Chapter 17: Nonparamatric Tests - Chi Square Flashcards
Chi square is sometimes used to determine what in regards to two variables??
- whether or not two variables are independent of each other or if they are related to each other.
What is a contingency table?
a two way table showing the contingency between two variables where the variables have been classified into mutually exclusive categories and the cell entries are frequencies.
Define contingency!
an event that may but is not certain to occur aka something that may happen.
Is chi square only used when examining two variables independence of one another?
- No - Its also used for when there is only one variable
What is a parametric test?
- one that depends considerably on population characteristics or parameters for its use. (mean, SD etc)
What statistical tests are used for parametric tests?
- Z-test, t-Test, and F-test
The requirements for a parametric test are _____.
minimal
Because nonparametric tests depend little on knowing the population distributions they are often referred to as what?
- distribution - free tests
If nonparametric tests require not many assumptions and characteristics than why do we not use them all the time and just scrap parametric tests?
- Many of the parametric inference tests are robot with regard to violations in the assumptions do not greatly disturb the sapling distribution of its statistic. 2. parametric tests are much more powerful and more versatile than nonparametric tests
What is the statistical inference used most often with nominal data?
- the nonparametric test = chi square (X^2)
What are the steps for calculating X^2? (4)
- determine fe ( expected frequencies) for each cell 2. calculate X^2 obt 3. determine df 4. compare X^2 obt to X^2 crit
What is the only difference in calculating X^2 for one variable vs two variables ?
- how we calculate the expected frequency for each cell.
What are the two types of statistical tests?
- Parametric 2. Nonparametric
What are the two assumptions of a parametric test>
- the scores of the Ho population are normally distributed 2. population variances are = L> much more powerful than nonparametric tests
When do we use nonparametric tests?
- when there is an extreme violation of an assumption of the parametric test or if the data was manipulated using a scaling technique which makes an abnormal distribution to a normal one.
What are the four types of nonparametric tests?
1.Chi square 2. wilcoxin matched pairs signed rank test 3. Mann-Whitney U 4. Kruskal-Wallis Test
What are the three assumptions underlying chi square?
- There is independence between each observation recorded in the contingency table. A) each subject may have only one entry in the table 2. Sample size must be large enough that the expected frequency in each cell is at least five for tables where there are more than two rows or columns 3. Normally used with nominal data A) however, can be used with ordinal, interval or ratio data.
For a one variable chi square test what would an Ho be written like?
Ho : There is no difference in the ___ in the population L> the proportion x and proportion y equal within the population
X^2 allows us to determine whether the scores are due to ____ of a population where individuals favouring x …etc..
random sampling
Describe what the frequency expected ( fe) is ??
- expected frequency under the assumption sampling is random from the Ho population L> what we expect to get in each cell
Describe what the frequency observed is! (fo)?
-in sample -what we actually got in each cell.
X^2 allows analysis of the difference scores between ___ and ____.
frequency expected and observed.
What is the formula for X^2 obt??
0=the frequencies observed
E= the requency of expected
Σ= the sum of…
