CORRELATION ANALYSIS Flashcards
It shows the relationship between 2 quantitative variables in a visual way.
Scatter plot
This data refers to data set with 2 variables.
Bivariate data
Linear is either ________ or _______.
positive or negative
4 Measures of Association
- Pearson’s Correlation
- Point Biserial Correlation
- Spearman’s Rank Order Correlation
- Chi-Square Test of Association
Measures the strength and direction of the linear relationship between 2 quantitative variables.
Pearson’s Correlation, r
Possible values of Pearson’s Correlation are always between ________.
+1 and -1
Magnitude of Pearson’s Correlation
0 to 0.2 very weak
- 2 to 0.4 weak
- 4 to 0.6 moderate
- 6 to 0.8 strong
- 8 to 1.0 very strong
True or False. In a Pearson’s Correlation, the value of the correlation coefficient does not depend on which of the 2 variables will be assigned as X and Y.
True
True or False. In a Pearson’s Correlation, the absolute value of the coefficient will not change if the units of measurements are changed.
True
True or False. Always use Pearson’s Correlation analysis even if the relationship is explained better by a different curve or pattern that is not linear.
False. DO NOT USE Pearson’s Correlation analysis if the relationship is explained better by a different curve or pattern that is not linear.
True or False. An observed relationship between 2 variables doesn’t automatically imply that there is some cause and effect relationship between the 2 variables.
True
Assumptions of Pearson’s Correlation
- The 2 variables must be at the interval or ratio level.
- There is linear relationship between 2 variables (use scatterplot).
- There should be no outliers.
- The variables should be approximately normally distributed.
Measures the strength and direction of the relationship between 1 continuous variable and 1 dichotomous (without natural ordering) variable.
Point Biserial Correlation, r↓pb
Assumptions of Point Biserial Correlation
- 1 variable must be continuous and the other is binary or dichotomous.
- There should be no outliers.
- The continuous variable is approximately normally distributed for each category of the dichotomous variable.
- The continuous variable has equal variances for each category of the dichotomous variable.
Measures the strength and direction of the monotonic relationship between 2 ranked variables.
Spearman’s Rank-Order Correlation, r↓s
What is the relationship called if one of these are true?
- As the value of one variable increases, so does the value of the other variable; or
- As the value of one variable increases, the other variable value decreases.
Monotonic relationship
Advantages of p↓s:
- Does not assume that the underlying relationship between X and Y is linear.
- No assumptions of normality are made regarding the distributions of X and Y.
- Variables measured in at least ordinal scale.
Aka Pearson’s Chi-square Test or the Chi-square Test for independence.
Chi-square Test of Association
Used to determine if a significant relationship exists between 2 categorical variables from a single population.
Chi-square Test of Association
Assumptions of Chi-square Test of Association
- 2 categorical variables
- 2 or more categories (groups) for each variables
- Independence of observations
a. No relationship between subjects in each category.
b. The categorical variables are not paired in any way (ex: pretest and posttest observations) - Data is in the form of observed frequency counts.
- Relatively large sample size
a. For 2x2 contingency table
i. All expected frequencies should be at least 5
b. For larger tables
i. Expected frequencies for each cell are at least 1
ii. Expected frequencies should be at least 5 for the majority (80%) of the cells
