Week 10: Tests of Relationships - Correlation; Regression

Question 1

Test difference (is group A different that group B/does this treatment cause this outcome) for what type of outcomes?

Answer 1

continuous outcomes

Question 2

Test proportions (is group A different that group B/does this treatment cause this outcome) for what type of outcomes?

Answer 2

categorical outcomes

Question 3

How do you test relationships between two groups?

Answer 3

1. Measure correlation between A and B

2. Fit a regression model for A and B

Question 4

Example: Is the male group different from the female group by their BMI level?

Answer 4

Test the difference of the mean BMI between the groups of male and female

Question 5

Example: Is the gender linked to a certain age group?

Answer 5

Compare the proportions of being older than 50 yrs between the groups of male and female

Question 6

Example: What is the relationship between BMI and DBP at baseline?

Answer 6

Does DBP increase as BMI increase?

Test relationship between DBP and BMI

Question 7

When you look at the relationship between two variables -

Answer 7

Correlation

Question 8

How do you calculate correlation of data?

Answer 8

1. Draw a scatter plot to visualize

2. Compute a correlation coefficient (r) to quantify

Question 9

If r = 0.96, how is weight loss and exercise time correlated?

Answer 9

• Weight loss is highly correlated with exercise time

- Weight loss increases as exercise time increases

Question 10

way of visualizing the relationship between two variables -

Answer 10

scatter plot

Question 11

T/F Scatter plot can visually clarify the strength and shape of a relationship

Answer 11

True

Question 12

T/F Correlation coefficient r is a measure of a linear association between two variables in the range of 0 and 1

Answer 12

False, in the range of -1 and 1

Question 13

T/F The sign of r indicates the direction of the correlation

Answer 13

True

Question 14

T/F The absolute value of r indicates the strength of the correlation

Answer 14

True

Question 15

Interpretation of Correlation Coefficient r:
0-.25 = 
.25-.5 = 
.5-.75 = 
.75-1 =

Answer 15

0-.25 = Little to no relationship
.25-.5 = fair
.5-.75 = moderate to good
.75-1 = good to excellent

Question 16

T/F Correlation Coefficient r values can be used as strict cutoff points.

Answer 16

False, values should NOT be used as strict cutoff points, as they are affected by:

1. sample size
2. measurement error
3. the types of variables being studied

Question 17

correlation coefficient r is a measure of what type of relationship only?

Answer 17

• Linear relationship only

- A curvilinear relationship won’t be described accurately using the linear correlation coefficient r

Question 18

For interpretation, look at what two things to determine if association in the set of data is linear or curvilinear?

Answer 18

1. r value

2. scatter plot

Question 19

What is the most commonly reported measure of correlation?

Answer 19

Pearson (produce-moment) correlation coefficient

Question 20

When is it appropriate to use Pearson (produce-moment) correlation coefficient?

Answer 20

when X and Y are continuous variables with underlying normal distributions

Question 21

What is a nonparametric analog of the Pearson r?

Answer 21

Spearman rank correlation coefficient

Question 22

When is it appropriate to use the spearman rank correlation coefficient?

Answer 22

when X and Y are ordinal variables

Question 23

When would you use phi coefficient?

Answer 23

• appropriate for use when both X and Y are dichotomous variables (2 variables)
• special case of the Pearson correlation coefficient, given only two values of X and Y

Question 24

When would you use The point biserial correlation coefficient?

Answer 24

• appropriate when a dichotomous X is correlated with a continuous variable Y
• a special case of the Pearson correlation coefficient

Question 25

Example: What coefficient would you use? The data representing the motor and verbal skills in a group of 60 adults with traumatic brain injury. Scores are graded pass or fail, and assign 1 to pass and 0 to fail.

Answer 25

Phi coefficient

Question 26

Example: What coefficient would you use? The data represents the developmental scores on tests of proximal (reaching) and distal (prehensile skill) behaviors in 12 normal infants, 30 weeks of age

Answer 26

Pearson (Product-Moment) Correlation Coefficient

Question 27

Example: What coefficient would you use? The data representing the ratings of elbow flexor spasticity (resistive force in kilograms) for patients who have had a stroke on the right (1) or left (0) sides

Answer 27

Point Biserial Correlation Coefficient

Question 28

Example: What coefficient would you use? | The data represents the scores of verbal and reading comprehension for a sample of 10 children with learning disability

Answer 28

Spearman Rank Correlation Coefficient

Question 29

Precautions in Using Correlation Coefficient: | Nonlinearity -

Answer 29

- Pearson correlation coefficient is all about linear relationship - A strong curvilinear relationship may be identified as no correlation (r=0)

Question 30

Precautions in Using Correlation Coefficient: | Outlier -

Answer 30

A single point can have a large influence on the correlation

Question 31

Precautions in Using Correlation Coefficient: | Interpretation is subjective -

Answer 31

- No hard and fast rules that determine an r value is strong, moderate or weak - Interpretation should base on the nature of the data, the purpose of the research and the researcher’s knowledge of the subject matter

Question 32

Precautions in Using Correlation Coefficient: | Causation -

Answer 32

- No causal relationship can be determined based on the correlation coefficient value - Correlation of A and B is the same as correlation of B and A - Correlation cannot be used to establish a cause-and-effect situation

Question 33

When you look at the relationship between two variables in a cause-and-effect situation?

Answer 33

Regression

Question 34

How do you calculate a regression line?

Answer 34

1. Draw a scatter plot with a regression line to visualize | 2. Compute a coefficient of determination (R2) to quantify

Question 35

Ex: if r = 0.96; R2 = 0.92, what is the relationship between weight loss and exercise time?

Answer 35

- Weight loss is highly correlated with exercise time | - Exercise time predicts the Weight loss

Question 36

Regression used to predict values of one variable to another: x-> y x = y =

Answer 36

``` x = independent (predictor/explanatory) variable y = dependent (outcome/response) variable ```

Question 37

used to examine the causal relationship of the two variables, X and Y, that are linearly related?

Answer 37

Linear regression | y=a +bX

Question 38

used to examine the causal relationship of the two variables, X and Y, when Y is binary?

Answer 38

Logistic regression | y=a+bX

Question 39

Example: Linear or logistic regression | Mobility and functional characteristics could predict whether a person did or did not have a history of falls.

Answer 39

Logistic

Question 40

Example: Linear or logistic regression The data consisting of the systolic blood pressure (Y) and age (X) in a sample of 10 women. Base it to predict a woman’s blood pressure by knowing her age

Answer 40

Linear

Question 41

Example: Linear or logistic regression | Physical/psychological function as predictors of successful return to work on year after traumatic brain injury

Answer 41

Logistic

Question 42

Logistic regression reports odds ratio (OR) to estimate what?

Answer 42

the odds of membership in the target group linked to the predictor variable

Question 43

T/F Confidence intervals can also be determined for each OR for logistic regression

Answer 43

True

Question 44

A significant OR will not contain what within its CI?

Answer 44

null value of 1.0

Question 45

How to determine if assumptions for regression analysis have been met?

Answer 45

Patterns of residuals (Y-axis) plotted against predicted scores (X-axis). 

Question 46

If Patterns of residuals (Y-axis) plotted against predicted scores (X-axis) provide horizontal band, what does that mean?

Answer 46

demonstrates that assumptions for linear regression have been met

Question 47

If Patterns of residuals (Y-axis) plotted against predicted scores (X-axis) provide curvilinear pattern, what does that mean?

Answer 47

indicates nonlinear relationship.

Question 48

Coefficient of determination R2

Answer 48

measure of proportion, indicating the accuracy of prediction based on X

Question 49

what does R^2 represent?

Answer 49

percentage of the total variance in the Y scores that can be explained by the X scores

Question 50

1-R^2 represents?

Answer 50

percentage of the total variance in Y not explained by the X scores

Question 51

Example: For the regression of blood pressure on age, r=0.87; R2=0.76

Answer 51

- 76% (R2) of the variance in systolic blood pressure explained by the variance in age - 24% (1-R2) of the variance in systolic blood pressure not explained by the variance in age

Question 52

What do the researchers use correlation for?

Answer 52

Identify the relationship between two variables

Question 53

What do the researchers use regression analysis for?

Answer 53

Predict the effect of one variable upon another

Question 54

T/F Correlation can be used to establish a cause-and-effect relationship

Answer 54

False, Regression not correlation

Question 55

T/F A hard and fast rule exists for its interpretation in terms of strong, moderate or weak correlation.

Answer 55

False, no hard and fast rule

Question 56

T/F It is important to include all the data points to compute the correlation coefficient correctly

Answer 56

False

Question 57

T/F A strong linear relationship can be identified as a high correlation coefficient value

Answer 57

True

Question 58

T/F Correlation coefficient is the ratio of risks of exposure vs. non-exposure groups

Answer 58

False, Odds ratio not correlation

Question 59

T/F Coefficient of determination (R2) is the percentage of variance in the predictor variable accounted for by the outcome variable

Answer 59

False, variance of outcome variable accounted for by the predictor variable

Question 60

T/F Coefficient of determination (R2) is the proportion of variance in the outcome accounted for by the predictor variable

Answer 60

True

Question 61

T/F Correlation coefficient (r) value ranges from 0 to +1

Answer 61

False, -1 to +1

Question 62

T/F Within the same study, the correlation coefficient (r) value can be computed by squaring the coefficient of determination (R2) value

Answer 62

False, the opposite

Question 63

T/F Coefficient of determination (R2) value ranges from -1 to 1

Answer 63

False, 0-1

Question 64

Which of the following statistical procedure is proper to use when you want to study the relationship between the two variables, being interested in knowing which would have caused the other?

Answer 64

Regression analysis

Question 65

T/F Logistic regression is used to predict a continuous outcome variable

Answer 65

False, linear regression -> continuous and logistic -> categorical

Question 66

T/F Coefficient of determination (R2) is a good measure for an index of predicted variance

Answer 66

True

Question 67

T/F Coefficient of determination (R2) is a measure of linear association between two variables

Answer 67

False, r is

Question 68

T/F Linear regression is used to predict a binary outcome variable

Answer 68

False, continuous outcome variable