Week 6 (Chi square)

Question 1

Explain degrees of freedom?

Answer 1

The Degrees of Freedom refers to the number of values involved in the calculations that have the freedom to vary

Question 2

What are inferential statistics

Answer 2

Inferential statistics makes inferences about populations using data drawn from the population. Instead of using the entire population to gather the data, the statistician will collect a sample or samples from the millions of residents and make inferences about the entire population using the sample

Question 3

What is a chi square goodness of fit?

Answer 3

The goodness of fit test is used to test if sample data fits a distribution from a certain population

it tells you if your sample data represents the data you would expect to find in the actual population.

Question 4

Chi square goodness of fit and null hypothesis?

Answer 4

Default assumption is that the proportion is uniformly distributed across categories

Question 5

What are the chi square goodness of fit data assumptions?

Answer 5

Data must be counts (categorical or ordinal)
Counts in each category must be independent (can’t contribute to more than one category)
Sample size must be large enough (have at least 5)

Question 6

Chi square formula goodness of fit?

Answer 6

Similar to variance
Deviation scores are calculated for every cell and summed

X^2 = sum of all cells (observed count-expected count)^2/expected count

Question 7

What chi square value indicated a perfect fit to the expected deviation and aligns with the null hypothesis?

Answer 7

0 means a perfect fit

Closer to 0, closer to null hypothesis

Question 8

How do you calculate degrees of freedom for a chi-square goodness of fit?

Answer 8

Number of cells - 1

Question 9

Explain cramers v in relation to chi-square goodness of fit?

Answer 9

Like a correlation coefficient
Possible range 0,1
Measure of association between variables

Square root of X^2/N(k-1)
N= total sample size
K-1 = degrees of freedom

Question 10

Explain cramers V values and strength of effect?

Answer 10

>.5 = large 
.3-.5 = medium 
.1-.3 = small 
0-.1 = trivial

Question 11

What does a chi-square test of independence measure?

Answer 11

Statistical independence or association between two or more categorical variables

Question 12

How do you calculate expected frequencies for a chi-square test of independence?

Answer 12

(Row total x column total)/N total

Question 13

How do you calculate degrees of freedom for a chi-square test of independence?

Answer 13

df = (# rows - 1) x (# colums -1)

Question 14

What causes a chi-square test of independence to become robust?

Answer 14

If 20% has small (less than five) expected frequencies

Solution is to collect more data!

Question 15

What type of data are chi-square tests used to analyse?

Answer 15

Categorical

Question 16

What is X^2?

Answer 16

Chi square statistic

Question 17

How do you summarise chi square statistics?

Answer 17

X^2(df, N= x)= chi square value, p = x, V= x

Question 18

What is the criticism towards using Pearson’s chi-square statistic?

Answer 18

Some say it over estimates the statistical significance for 2 x 2 tests

Used to be recommended that Yates’ continuity correction should be used however this over compensates so no longer recommended

Question 19

What is recommended now when one of the cells has expected counts less that 5?

Answer 19

Fisher’s exact test.
Report p value for this test instead of the Pearson’s chi-square test p value.
Need to state is is fishers

Another alternative is to collect more data

Question 20

Does Jamovi produce a cramers V value for a chi-square goodness-of-fit test?

Answer 20

No it does not.
Provided with excel worksheet to calculate. Need chi-square statistic, the total sample size and the number of levels of the categorical variables (k)