Exam
enla
comm3023_ch12p2_2020.pptx
Chapter 12
Quantitative Data Analysis: Part 2
Logic of Hypothesis Testing
Calculating inferential statistics allow us to test hypotheses to determine:
If 2 or more variables have linear relationships (hypothesis of covariation)
If 2 or more groups differ on an outcome variable (hypothesis of difference)
Statistical tests examine the probability that an observed linear relationship between variables or differences between groups occurred by chance
Errors in Hypothesis Testing
| Null should not be rejected in reality | Null should be rejected in reality | |
| Decide to reject the null based on test | Type I error – Null is rejected even though it should not be | Decision 1 – Null is rejected when it should be |
| Decide not to reject the null based on test | Decision 2 – Null is not rejected when it should not be | Type II error – Null is not rejected even though it should be |
Testing Hypotheses of Covariations
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Hypotheses of covariation focus on predicting linear relationships between two or more interval/ratio-level variables.
There are 2 options available for testing linear relationships:
Regression
Both tests are similar in their abilities to test for a linear relationship between variables, but not a curvilinear relationship.
Key difference is in interpretation of the 2 variables examined.
Correlation – either variable can be the IV or DV
Regression – there is a clear indicator of the IV and the DV
Correlation
Correlations
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Correlation coefficient r has values ranging from -1.00 to 1.00
Number provides an indicator of strength of the linear relationship
Sign provides direction of relationship
Four common types:
Pearson correlation
Point-biserial correlation
Phi correlation
Spearman rho correlation
Interpreting the Coefficient
Direction
of relationship
Positive- both variables increase or both variables decrease
Negative – one variable increases while the other decreases
Relationship strength
< .20 – slight, almost negligible
.20-.40 – low, definite but small
.40-.70 – moderate, substantial
.70-.90 – high; marked
>.90 – very high or dependable
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Regressions
Estimates the linear relationships between one or more independent variable(s) and a dependent variable.
Regression analysis focuses on finding the best fitting straight line to predict the dependent variable based on the data.
General formula for regression line: Y = a + bX
a is the Y-intercept
b is the slope/regression coefficient:
Scatterplot: Cumulative GPA and Semester GPA
Scatterplot: Cumulative GPA and Number of Drinks
Regressions
Regression coefficient indicates magnitude of the effect
There are 2 basic types of regressions:
Simple linear regression
Multiple regression
Other Forms of Regression
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Hierarchical regression Researcher enters IVs in the order in which they are theoretically presumed to influence the DV.
Stepwise regression
Order of variables is determined by statistical analysis based on the degree of influence each IV has on the DV.
Beta Weights
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Also known as beta coefficients (β)
Provides a standardized measure of the magnitude of influence for different IVs on the DV.
Coefficients range from +1.00 to –1.00
