Week 6 day 1 Flashcards
In a chi-square test, what is the type of data that is the outcome?
Nominal.
In a chi-square test, is the nominal outcome variable compared to a theoretical prediction?
Yes.
What is an example of a research question that would use a chi-square test?
What is the difference between a research hypothesis and a statistical hypothesis?
The research hypothesis is our belief about a research question.
A statistical hypothesis is what we actually measure, and is framed in terms of null and alternative hypotheses.
Why is the test statistic used in a chi-squared analysis not the mean?
What is it instead?
The test statistic in a chi-square is, surprise surprise, chi-squared (chi looks like a fancy x) and is called our Goodness of Fit statistic.
Our outcome variable is nominal data. The mean of nominal data does not make sense.
Instead we look at expected frequencies and compare them to our observed frequencies.
If they are statistically the same we accept the null hypothesis and reject the alternative. If they are statistically different we reject the null and accept the alternative.
When using a test statistic, can we have more than one number?
No. We need to convert our data into one test statistic so that we can measure it on a sampling distribution of that statistic.
In a chi-square analysis, what does a larger x-squared stat mean?
The larger x2, the worse the fit of our observed frequencies to our expected frequencies.
How do we calculate the expected frequencies in a chi square analysis?
We do this by multiply the expected probability by the sample size.
So, if we expected that there would be equal probability that people would choose to drink milk, coffee, water, or soda, and we had a sample of 10, then our expected frequency for number of people who would choose to drink soda would be = 0.25x10=2.5.
What would the chi-square statistic be if the observed and expected frequencies exactly matched?
It would be zero.
What is the general shape of a chi-square distribution?
It looks kind of like a normal distribution/bell curve that is heavily positively skewed and has. a long tail off to the right.
What happens to a chi-swuare distribution as the degrees of freedom increase?
It becomes more leveled out/spread out.
What is the degrees of freedom for a chi-squared goodness of fit test?
The number of categories being tested minus one. So, for our above example there are four categories: milk, water, coffee, soda.
For this example, our degrees of freedom would be 4-1=3.
What do compare our observed chi-squared statistic to?
To the expected chi-squared sampling distribution, i.e the sampling distribution we would expect to see if the null hypothesis was true.
This distribution has a shape that resembles a kind of bell curve that has a large postive skew and tappers off to the right.
With chi-square, when do we rejecrt the null hypothesis?
We reject the null if the test stat (observed chi-square) is equal to or LARGER than quantile for the choses alpha. So, if alpha is 0.5, then we would reject the null if the observed chi-squared stat is equal to or larger than the 95th quantile on our sampling distribution of the expected chi-squared statistic. The p value is calculated as the percentage of time we would expect to see the observed chi-square.
How do you write up chi-squared statistics?
