

What are the degrees of freedom in a chi-square test for independence involving an r*c table?

Answer 44

(r-1)(c-1)

Question 45

When does the chi-square test for independence work well?

Answer 45

when e_ij GT= 5

Question 46

What two hypotheses tests are there for categorical data?

Answer 46

1) goodness of fit test 2) chi-square test of independence (both are chi-square tests!)