Week 6 (Chi square) Flashcards
Explain degrees of freedom?
The Degrees of Freedom refers to the number of values involved in the calculations that have the freedom to vary
What are inferential statistics
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
What is a chi square goodness of fit?
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.
Chi square goodness of fit and null hypothesis?
Default assumption is that the proportion is uniformly distributed across categories
What are the chi square goodness of fit data assumptions?
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)
Chi square formula goodness of fit?
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
What chi square value indicated a perfect fit to the expected deviation and aligns with the null hypothesis?
0 means a perfect fit
Closer to 0, closer to null hypothesis
How do you calculate degrees of freedom for a chi-square goodness of fit?
Number of cells - 1
Explain cramers v in relation to chi-square goodness of fit?
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
Explain cramers V values and strength of effect?
>.5 = large .3-.5 = medium .1-.3 = small 0-.1 = trivial
What does a chi-square test of independence measure?
Statistical independence or association between two or more categorical variables
How do you calculate expected frequencies for a chi-square test of independence?
(Row total x column total)/N total
How do you calculate degrees of freedom for a chi-square test of independence?
df = (# rows - 1) x (# colums -1)
What causes a chi-square test of independence to become robust?
If 20% has small (less than five) expected frequencies
Solution is to collect more data!
What type of data are chi-square tests used to analyse?
Categorical
What is X^2?
Chi square statistic
How do you summarise chi square statistics?
X^2(df, N= x)= chi square value, p = x, V= x
What is the criticism towards using Pearson’s chi-square statistic?
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
What is recommended now when one of the cells has expected counts less that 5?
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
Does Jamovi produce a cramers V value for a chi-square goodness-of-fit test?
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)
