Psych 308 Lecture Quiz 14 (Chi-Square)

Effect size Cramer's V for chi-square tests of independence is interpreted like which other effect size, but for nominal variables? A) d B) R2 C) r D) OR

C) r

What is the key difference between goodness-of-fit and tests-of-independence?

Chi-square goodness-of-fit analyses involve one nominal variable, while chi-square tests of independence involve two nominal variables.

Which of the following possible studies of gender and depression would most likely involve chi-square goodness-of-fit analyses?

Examine whether people diagnosed with depression are more likely to be male or female.

What is the unit of analysis for chi-square?

Frequencies

How is the Odd Ratio interpreted?

LDS youth are 5.5 more likely to be heterosexual than Other youth.

What is the appropriate interpretation of these results?

LDS youth are less likely to be sexual minorities than youth from other religious identifications

Which of the following yields more power for chi-square?

Larger difference between Os and Es

How do we interpret the size of this effect?

No effect size was reported

Define: Non-parametric statistics

Non-parametric statistics are statistics that don't involve population parameters. They don't assume a particular population shape. They also typically focus on nominal (or ordinal) variables. Oftentimes, people make non-parametric versions of parametric statistics (for use with nominal or ordinal). This would be statistics like chi-square.

Define: Odds Ratio (OR)

Odd's ratio is another type of effect size that we can calculate during Chi-square analysis. Also called a d class effect size, it's a ratio of the odds of one thing to the odds of another thing.

What kind(s) of variables are needed to run a chi-square?

Only nominal variables

How is the Cramer's V interpreted?

Religious affiliation is moderately linked to sexual orientation.

The Foundations researchers suspected that the proportion of sexual minorities (non-heterosexual) would be lower among Latter-day Saint youth than those of other religious identifications. They examined this hypothesis using a chi-square test of independence, χ2(1) = 91.67, p < .001, Cramer's V = .23, OR = 5.50. Below is the cross-tabs table. How is the chi-square interpreted?

Religious affiliation is significantly linked to sexual orientation.

What kinds of research questions are chi-square goodness of fit analyses used to answer?

Research questions involving particular univariate frequency distributions.

What does the typical null hypothesis look like for chi-square goodness-of-fit?

The frequencies are equally distributed across groups in the population.

What do the top and bottom of chi-square formula represent?

The pattern of frequencies you observed over the pattern of frequencies you would expect to get if the null hypothesis were correct.

How is an Odds Ratio of 1.0 interpreted in a chi-square test of independence?

The two nominal variables are independent.

What does the typical null hypothesis look like for chi-square test of independence?

The two nominal variables are independent.

What does the typical alternative hypothesis look like for chi-square test of independence?

The two nominal variables are related (odds of being in a particular group on one variable depend on which group in on the other variable).

What does the typical alternative hypothesis look like for chi-square goodness-of-fit?

The percentage of people are not equally distributed across groups in the population.

The Foundations researchers wanted their sample to be 50% Latter-day Saint families and 50% families of other religious identifications. They created a dichotomous nominal variables coded as 0 = Other (N = 809), 1 = LDS (N = 882), and ran a chi-square goodness-of-fit test on it, χ2(1) = 3.15, p = .08. What can be concluded from this chi-square goodness of fit test?

The proportion of LDS families is not significantly different from that of the other families.

When you retain the null hypothesis in a chi-square, how do you statistically interpret the results?

There is greater than a 5% chance of getting your size of chi-square coefficient, with your sample size, if the null hypothesis were true.

When you reject the null hypothesis in a chi-square, how do you statistically interpret the results?

There is less than a 5% chance of getting your size of chi-square coefficient, with your number of cells and people, if the null hypothesis were true.

Define: Observed frequencies

These are the frequencies that you observe in your data that you collected.

Define: Expected frequencies

These are the frequencies that you would expect in your data if the null hypothesis was true in the population.

Which of the following is true of non-parametric statistics?

They do not involve estimating population parameters (mean and standard deviation).

Define: Cramer's V

This is the correlation coefficient we use in Chi-square tests. It's the correlation coefficient between nominal variables. So far we have just been using it to determine correlation between 2 variables. For 2 nominal variables, a Cramer's V of ~0.1 is considered small, ~0.3 is considered medium, and ~0.5 is considered large.

What is the underlying logic of hypothesis tests for chi-square goodness-of-fit?

We are trying to figure out the probability of getting the univariate frequency distribution we observed if the null hypothesis is correct and there is a particular (usually equal distribution across cells) expected distribution in the population.

Which of the following is the chi-square formula? A)∑(O−E)2E B)∑(O−E)2E C)∑(O−E)2E D)∑(O−E)2

E(O-E)^2/E

Which of the following possible studies of gender and depression would most likely involve chi-square test of independence?

Examine gender differences in likelihood of a depression diagnosis.

Describe what makes chi-square unique compared to all the other stats we have learned (z-tests, t-tests, ANOVA, correlation, and regression). Include in your answer (a) the type of inferential statistic it is, (b) what makes it that type of statistic, (c) the type of data involved, (d) the unit of analysis, and (e) the types of research questions you can address.

a) Chi-square is a non-parametric statistic b) Chi-square is non-parametric because it doesn't involve population parameters, it doesn't assume a particular population shape, and it typically only focuses on nominal (or ordinal) variables c) Chi-square uses one sample, one wave, and one nominal variable if doing a goodness of fit test, or one sample, one wave, and two nominal variables if doing a test of independence d) The unit of analysis is frequencies or proportions e) You can address research questions like "Do frequencies on a single nominal variable have a certain distribution (typically equally distributed across categories)?" That would be for a Chi-square goodness of fit test. You could also address a question like "Are the two nominal variables related?" That would be for a Chi-square test of independence.

Think of how you might use chi-square goodness of fit to analyze a variable of interest to you. Then, (a) list your chosen variable and the type of variable (nominal, ordinal, ratio), (b) state your research question, (c) state the research hypothesis, (d) state the null hypothesis, (e) state the alternative hypothesis.

a) I would analyze whether people prefer hamburgers over hot dogs or if they have no preference. This would be a nominal variable. Essentially I would be saying "Do people prefer hamburgers, or do they have no preference?" b) Are frequencies on hamburger preference equally distributed between preference and no preference ? c) People are more likely to choose hamburgers over hot dogs. d) People are just as likely to choose hamburgers as they are to choose hot dogs. e) People significantly prefer hamburgers over hot dogs.

Think of how you might use chi-square test of independence to analyze variables of interest to you. Then, (a) list your chosen variables and the types of variables (nominal, ordinal, ratio), (b) state your research question, (c) state the research hypothesis, (d) state the null hypothesis, (e) state the alternative hypothesis.

a) I would measure hamburger preference in men vs women. So my chosen variables would be hamburger preference (or absence of) and gender (male or female). These would both be nominal variables. b) My research question would be "Are hamburger preference and gender related?" c) My research hypothesis would be "Women are more likely to choose hamburgers than men." d) The null hypothesis would be "Hamburger preference is independent of gender. Men and women are equally likely to choose hamburgers over hot dogs." e) The alternative hypothesis would be "Hamburger preference is related to gender. Specifically, women are more likely to choose hamburgers than men."