Empirical Political Analysis Quiz 3

how do you do a controlled comparison

examine the relationship between the IV and the DV while holding rival causal variable constant

what does “controlling for” a variable mean

holding that variable constant (neutralizes its effect)

when you control a variable, you..

keep it at a single value

controlling for rival hypotheses can possible reveal

1. spurious relationship

2. additive relationship

3. interactive relationship

what is a zero-order relationship (uncontrolled relationship)

a direct association between two variable without controlling for the influence of any third variables (doesn’t take into account any other possible differences between the cases)

what is a partial relationship

when you are only looking at a subset of the data (X and Y when Z=n)

what is learned from controlled comparisons

1. controlled effect of x on y for a given value of z

2. we also can see what effect z has on y for each value of x

spurious relationship

where the control variable defines the variation in x and the compositional difference is the cause of Y

additive relationship

IV and control variable are not correlated

• both x and z cause y to increase and x and z are unrelated

interactions

value of the control variable shapes the effect that x has on y

• x may have a stronger or weaker effect on y when in the presence of z

a cross tab analysis only workin on what types of data

ordinal or nominal

when do we use a means comparisons

with interval level dependent variables

we should graph mean comparisons with what type of graph

line graph

what do the lines in the line graph of a mean comparisons tell us

1. if lines do not overlap, the control variable has an effect on y

2. if the lines has a pos/neg slope the iv affects the dv

what is inferential statistics

used to determine whether the relationship we observe in our sample reflects the (unobserved) dynamics of our population

population

the entire possible group

sample

selected from the population but does not include all members of the population

sample

selected from the population but does not include all members of the population

census

when you have data on the entire population - every single individual

population parameter

some characteristic or property of the population that we are interested in

why are population parameters often unknowable

we cannot do a census

sample statistic

estimate of the population parameter that you get from looking at a sample

random sampling error

occurs when the sample selected for analysis is not perfectly representative of the entire population due to chance

the distribution of sample statistics for any variable is

normally distributed

central limit theorem

regardless of how the variable is distributed, if you do an infinite number of samples, the sample means will have a normal distribution

the standardized variable has a mean of what and the x axis is

0, how many standard deviations away from the mean

culmative density

percentage of cases under the curve

what are influences on how well your sample statistics match the population parameter

1. sample quality

2. sample size

3. variance

what are the different ways to reduce standard error

1. random sampling

2. bigger sample sizes

3. data with less variance will have a lower standard error

   1. SE is how much on average the sample statistic will vary when done repeatedly through random samples

if you have a nominal or ordinal variable, you can only calculate

what proportion of cases belong to that category

confidence intervals

range of values so defined that there is a specified probability that the value of a parameter lies within in it

95% confidence interval

95% of the time, the population parameter falls within this interval

margin of error

statistic expressing the max unexpected difference between true population results and survey findings

if there is a small sample size and an unknown population standard deviation, what do you need to use

students t distribution

t distributions are different depending on what and they have different critical values for the confidence intervals depending on what

n, sample size

tests of statistical signficance

procedure for determining whether a hypothesis about a population parameter should be rejected based on a sample

what are the 5 steps to hypothesis testing

1. propose a research hypothesis (which implies a null hypothesis)

2. set the significance level (usually 0.05)

3. estimate relevant population parameters using sample data

4. calculate the confidence interval or p value

5. reach a conclusion about the null hypothesis

you don’t test the null directly instead you

attempt to disprove it using a proof by contradiction

• null asserts that differences between the sample and the population are purely due to random chance

to test the null you need to

choose a confidence interval that you are willing to accept

Hypotheses can be either

directional or non directional

based on the sample you can either blank or blank

fail to reject the null or reject the null

type 1 error

when you falsely find a relationship where there is none

why is type 1 error sometimes called false positive errors

you falsely find a relationship where none exists

type II errors

when you fail to reject a null hypothesis that is false

• you may find a difference but not a strong enough one to confidently reject the null

why do we have a high standard for tests of statistical signifance

wee want to be conservative about making false positive claims, so we risk making type 2 errors over type 1

what are the levels of significance

a (alpha)

p value

confidence interval

a (alpha)

the predetermined confidence interval you require to reject the null hypothesis

p value

the probability of finding that result assuming the null is true

• range

  • 0 to 1, least likely to most likely

confidence interval

range around the mean/proportion where the population parameter can lie

when p <a you can

reject the null

p < 0.05 means

you can reject the null hypothesis with 95% confidence

usually the null is equal to zero, so if zero is not in the confidence interval you chose, you can reject the null

true

one tail test

only looks one directionally

two tailed test

considers whether there is a positive or negative relationship

• have to use a different critical value

testing one sample hypotheses requires what

having some artificial baseline for comparison against

2 sample hypothesis test compares what

two samples against one another instead of to a hypothesized value

when working with two samples you calculate what

the standard error for the difference

when do you use error bar charts

to test hypothesis as well as part of a difference in means test

what do error bar charts show

the sample mean and the confidence interval around it

if the confidence intervals do not overlap in an error bar chart what does that mean

they are statistically different from each other

to calculate a difference in means test

use a t distribution