HLTH 200
Analysis for Research Design
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Understanding Two-Variable Linear Model & t-Tests: Inferential Stats & Regression - Prof. , Study notes of Health psychology
An in-depth exploration of inferential statistics, focusing on the two-variable linear model and t-tests. The two-variable linear model is a statistical technique used to establish a relationship between two variables, while t-tests assess the statistical significance of the difference between the means of two groups. Key concepts include the general linear model (glm), components of the linear model, dummy variables, and the use of dummy variables in regression equations. The document also covers the t-test formula, idealized distributions for treated and control group posttest values, and three scenarios for differences between means.
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2012/2013
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HLTH 200
Analysis for Research Design
Inferential Statistics
- (^) Process of trying to reach conclusions that extend beyond the immediate data
- (^) “Inferring” information about the population from the sample data
- (^) All are based on the general linear model (GLM)
The Two-Variable Linear Model: A
Bivariate Plot
The Two-Variable Linear Model: A
Straight-Line Summary of the Data
The Two-Variable Linear Model: The
Two-Variable Linear Model
The Two-Variable Linear Model:
What the Model Estimates
Dummy Variables
- (^) A numerical variable used in the GLM to represent subgroups of the sample in your study
- (^) Typically used to distinguish different treatment or program groups (e.g., to distinguish the treatment group from the control group)
- (^) Eliminates the necessity of separate equation models for each group
- (^) Dummy variable, although nominal level (i.e., 1, 0), can be treated statistically like an interval-level variable
Use of a Dummy Variable in a
Regression Equation
where: y i = Outcome score for the i th unit β 0 = Coefficient for the intercept β 1 = Coefficient for the slope z i = 1 if i th unit is in the treatment group 0 if i th unit is in the control group ei = Residual for the i th unit y i = β 0
- β 1 z i
- e i
Determining the Difference between Two
Groups by Subtracting the Equations Generated
through Their Dummy Variables
The t -Test (Brown & Melamed, 1990)
- (^) Assesses whether the means of two groups are statistically different from each other (i.e., whether there is a statistically significant difference between group mean scores)
- (^) Assesses the difference in mean scores relative to the variability of scores (i.e, the standard error of the difference)
Three Scenarios for Differences
between Means
Formula for the t -Test:
How the t -Test Formula Relates to the
Distribution of the Data for the Groups
Formula for the t -Test
The t -Test (cont’d)
- (^) Determination of whether or not a t -value is large enough to be significant can be determined from a standard table of significance given: (^) t -value (^) alpha level (most commonly .05) (^) df (number of persons in both groups minus 2)