AP Stats Chapter 12

what is the chi squared formula

high x² value means ??

greater evidence against the null hypothesis, sample is far from what we expected

low x² value means ??

null hypothesis is true, value close to zero means sample is close to what expected

what should your large counts be greater than? and how do u format it

(expected values) > 5

what is x² cdf? like what does it calculate / mean

the probability that x² is less than or equal to a specific value, given df.

ALSO

total area under the curve from 0 to that specific value.

what is the layout you should follow when inputting x² cdf?

x² cdf (x², 99999, df)

when do you need to include a follow up analysis ?

when Ho is rejected

what is the sentence structure for the follow up analysis

the largest component of x² is _____ because the observed counts of ____ was higher/lower than expected

if there is an association given in the prompt, wjhat procedure do u choose?

chi squared test for INDEPENDENCE

how would you find the expected count? ( this is just the formula )

expected counts = ( row total ) * ( column total ) / grand total

how do you find df in table

(rows - 1) * (columns - 1)

how to calculate on calculator for expected after observed

first edit the matrix. only enter the observed. leave one matrix empty for the expected

go to stats, test, then choose x² - test and input the matrixes.

how do you find expected count when there is only one category / row?

n * p … sample size * probability

if < .05, we …? ( do we fail and reject or not? )

If < .05, we REJECT Ho and we DO have evidence for Ha

if > .05, we …? ( do we fail and reject or not? )

If >.05, we FAIL TO REJECT Ho and we DON’T have evidence for Ha

when should you use test for GOF?

when you only have 1 sample and 1 variable

when should you do a homogeneity test?

when you have 2+ samples and 1 variable

how do you know when the test is for independence?

1 sample and 2 variables

when looking at data in a table, how can you know if the test is or isn’t GOF?

single row / column OR one - way table = GOF

two - way table = NOT GOF

what should you write for the hypothesis for each different test?

GOF: decimals (ex: if 10% claimed, p = 0.10) OR words (xxx’s claim is/isn’t correct)

Independence: WORDS ONLY || There IS/ISN’T an ASSOCIATION between variables ….

Homogenity: WORDS ONLY || There IS/ISN’T a DIFFERENCE in the distribution of ….

what is large counts formula for chi squared

n * pi > 5

how to find minimum sample size needed? ( Large Count Condition )

1) find smallest proportion

2) 5 / smallest proportion

How does increasing Degrees of Freedom affect the chi² distribution?

The curve becomes less skewed (looks more Normal).

The mean of the distribution increases

The critical value required to reject H0 gets larger ( becomes harder to reject null hypothesis).

hypothesis template for GOF

Ho: the claimed distribution of [ variable ] is correct / stay the same

Ha: At least one of the proportions in the distriubution of [variable] is different from the claim

what does the P value MEAN?

the probability of getting a test statistic at least as large as the one you calculated

OR

P(x² > your value)

format layout for p - value interpertation

Assuming that Ho (explain what it is) is true, there is a [P-value] probability of getting a x² test statistic of (your x² value) or greater purely by chance

how to find expected counts for homogenity

row total * column total / grand total

a low x² value means …?

observed and expected are close

if they ask u to find the p value / probability , use ??

x² cdf

“there IS / ISN’T convincing evidence” … when do you use either statement (p-val)