Chi Square- Goodness of fit Flashcards
Define nominal, ordinal, interval, and ratio scales of measurement with examples.
- Nominal (or categorical): these are categories with no rank. e.g. hair colour, religion.
- Ordinal: there are categories that are ranked or ordered. E.g. grades, likert scale. Only >< apply to these.
- Interval: Quantitative measures without a true zero. They are usually scales constructed to quantify a property. e.g. temp, IQ, ph balance. Can perform +,-
- Ratio: These are quantitative measure with a true zero. E.g. age, length, time, weight. Can perform +,-,x,/
What are the two different ways of classifying variables that determines the type of statistical test we use?
- Discrete (Nominal and Ordinal)- these can only have certain values within a range.
- Continuous (Interval and Ratio)- These can have any value in a range.
Refer back to first powerpoint for inferential test decision
What is the difference between discrete and continuous variables?
- Discrete variables have distinct and separate values, often represented by integers, and there are gaps between possible values
- Continuous variables for a continuum with no gaps between values, can take any value within a range, and are often represented by real numbers.
What are classifications and when are they most useful to a researcher?
- Classifications are a form of measurement.
- They are of interest to a researcher when they are exhaustive and mutually exclusive.
- Statistical analyses require that data be classified into four scales of measurement (nominal, ordinal,interval, and ratio)
What type of data is the chi-square test primarily used for?
Nominal data. Although also ordinal.
What does it mean for events to be exhaustive and mutually exclusive?
- Exhaustive means that the data encompasses all the members of a population.
- Mutually exclusive means that no member of the population can belong to more than one category.
What is a contingency table?
A table used to present data classified with respect to two or more categorical variables.
- They also help us understand the two types of chi-square test.
What are the two kind sof chi-square test?
- Goodness of fit (unidimensional- one variable) Used to test a single dimension of data.
- Test of contingency- multidimensional (two variables) Useful to test whether two variables are associated (are they contingent on each other?)
What is the rule about values in the cells of a contingency table?
The values should be absolute frequencies and not proportions or percentages
What is the main purpose of the chi-square test?
The chi-square test analyses frequency data to determine if there is a significant difference between observed and expected frequencies.
What are the three assumptions underlying the chi-square test? (MEI)
- Mutually exclusive classification.
- Exhaustive categories
- Independence of observations (each count should be independent of another)
What three questions does the chi-square test ask?
- Do the observed values differ significantly from the expected values?
- Are the data (O) a good fit to the model (E)
- Does the data fit the expected pattern?
How do you find the expected values in a contingency table?
- Usually a 50/50 split but there is a formula.
Expected frequency= (total of cell rows x total of cell columns)/grant total of all subjects.
What are the 6 steps for decision making in inferential statistics?
- Set up the research hypothesis (H1)
- Set up the null hypothesis (H0)
- Choose a significance level (a)
- Calculate the sample statistic
- Calculate the probability from hypothetical sampling distribution (p-value)
- Decide if result is representative of hypothetical distribution. If unlikely (p<a) reject the null hypothesis. It is reasonable to assume research hypothesis.
*Note if you’re using one those table where you find the critical x^2 value using df and a, then you can reject the null hypothesis if the chi-squared statistic is greater than the critical value.
