Analyzing Bivariate Relationships: Chapter 9
- The remaining topics for this course cover cases where two variables are assessed – bivariate relationships
- When the values of one variable change, how do these changes influence the values on the other variable?
- We want to look at the effect or influence of the IV on the DV.
- It is critical to be able to identify the IV and DV in research.
Selecting the Appropriate Statistical Test to Analyze a Relationship
Required steps are:
1. Identify the independent and dependent variables
2. Classify each as being qualitative or quantitative
3. Classify the independent variable as being between-subjects or w/in-subjects in nature
4. Note the number of levels that each variable has.
Our discussion of statistics relevant to the analysis of bivariate relationships will consistently focus on three questions:
1. Given sample data, can we infer that a relationship exists between two variables in the population?
2. If so, what is the strength of the relationship?
3. If so, what is the nature of the relationship?
Principles of Research Design: Statistical Implications
- Two Strategies of Research
- Experimental Strategy – a set of procedures or manipulations is performed to create different values of the independent variable for research participants.
- Observational Strategy (or nonexperimental strategy) – involves measuring differences in values that naturally exist in the research participants.
- Random Assignment to Experimental Groups
- Major goal of research design is to control for alternative explanations.
- To control for differences in participants from one group to another, investigators typically assign individuals to groups.
- Random assignment helps to control for alternative explanations of results.
- Random assignment does not guarantee that the research groups will not differ beforehand on the DV.
- In order to draw unambiguous inferences about relationships between IVs and DVs, it is necessary to control for other variables in the research setting.
- Confounding Variable- is one that is related to the independent variable (the presumed influence) and that affects the dependent variable (the presumed effect), rendering a relational inference between the IV and DV ambiguous.
- Random assignment is one way to control for confounding variables.
- Between-Subjects (independent-groups) – different individuals in each level of the independent variables.
- Interested in the difference between groups of individuals exposed to the IV.
- Within-Subjects (correlated groups or repeated measures) – same individuals are exposed to each level of the independent variable.
- Interested in the differences within individuals exposed to the IV.
Independent Groups t Test: Chapter 10
- First bivariate test statistic we’ll cover – independent groups t test
- Different from one-sample t test
- Typically used to analyze the relationship between two variables under these conditions:
- DV is quantitative in nature and measured on a level that at least approximates interval characteristics
- The IV is between-subjects in nature (generally is qualitative in nature)
- The IV has two and only two levels.
Want to answer three questions:
EXAMPLE:
- Research Question: Can people manipulate their scores on personality test by "faking" a good impression?
1) IS THERE A RELATIONSHIP BETWEEN THE IV AND DV?
- Step 1: State the null and alternative hypotheses:
(the population means for the two groups are equal)
(the population means for the two groups are not the same)
- Step 2: Get the critical values and state decision rules
- We’ll hold off on this step until we talk about the test statistic
- Step 3: Compute the relevant values for your test statistic:
- Compute the 
’s
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Instead of:
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We now test:
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- Just like before, we’re comparing our observed sample value to our hypothesized population value – taking into account the sampling error in our sample value.
- This is basically an extension of the one-sample t statistic we already covered.
- So, we need to compute sample means for the numerator and our "standard error" estimate for the denominator.
- Since we’re now testing the difference between means, our denominator is the estimated standard error of the difference between means 
- The book gives a couple versions of the formula for this statistic – here’s one:
- n1 and n2 refer to the number of people/scores in each group
- just like our previous standard error of the mean, as N gets bigger, the standard error of the difference gets smaller
, we first need to "pool" the two sample variances 
- Step 4: Compute the test statistic (independent groups t-test)
- Step 5: Compare to expected results/critical values.
- The "underlying sampling distribution" has the same shape as the one-sample t.
- So, we get our critical values from Appendix D
- The only difference now is that we figure our df differently
- For the one-sample t, df = N-1
- For the independent-groups t, df = (n1-1) + (n2-1) = n1 + n2 – 2
- This is the same df we used in our pooled variance formula
