Tests of Relationships- Correlation; Regression

Question 1

The questions below test _________ or __________.

• Is group A different from group B?
• Does this treatment cause this outcome?

Answer 1

Difference or proportions depending on the outcome variable type.

Question 2

• Test difference for _________ outcomes.

- Test proportions for ________ outcomes.

Answer 2

• continuous

- categorical

Question 3

The questions below test _____________.

• What is the relationship between A and B?
• Does variable A increase with variable B?

Answer 3

relationship

Question 4

Examples:
Which tests would be appropriate for the following questions?

1. ) Is the male group different from the female group by their BMI level?
2. ) Is the gender linked to a certain age group?
3. ) What is the relationship between BMI and DBP at baseline?

Answer 4

1. ) Test the difference of the mean BMI between groups of male and female.
2. ) Compare the proportions of being older than 50 yrs between the groups of male and female.
3. ) Test relationship between DBP and BMI.

Question 5

Tests of Differences (parametric vs non-parametric):
-What 2 tests are used for two group independent comparison? Which is used for parametric data? Which is used for non-parametric data?

• What 2 tests are used multi group independent comparison? Which is used for parametric data? Which is used for non-parametric data?
• What 2 tests are used two group paired comparison? Which is used for parametric data? Which is used for non-parametric data?
• What 2 tests are used for multi group paired comparison? Which is used for parametric data? Which is used for non-parametric data?

Answer 5

• Independent t-test, Mann-Whitney U Test
• Independent t-test = parametric
• Mann-Whitney U Test = non-parametric
• ANOVA, Kruskal-Wallis H Test
• ANOVA = parametric
• Kruskal-Wallis H Test = non-parametric
• Paired t-test, Wilcoxon Signed Rank Test
• Paired t-test = parametric
• Wilcoxon SIgned Rank Test = non-parametric
• Repeated Measures ANOVA, Friedman Test
• Repeated Measures ANOVA = parametric
• Friedman Test = non-parametric

Question 6

Tests of Proportions (parametric vs non-parametric):
-What 2 tests are used for two group independent comparison? Which is used for data that isn’t sparse? Which is used for sparse data?

• What 2 tests are used for multi group independent comparison? Which is used for data that isn’t sparse? Which is used for sparse data?
• What 2 tests are used for two group paired comparison? Which is used for data that isn’t sparse? Which is used for sparse data?
• What 2 tests are used for multi group paired comparison? Which is used for data that isn’t sparse? Which is used for sparse data?

Answer 6

• Chi-Square, Fisher’s Exact
• Chi-Square = data not sparse
• Fisher’s Exact = data sparse
• Chi-Square, Fisher’s Exact
• Chi-Square = data not sparse
• Fisher’s Exact = data sparse
• McNemar Test, McNemar Exact Test
• McNemar Test = data not sparse
• McNemar Exact Test = data sparse
• Stuart-Maxwell Test, Generalized Stuart-Maxwell
• Stuart-Maxwell Test = data not sparse
• Generalized Stuart Maxwell = data sparse

Question 7

Tests of Cerrelation; Regression:

Answer 7

1

Question 8

• Correlation is when you look at the ____________ between two variables.
• Draw a ______________ to visualize
• Compute a ________________ to quantify

Answer 8

• relationship
• scatter plot
• correlation coefficient (r)

Question 9

_____________ is a way of visualizing the relationship between two variables. Each point represents the intersection of a pair of related observations. They can visually clarify the _______ and shape of a relationship.

Answer 9

• Scatter plot

- strength

Question 10

________ _________ is a decimal number in the range of -1 to +1 and is a measure of linear relationships between two variables.

Answer 10

Correlation coefficient (r)

Question 11

• What is a perfect positive correlation value?

- What is a perfect negative correlation value?

Answer 11

+1

-1

Question 12

With correlation coefficient:

• The sign of r indicates __________.
• The absolute value of r indicates __________.

Answer 12

• direction

- strength

Question 13

• How do we interpret correlation coefficient (r) values?

- Should these values be used as strict cutoff points? Why or why not?

Answer 13

• 0-0.25 = little or no relationship
• 0.25-0.50 = fair
• 0.50-0.75 = moderate to good
• 0.75-1 = good to excellent

-No, because they are affected by sample size, measurement error, and the types of variables beinig studied.

Question 14

Correlation coefficient is a measure of ________ relationship only. It cannon be used for _____________ relationship.

Answer 14

• linear

- curvilinear

Question 15

What are 4 types of correlation coefficients?

Answer 15

• Pearson (Product-Moment)
• Spearman Rank
• Phi
• Point Biserial

Question 16

• _________ Correlation Coefficient is the most commonly reported measure of correlation.
• It is appropriate when X and Y are __________ variables with underlying ________ distributions.

Answer 16

• Pearson

- continuous, normal

Question 17

• __________ Correlation Coefficient is a __________ analog of the Pearson (r).
• It is appropriate for use when X and Y are ________ variables.

Answer 17

• Spearman Rank, non-parametric

- ordinal

Question 18

• _________ Correlation Coefficient is a special case of the Pearson (r), given only ____ values of X and Y.
• It is appropriate for use when both X and Y are ___________ variables.

Answer 18

• Phi, two

- dichotomous

Question 19

• _____________ Correlation Coefficient is a special case of the Pearson (r).
• It is appropriate when a ___________ X is correlated with a ___________ variable Y.

Answer 19

• Point Biserial

- dichotomous X, continuous Y

Question 20

What are some precautions in using Correlation Coefficient?

Answer 20

Nonlinearity
-A strong curvilinear relationship may be identified as no correlation.
Outlier
-A single point can have a large influence on the correlation.
Interpretation is subjective
-No hard and fast rules that determine an (r) value is strong, moderate, or weak
-Interpretation should be based on the nature of the data, purpose of the research, and the researcher’s knowledge of the subject matter
Causation
-No causal relationship can be determined based on the (r) 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 21

• Regression is when you look at the relationship between two variables in a ______________ situation.
• Draw a _________ with a _________ line to visualize.
• Compute a ________________ to quantify.

Answer 21

• cause-and-effect
• scatter plot, regression line
• coefficient of determination (R²)

Question 22

___________ is used to predict values of one variable from another:
-(X -> Y) where X is the ___________ (predictor/explanatory) variable, and Y is the ___________ (outcome/response) variable.

Answer 22

• Regression

- independent,dependent

Question 23

What are the 2 types of regression?

Answer 23

• Linear

- Logistic

Question 24

• __________ Regression is used to examine the causal relationship of the two variables, X and Y, that are linearly related.
• Fits a regression line Y=a+bX through the points and estimate a and b

Answer 24

Linear

Question 25

- __________ Regression s used to examine the causal relatonship of the two variables, X and Y, when Y is ______. - It reports the _________ to estimate the odds of membership in the target group linked to the predictor value. - ______________ can also be determined for each OR. - a significant OR will not contain the null value, 1.0, within its confidence interval.

Answer 25

- Logistic, binary - odds ratio (OR) - Confidence Intervals (CI)

Question 26

Assumptions for Regression: - examine a plot of ________ where residual = Y-Ŷ - the residual scores will be randomly dispersed close to zero - Figure: patterns of resduals (Y-axis) plotted against predicted scores (X-axis). - _________ band demonstrates that assumptions for linear regression have been met. - residuals ________ as predicted values increase. - Curvilinear pattern indicates __________ relationship.

Answer 26

-residuals - horizontal band - increase - nonlinear

Question 27

- The ______________ is the square of the Correlation Coeffecient (r). - R² represents the percentage of total variance in the Y scores that can be explained by the X scores. - 1-R² is the percentage of the total variance in Y not explained by the X scores. - A measure of proportion, indicating the accuracy of prediction based on __.

Answer 27

- Coeffecient of Determination (R²) | - X

Question 28

Tests of Relationships (correlation; regression):

Answer 28

1

Question 29

Quiz 1: What do the researchers use correlation for? 1. ) Test the differences between two variables 2. ) Compare the proportions between two variables 3. ) Predict the effect of one variable upon another 4. ) Identify the relationship between two variables

Answer 29

4.) Identify the relationship between two variables

Question 30

Quiz 2: What do the researchers use regression analysis for? 1. ) Test the differences between two variables 2. ) Compare the proportions between two variables 3. ) Predict the effect of one variable upon another 4. ) Identify the relationship between two variables

Answer 30

3.) Predict the effect of one variable upon another

Question 31

Quiz 3: Which of the following is a correct statement about correlation analysis?   1.) A strong linear relationship can be identified as a high correlation coefficient value 2.) It is important to include all the data points to compute the correlation coefficient correctly 3.) Correlation can be used to establish a cause-and-effect relationship 4.) Correlation coefficient is the ratio of risks of exposure vs. non-exposure groups 5.) A hard and fast rule exists for its interpretation in terms of strong, moderate or weak correlation

Answer 31

1.) A strong linear relationship can be identified as a high correlation coefficient value

Question 32

Quiz 6: Which of the following is a correct statement about the correlation coefficient (r) and the coefficient of determination (R2)? 1. ) Coefficient of determination (R2) is the percentage of variance in the predictor variable accounted for by the outcome variable 2. ) Correlation coefficient (r) value ranges from 0 to +1 3. ) Within the same study, the correlation coefficient (r) value can be computed by squaring the coefficient of determination (R2) value 4. ) Coefficient of determination (R2) is the proportion of variance in the outcome accounted for by the predictor variable 5. ) Coefficient of determination (R2) value ranges from -1 to 1

Answer 32

4.) Coefficient of determination (R2) is the proportion of variance in the outcome accounted for by the predictor variable

Question 33

Quiz 7: 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? 1. Chi square test 2. Student’s t-test 3. Correlation analysis 4. Analysis of variance 5. Regression analysis

Answer 33

5. Regression analysis

Question 34

Quiz 8: Which of the following is a correct statement about regression analysis? 1. Logistic regression is used to predict a continuous outcome variable 2. Coefficient of determination (R2) value ranges from -1 to +1 3. Coefficient of determination (R2) is a measure of linear association between two variables 4. Coefficient of determination (R2) is a good measure for an index of predicted variance 5. Linear regression is used to predict a binary outcome variable

Answer 34

4. Coefficient of determination (R2) is a good measure for an index of predicted variance

Question 35

Summary for Tests of Relationships; Correlation, Regression (1): - The association between two variables can be measured using ___________ ____________ - _________ (product-moment) correlation coefficient measures the linear correlation between two continuous variables X and Y - __________ _____ correlation coefficient is a nonparametric analog of the Pearson r and also appropriate for use when X and Y are ordinal variables - _____ ________ correlation coefficient is appropriate for use when X is dichotomous and Y continuous - ____ coefficient is appropriate for use when both X and Y are dichotomous variables

Answer 35

- correlation coefficients - Pearson - Spearman Rank - Point Biserial - Phi

Question 36

Summary for Tests of Relationships; Correlation, Regression (2): - Correlation coefficient value r quantitatively describes the ________ and __________ of a relationship between two variables - The prediction of an outcome from a variable can be tested using __________ analysis - ________ regression examines the causal relationship of X to Y when Y is continuous - _________ regression examines the causal relationship of X to Y when Y is dichotomous - The coefficient of determination R2 quantitatively describes the percentage of the total variance in the Y scores that can be explained by the __________

Answer 36

- strength and direction - regression - Linear - Logistic - X scores