poli 209 unc macdonald final key ideas

What is a nominal variable?

Response categories that are mutually exclusive and exhaustive. Mutually exclusive means that the categories do not overlap, so a response cannot go into more than one category. Exhaustive means that there is a category for every response. The response categories are distinct, but they are not ordered in any meaningful way. [Example is religpref.]

What is an ordinal variable?

Response categories that are mutually exclusive and exhaustive and the categories exhibit a meaningful order or ranking - for example, from low to high or from always to never. The response categories are distinct and ordered, but they do not have any intrinsic numeric quality. [Example is govtrust.]

What is an interval variable?

Response categories that are mutually exclusive and exhaustive, exhibit a meaningful order, and are intrinsically numeric with equal intervals between the successive categories - for example, years of age or number of children. [Example is yearschool.]

The Macdonald Rule for Quasi-Interval Variables

If the wording of the question, as posed by the interviewer, directs the respondent to think of a numerical scale with equal intervals, then we will consider the variable to be interval level.

What is the mode of a variable?

Most frequently given response (or the response category that occurs most frequently). The mode is appropriate for each of the levels of measurement. It is the only measure of central tendency appropriate for nominal variables.

What is the median of a variable?

Response given by the middle respondent in an ordered distribution of respondents (or the response category that comes closest to being in the middle of the ordered distribution). The median depends on an ordered distribution of responses, so it is only appropriate for variables at the ordinal and interval levels.

What is the mean of a variable?

Average of all the valid responses given. For grouped data, we multiply the frequency times the numerical value, sum them up, and divide by the total number of valid responses. Because the mean involves mathematical calculations, it is only appropriate for interval-level variables.

___ = Sum fv/N

Nominal Level dispersion

Display bar charts to see the extent of variation in the responses.

Ordinal Level dispersion

Consensus is a situation in which almost everyone takes roughly the same position on an issue. (low dispersion)

Dissensus is a situation in which opinion is spread out fairly evenly across positions on an issue. (high dispersion)

Polarization refers to the situation in which opinion is split between opposing sides on an issue with relatively few people taking the moderate or middle-of-the-road position.

The bar chart will have a U or V shape.

Interval Level dispersion

Symmetry or Skewness

Determine whether the distribution is symmetrical or skewed.

A symmetrical distribution has a similar pattern on each side of the middle value.

A skewed distribution is asymmetrical with a long skinny tail on one side of the distribution. When the tail is on the right-hand side, we say the skew is positive; when the tail is on the lefthand side, the skew is negative.

also variance and standard deviation but she said she won't make us calculate those but to know higher variance and standard deviation means more spread in the responses than a lower value does, given that the variables are measured in the same way.

Causal hypothesis

Asserts an explicit relationship between an independent variable and a dependent variable. It states that the independent variable influences the dependent variable and in what way.

Perfect Relationship

We would see 100% in each of the cells on the diagonal, and 0% in the off-diagonal cells. In other words, all of the first group of the IV would be in the first row of the DV, all of the second group would be in the second row, and all of the third group would be in the third row. The percentage point difference (PPD) would be 100.

No Relationship

The values are constrained by the marginal distribution of the DV, the view of creation. So the distribution within each column (i.e., each group) must be the same as the total distribution.

Measures of association can vary between + and - 1.0. There are many different measures of association, but they all share the following five characteristics:

The absolute value of a measure of association equals 1.0 if there is a perfect relationship between the two variables.

The measure of association equals zero if there is no relationship.

The larger the absolute value of the measure of association, the stronger the relationship.

A value greater than zero indicates a positive relationship.

A value less than zero indicates a negative relationship.

Hypothesis in ordinal style:

The more liberal a person is, the more likely they are to disapprove of the job Trump is doing as President. OR The more conservative a person is, the more likely s/he is to approve of the job Trump is doing as President.

monotonicity

Moves in a consistent direction across the categories of the independent variable. In other words, the percentage of people giving a certain response on the dependent variable consistently rises across the categories of the independent variable, or consistently falls, but does not go up and down.

margin of error

you can say with 95% confidence that your data is between +- MOE from the percent you got. So, say one of your percents is 43% and the margin of error was +-3%, then you could say w 95% confidence that your data is between 40% and 46%

MoE = 1.96 x [sq rt of (p ( 1 - p ))] / n -1

MoE = 1 / sqrt of N

The margin of error depends on the size of the sample: The larger the sample, the smaller the margin of error.

So size matters in probability sampling. In fact, you have to quadruple the sample size in order to cut the margin of error in half.

There is an inverse relationship between the margin of error and the square root of the sample size.

Graphing a Relationship Using a Clustered Bar Chart with Percentages

DV = category axis

IV = cluster variable

Four Tests for a Causal Relationship

he relationship must pass four tests. These are summarized below, and we will discuss them.

Association - a change in one variable should be associated with a change in the other.

Temporal order - a change in the presumed cause should precede the change in the presumed effect.

Alternative causes - the researcher must rule out alternative causes (or rival explanations) that might account for the relationship between the two variables.

Causal mechanism - the researcher should provide a plausible explanation of how the independent variable might influence the dependent variable. (We call this "theory.")

spurious relationship

a relationship between two variables that is produced by their joint dependence on a prior variable

When we perform a control for a prior variable, several different results can occur:

(1) The original relationship can be maintained within each control group; then we conclude that the relationship is not spurious due to that variable.

(2) The original relationship can vanish within each control group; then we conclude that the original relationship was spurious due to that variable.

(3) The original relationship can weaken within each control group; then we conclude that the original relationship was partially spurious due to that variable.

(4) The original relationship can be maintained within one control group and vanish (or weaken significantly) within another control group; then we conclude that the relationship is conditional upon the value of the control variable. This is also called specification or an interaction effect.

Analyzing 2 independent variables to explain 1 dependent variable

To do this, we perform a controlled analysis, as we have done before. Either explanatory variable can be the independent variable in the analysis and the other one will be the control (or layer) variable

index

Combination of two or more variables that creates a new variable.