Chi square is a statistical test of association between variables that compares Quizlet

Test of independence. A single random sample of observations is selected from the population of interest, and the data are categorized on the basis of the two variables of interest. For example, in the marketing research example above, this sampling strategy would indicate that a single random sample of companies is selected, and each selected company is categorized by size (small, medium, or large) and whether that company returned the survey.
In this case, you have two variables and are interested in testing whether there is an association between the two variables. Specifically, the hypotheses to be tested are the following:
H0: There is no association between the two variables.
Ha: The two variables are associated.

Test for homogeneity. Separate random samples are taken from each of two or more populations to determine whether the responses related to a single categorical variable are consistent across populations. In the marketing research example above, this sampling strategy would consider there to be three populations of companies (based on size), and you would select a sample from each of these populations. You then test to determine whether the response rates differ among the three company types.
In this setting, you have a categorical variable collected separately from two or more populations. The hypotheses are as follows:
H0: The distribution of the categorical variable is the same across the populations.
Ha: The distribution of the categorical variable differs across the populations.

Narrative for the Methods Section
"A chi-square test was performed to test the null hypothesis of no association between type of crime and incidence of drinking."

Narrative for the Results Section
"An association between drinking preference and type of crime committed was found χ2 (5, N = 1,426) = 49.7, p < 0.001."

Or, to be more complete,
"An association between drinking preference and type of crime committed was found, χ2 (5, N = 1,426) = 49.7, p < 0.001. Examination of the cell frequencies showed that about 70% (144 out of 207) of the criminals convicted of fraud were abstainers, while the percentage of abstainers in all of the other crime categories was less than 50%."

They are for FREQUENCY DATA. (like frequency distribution- how many times a variable occurred)

Chi Squared test when you collect the data and compare it with your expected results/expected frequency. (ANOVA looks at the difference between means, which mean is significantly bigger/is there a significant difference between these two mean: men and women's scores on sexual drive. Men have higher mean, you test to see if its significant)

- in Chi square tests, you don't have 2 means, but you have an observed DATA (you collect data) and then you compare it to what you would EXPECT. ex: if u flip a coin 20x, you expect to get 10 H and 10T..but when you actually flip it, b/c of error you can get 12H and 8T...in CHI squared, you compare the two , the observed and the expected.

About the Chi-Square Test

Generally speaking, the chi-square test is a statistical test used to examine differences with categorical variables. There are a number of features of the social world we characterize through categorical variables - religion, political preference, etc. To examine hypotheses using such variables, use the chi-square test.

The chi-square test is used in two similar but distinct circumstances:
a.for estimating how closely an observed distribution matches an expected distribution - we'll refer to this as the goodness-of-fit test
b.for estimating whether two random variables are independent.

They are Nonparametric tests. Means they DO NOT assume/ they don't HAVE to have the following:

1) interval level of measurement--means instead of having solid numbers like in a normal distribution (mean) , you use nominal/categorical data.
2) data normally distributed--means in Chi square ur assuming that u have a SKEWED distribution instead of a normal distribution"

(meaning in order to use the Chi test, you don't HAVE to have interval level measurement and ur data does NOT have to be normally distributed)

If ur data is normally distributed AND you have interval measurments (#'s), then its MUCH better to use Parametric tests (ANOVA, t-test, MANOVA, Regression)

Parametric tests deal with normally distributed data, but non parametric deals with data that is skewed.."we don't have the perfect normally distributed data, but we use nonparametric test like the Chi Squared , were gonna take this data and make our best inference about the population" parametrics uses mean..the best predictor...in non parametrics, bc u don't have the mean you use the median (cuz in a skewed distribution u use median)

1) both types of chi square tests are based on the difference between OBSERVED frequencies and EXPECTED frequencies (in 2-way, these are frequencies expected if there is NO relationship between the 2 variables).

2) Chi square tests are used with data in the form of COUNTS (not scores). If you have any of these 3 FREQUENCY datas, you can use CHI square:

- frequency data (f) ex:
- *proportions (f/N) ex:
- *percentages (proportion x 100) ex: 80% of ppl have depression

Note: proportions and percentages can be CONVERTED to Frequency data, and then you can see if the OBSERVED frequencies are different from the EXPECTED frequencies

How to convert: ex: .5 of 100 participants = 50
35% of 100 participants = 35/100 x
100 = 35

3) If you wanna use a Chi Square test, the IV 's have to be - discrete CATEGORIES , meaning the data HAS to be be NOMINAL/Categorical
- and the categories can NOT overlap (meaning s/one can only be in 1 category--either you are in Systematic Desensitization or the other therapy, can't be in both)

4) You can have a One way Chi square design or a TWO way chi square design. And each IV can have 2 or more levels ex: Type of therapy< Systematic Desensitization or Implosion,

or say u wanted to know if religion was related to ethnicity ex: Religion< Jewish, Christian, Muslim, Other by Ethnicity < Middle Easter, White, Latino, Other (here you have 2 Iv's you'd use a 2 way Chi square)

5) A participant can ONLY be in ONE cell of the table. ex: if someone says they're a mix of middle eastern and white, you CANT put them in both groups and then do a chi square. You'd have to take this person out or make a new level Middle eastern white.

this is a type of contingency analysis.

To use this, you have to have 2 Iv's, both NOMINAL/categories, and each with 2/more levels, and a DV that is a FREQUENCY (frequency, proportion, or percentage).

Purpose is to test if 2 IV's are INDEPENDENT of each other. ex: if Outcome is Independent of type of therapy. If not, you can say that outcome (whether a person can get on a plane or not) is RELATED to type of therapy.

SO what ur calculating is really how much the OBSERVED frequencies differ from the frequencies that would be EXPECTED if the 2 IV's were INDEPENDENT.

You're Null and Alternatives in a Two WAY chi square is:

- H◦= variables A and B are INDEPENDENT in the population
- H1= variables A and B are RELATED

If ur data were percentages, you can CONVERt the percentages to frequencies.

Draw chart Packet H pg. 5):

*if you put in the cells "observed frequency = 40" then this is called a "CONTINGENCY TABLE"

To get chi square, use the same formula as in one way chi square and get your OBSERVED χ2 and then compare with the Critical value of χ2. And if your OBSERVED is BIGGER than the critical, then u reject the H◦.

What does the chi

What does the chi

What does the chi

What is a chi