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Examining Relationships in Quantitative Research

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Examining Relationships in Quantitative Research

12

- Understand and evaluate the types of relationships between variables
- Explain the concepts of association and covariation
- Discuss the differences between Pearson correlation and Spearman correlation

- Explain the concept of statistical significance versus practical significance
- Understand when and how to use regression analysis

Presence

Direction

Strength

of association

Type

- Is there a relationship between the two variables we are interested in?
- How strong is the relationship?
- How can that relationship be best described?

- Covariation is amount of change in one variable that is consistently related to the change in another variable
- A scatter diagram graphically plots the relative position of two variables using a horizontal and a vertical axis to represent the variable values

- Pearson Correlation Coefficient–statistical measure of the strength of a linear relationship between two metric variables
- Varies between – 1.00 and +1.00
- The higher the correlation coefficient–the stronger the level of association
- Correlation coefficient can be either positive or negative

- The two variables are assumed to have been measured using interval or ratio-scaled measures
- Nature of the relationship to be measured is linear
- Variables to be analyzed come from a bivariate normally distributed population

- Coefficient of Determination (r2) is a number measuring the proportion of variation in one variable accounted for by another
- The r2 measure can be thought of as a percentage and varies from 0.0 to 1.00
- The larger the size of the coefficient of determination, the stronger the linear relationship between the two variables under study

- Spearman Rank Order Correlation Coefficient is a statistical measure of the linear association between two variables where both have been measured using ordinal (rank order) scales

- A method for arriving at more detailed answers (predictions) than can be provided by the correlation coefficient
- Assumptions
- Variables are measured on interval or ratio scales
- Variables come fro a normal population
- Error terms are normally and independently distributed

- y=a + bX + ei
- y=the dependent variable
- a=the intercept
- b=the slope
- X=the independent variable used to predict y
- ei=the error for the prediction

- OLS is a statistical procedure that estimates regression equation coefficients which produce the lowest sum of squared differences between the actual and predicted values of the dependent variable

- Adjusted R-square
- Explained variance
- Unexplained variance
- Regression coefficient

- Answers these questions
- Is there a relationship between the dependent and independent variable?
- How strong is the relationship?
- How much influence does the relationship hold?

- Multiple regression analysis is a statistical technique which analyzes the linear relationship between a dependent variable and multiple independent variables by estimating coefficients for the equation for a straight line

- A beta coefficient is an estimated regression coefficient that has been recalculated to have a mean of 0 and a standard deviation of 1 in order to enable independent variables with different units of measurement to be directly compared on their association with the dependent variable

- Assess the statistical significance of the overall regression model using the F statistic and its associated probability
- Evaluate the obtained r2 to see how large it is
- Examine the individual regression coefficient and their t-test statistic to see which are statistically significant
- Look at the beta coefficient to assess relative influence

- Multicollinearity is a situation in which several independent variables are highly correlated with each other and can cause difficulty in estimating separate or independent regression coefficients for the correlated variables