Chi-Square Flashcards
what’s the equation for chi-square?
Χ^2=∑(𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 −𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑)^2/𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑
what does the chi-square equation tell you?
The chi-square statistic tells you how far off your observed values are from your expected values.
measure of how much the observed data deviates from what you would expect.
degrees of freedom
categories - 1
you need df bc when you use chi-square, you’re not working with a normal distribution.
Unlike the normal distribution, the chi-square distribution is not…
…symmetrical, and its shape changes depending on the degrees of freedom.
The chi-square formula is used to test the relationship between what kind of variables?
categorical
The Central Limit Theorem (for mean)
When you take a large number of samples from any population (with any distribution), the sampling distribution of the sample mean will be approximately normal, regardless of the population’s original distribution, as long as the sample size is sufficiently large
standard error equation for proportion vs mean
proportion: √((𝑝(1−𝑝))/𝑛)
mean: 𝜎/√𝑛
What are the two conditions required to model the sample mean with an approximately normal sampling distribution
- independence - simple random sample
- normality (n greater than about 30)
for the equation 𝜎/√𝑛 for sd of mean, since we don’t know the actual 𝜎, we use
𝑠/√𝑛, we estimate it with the sd of the sample
The t-distribution(s)
A family of distributions that are very similar to the normal distribution but with fatter tails
since the t-distribution takes on an additional parameter aka df (K-1) what do you think lower degrees of freedom versus higher degrees of freedom would look like on the graph?
Lower degrees of freedom = fatter tails
At infinite degrees of freedom, the t-distribution is identical to the normal distribution, skinnier tails
We use the t-distribution(s) instead of the normal distribution because we tend to…
…under-estimate the population standard deviation with small samples
