Logic of Control & Sampling Chs. 4 & 6

The Case of the Surgeon… Test Group & Control Group (We need a comparison!) ▫Test Group=The subjects who receive a treatment that the researcher believes is causally linked to the dependent variable. ▫Control Group= The subjects who do not receive the treatment…(see above) We need the groups to be identical in every other way to get an effective measurement! WHY?

Rival Explanations Exist Surgery example: Was it just the surgery that increased survival rates? What other factors could be impacting the dependent variable? In other words we have to control for rival explanations…i.e. age, health, etc. What about in politics? (Hint: True for us too!)

Rival Explanations in Politics Favor/Oppose gun control & political party affiliation. ▫H1: Democrats will be more likely than Republicans to support gun controls. What should we control for though? ▫Gender? Women are more likely to be Democrats than Republicans…so is it gender or political affiliation that determines support/opposition to gun control?

Research Design Using a strong research design will help us to rule out the alternative explanations (controls) that might otherwise impede our ability to evaluate the impact of the independent variable on our dependent variable. Experimental vs. Controlled comparison design (most common in our field)

Experimental Designs: 2 Types Laboratory Experiments= Environment is created by the investigator for both the test and control groups. Field Experiments= Control & test groups are observed in their natural setting/environment. Common Thread? ▫Individual subjects are randomly assigned to the control/test groups. (Random Assignment)

Random Assignment What is it? Random assignment “occurs when every prospective participant has an equal chance of being in the control group or the test group. So, if we have just those two groups, individuals should have a.5 or 50% chance of being selected for each group.

Random Assignment Cont. Random assignment takes prior differences out of play. Media Coverage example. (p. 81) Research designs that do not use random assignment are vulnerable to selection bias- which indicates that individuals in the test group are different from those in the control group.

Laboratory Experiments Validity ▫Internal: Within the artificial environment set up by the researcher, the effect of the independent variable on the dependent is isolated from other plausible explanations. ▫External: The results of the study can be applied to real-life or real-world situations. (Can we generalize our results?)  Limitation: In a controlled setting we may not have a good representation of the real-world.

Field Experiments Field experiments can help us overcome the limitations of lab experiments because the study occurs in natural environment. Limitations: Internal validity (are other factors impacting Y being isolated?) Experimental Research designs are not always possible (especially in Political Science) so….

We use Controlled Comparisons In other words, after making a comparison in our hypothesis, we examine the relationship between X & Y while holding other variables constant. Remember the gun control & party ID example. (Party ID is not a random process) Democrats and Republicans might have a difference in support for gun control, but how else might Republicans & Democrats be different?

Compositional Differences Republicans & Democrats have compositional differences…such as gender, age, race, & income. These differences all offer rival explanations for explaining support for gun control. We must account for these to avoid the risk of confusing effects. We will refer to these as “Z” variables.

Z-Variables X (Independent variable) Y (Dependent variable) Z (Rival Causal variable) We have to hold Z constant- in other words if we have a group both Republican and Democratic Women in our study and determine favor/opposition to gun control we know that gender (Z) is not impacting the results of our study.

3 Scenarios after Controlling for Z Spurious Relationship between X & Y ▫This means after keeping Z constant, X does not cause Y. Additive Relationship ▫X retains a causal relationship with Y, but Z also explains Y to some degree. Interaction Relationship ▫Different values of Z have different impacts on X & Y’s relationship.

Ch.6 Inferential Statistics ▫Procedures that tell us how closely a relationship we observe in a sample corresponds to the unobserved relationship in the population. ▫Essentially, applying our small study to the real- world.

The Basics Population-What is it? ▫A population includes the entire universe of cases a researcher wants to describe.  If you were studying Congressional elections, your population might be all voting-eligible adults. ▫You might be more interested in a characteristic of the population called a population parameter.  From the above example, you may want to study just those voting-eligible adults who voted in the last Congressional Election.

Basics cont. Sample-What is it? ▫A sample is simply a number of cases drawn from a population. (sample size is often denoted as “n”, n=100 means you have 100 cases in your sample.) But we also have sample statistics ▫These are estimates of population parameters based upon a sample drawn from the population.  An example of this is public polling…we may interview only 500 voters in New Hampshire to determine how the entire state will likely vote.

Factors to Consider Several factors determine how closely a sample statistic represents a population parameter. We must use random sampling to avoid selection bias! (1936 Literary Digest) We must have random selection. Even though we can eliminate selection bias, we cannot eliminate error…

Random Sampling Error This refers to the extent to which a sample statistic differs, by chance from a population parameter. Population Parameter= Sample Stat. + RSE The magnitude of RSE depends on the sample size and the amount of variation in the population characteristic being measured.

RSE Cont. Sample size & RSE have an inverse relationship. ▫As the sample size increases, RSE decreases. Variation & RSE have a direct relationship. ▫AS variation increases, RSE increases. RSE = variation component/sample size component

RSE Formulae Sample size component can be found by taking the square root of n (# of cases). When n=400, the sample size component would be 20. To find the RSE we would take the variation component/20.