Stats Exam 4

Question 1

Chi Square Null

Answer 1

Ho: There is no relationship between the two categorical variables.
Alternative

Question 2

Chi Square Alternative

Answer 2

Ha: There is a relationship between the two categorical variables.

Question 3

Assumptions of The Chi-Square Test for Independence

Answer 3

1. The sample should be random.
2. In general, the larger the sample, the more accurate and reliable the test results are. All expected counts need to be greater than 1, with at least 80% exceeding 5 to ensure reliable use of the test. Note: this rule applies only to expected frequencies. It is acceptable for an observed frequency to be 0, provided the expected frequencies meet the criterion

Question 4

Linear correlations

Answer 4

-Have two components: direction & size
-Both described by “r”(sample) or “ρ” (rho, population)
r = Pearson’s Correlation Coefficient

Question 5

Properties of linear correlation coefficient r

Answer 5

• Range: -1 ≤ r ≤ 1
  Scale is irrelevant (based on standardized scores)
  Only measures strength of linear associations
  DOES NOT IMPLY CAUSALITY

Question 6

r^2

Answer 6

r2 = proportion of the variation in y that is determined by x

Question 7

interpreting r

Answer 7

0.5 0.9 : correlation is very strong

r = ±1.00 : correlation is perfect

Question 8

Is the given r value statistically significant?

Answer 8

A weak correlation (small r) can be significant.

A moderate/large correlation can occur by chance alone and be statistically insignificant.

If r is NOT significant…
the best predictor of x is x_
the best predictor of y is y_

Question 9

Regression line

Answer 9

= A “best fit line”, y = mx + b.

Question 10

Residuals

Answer 10

variation not explained by the regression model

Question 11

Least Squares Property

Answer 11

Linear regression produces the smallest possible sum of squares for residuals.
S.O.S. Residuals= Unexplained Variation

Question 12

If no significant correlation exists, the best estimate of Y is

Answer 12

the MEAN of Y

Question 13

F statistic

Answer 13

Mean Square Regression / Means Square Residual

Question 14

F Test for Regression

Answer 14

Tells us if the regression model is statistically significant.

Question 15

Multiple Regression

Answer 15

Bivariate regression can be extended to multivariate data
-When 2 or more independent variables may be related to a dependent variable

Advantages

• Improved predictive value (r square)
• Estimates are more precise

Question 16

r^2 (R^2)

Answer 16

Multiple Coefficient of Determination

r2 still equals the amount of variation in one variable, explained by other predictor variables.

Question 17

Adjusted Coefficient of Determination

Answer 17

Adding predictor variables will increase r2, even if the contribution is trivial.
The best regression equation may not have the largest r2.
For multiple regression, use an adjusted r2

k = number of predictor variables

The adjusted r square increases only if the new variables contribution is more than what would be expected by chance alone.

Question 18

What independent variables to include as predictors?

Answer 18

1) Consider thCommon sense & practical considerations.
- Bear “Age” may be predictive, but impractical to measure.
2) e standardized coefficients
- Independent variables converted to Z scores. “Standardized coefficients” indicated relative strength influence
3) Evaluate several regression models
Choose the model with the highest adjusted r square and the fewest variables possible
Avoid multicollinear variables (head width & ear tip distance)
Choose the equation with the lowest P value (based on F statistic in ANOVA table)

Question 19

χ2

Answer 19

χ2 = quantifies difference from expected frequencies
Small χ2 &raquo_space; due to random variation.
Large χ2&raquo_space; unlikely to occur by chance.
No negative values & always a one tailed test

Question 20

If the observed frequencies perfectly match the expected frequencies…

Answer 20

you would see 0

Question 21

If the observed frequencies are vastly different than the expected frequencies…

Answer 21

you would see a big value

Question 22

chi square calculations

Answer 22

Sigma[(O-E)^2/E]

Question 23

Chi-Square Distribution

Answer 23

Skewed right
χ2 = 0 to ∞
Different curve for every degree of freedom
Degrees of freedom = (rows–1)*(columns–1)

Question 24

Chi Square Review

Answer 24

Evaluates C  C relationships
Compares expected to observed frequencies

Tests of Independence
Expected = Pn = (row totalcolumn total)/total
Used to test any frequency related hypothesis
E.g.: Car accidents are 5 times more common on weekdays than on weekends.

Question 25

Number Needed to Treat to prevent one case

Answer 25

The number of subjects we would need to treat, to prevent one case of disease

Question 26

Risk

Answer 26

Probability for a condition/disease

Question 27

Risk Ratio

Answer 27

a ration of two sample risks

Question 28

Risk & Risk Ratio Hypotheses

Answer 28

H0: RR = 1.0 Ha: RR ≠ 1.0

Question 29

CI for Risk Ratio

Answer 29

• -RR captures 1.0  Fail to reject H0,Fail to support Ha

- -RR does not include 1.0  Reject H0, support Ha

Question 30

Risk Ratio Caveat

Answer 30

Only applies to “natural” data, that are not “case controlled”.
Includes Prospective Studies
Randomized Controlled Trials (E.g. Salk Vaccine)
The natural incidence of disease is observed
Excludes most Retrospective Studies
Case controlled studies
Experimenter decides how many cases of each condition to include
Odds Ratios can be used in these cases
Odds compare the incidence of one condition to another (not to the total)

Question 31

Odd

Answer 31

A ratio of the incidence of one condition to it’s complimentary condition. Not a probability.

Question 32

Risk vs Odds Ratio

Answer 32

An odds ratio is always valid
A risk ratio is valid only if the incidence of the the response variable occurs naturally.
The component risks must be valid
Often not valid in retrospective studies
Hypothesis Testing and Confidence Interval Interpretation are the same.
H0: RR = 1.0 Ha: RR ≠ 1.0
H0: OR = 1.0 Ha: OR ≠ 1.0