Chi-square

Which of the following is the chi-square formula?

C

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 O"s and E's

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. How do we interpret the size of this effect?

No effect size was reported

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.

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.

Non-parametric statistics

Statistics associated with frequency, are only used for all nominal, and do not use population parameters such as mean, You also need to mention that they don't assume a particular shape (like a normal distribution).

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.

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

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

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.

Effect size Cramer's V for chi-square tests of independence is interpreted like which other effect size, but for nominal variables?

r

Observed frequencies

the number of times that a specific instance of a nominal variable occurs

Expected frequencies

the number of times that a specific instance of a nominal variable would occur if the null is true in the population, typically equal distribution

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) Non-parametric statistic b) made up of nominal variables and the measure of how many or frequency c) 1 group, 1 wave, nominal variable or 1 group, 1 wave, nominal variables d) frequencies, proportions, or percentages e) Are two nominal variables related? Is the likelihood of being in a particular category on one variable dependent on which category a person is on the other variable? Do frequencies on a single nominal variable have a certain distribution?

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) school-nominal, relationship status-nominal b) Is the likelihood of being in a relationship dependent on going to BYU or UofU? c) The likelihood of being in a relationship changes depending on whether someone goes to BYU or UofU d) The likelihood of being in a relationship is not dependent on going to BYU or UofU e) The likelihood of being in a relationship is dependent on going to BYU or UofU

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) type of listening devices (nominal) b) What is the preferred type of listening device for BYU students? c) More BYU students will prefer AirPods headphones d) BYU students will like all types of listening devices the same e) BYU students will prefer AirPods headphones over other types of phones

Odds Ratio (OR)

bivariate effect size for chi-square, ratio of odds of something to odds of something else

Cramer's V

correlation coefficient between two nominal variables