Final Session 10a Flashcards
The methods for hypothesis testing that we have learned thus far make assumptions about what
population distributions and their properties:
Normal distributions Equal variances (homogeneous variances) Equal covariances (homogeneous covariances)
what are the parametric tests
test, t-test, and F ratios from one-way (between or repeated
measures) and two-way ANOVAs
The mean and variance are sufficient to describe what
the shape and location of normal distributions
For a normal distribution, the mean and variance are called what
parameters
Statistical tests that assume a distribution and use parameters are calledwhat
parametric tests
Statistical tests that do not assume a distribution or use parameters are called what
nonparametric tests
what is another name for nonparametric tests
distribution-free tests
Nonparametric tests make few assumptions or restrictions on the data. They can be used when what
assumptions underlying parametric tests are questionable
For example, non-normal data
10 dieters following Atkins diet
10 dieters following Jenny Craig diet Hypothetical result:
Atkin’s group lost an average of 34.5 lbs J. Craig group lost an average of 18.5 lbs
Conclusion: Atkin’s diet is better?
what kind of data is this
Non-normal data
when to use non parametric tests
Can be classified according to the following criteria:
The level of measurement (nominal, ordinal)
Which information is used (frequency, sign or rank) Independent or dependent samples
The number of groups to be compared (k = 1, 2, … or more)
and: There is at least one nonparametric test that could be used instead of an equivalent parametric test
Many non-parametric tests are precursors to. ..
Robust” analysis techniques
In almost every chapter in Field (your textbook) there is some mention of a robust method
These “robust” methods are good or bad?
typically still perform well even under assumption violations
A (Pearson) chi-square statistic (χ2) can be used for testing what
independence of nominal variables
what is independence
When variables are not associated
Scores on one variable do not depend on scores on the other
A (Pearson) chi-square statistic (χ2)
The data for this test are arranged in the form of a table called a what
contingency table
Prior assumptions/requirements: of Chi-Square (χ2) test
Random samples
Independent observations
A sufficiently large sample size is required (usually > 20) Average cell frequency should be ≥ 5
what are the hypotheses for Chi-Square (χ2) test
H0: Two (nominally scaled) variables are statistically independent (no association) in the population
H1: The two variables are not independent (association) in the population
In many nonparametric procedures, the null hypothesis under the test is formulated in a more general form because either no parameters (e.g., means) are specified to be compared, or writing the hypotheses in terms of some numerical quantities would require much more notation
what does Chi-Square as a test of independence compare
Compares observed and expected
frequencies
(Ogj − Egj )2 ≈ squared
deviations between observed responses and the model
what is the model
Expected frequencies are
computed as if the two variables were independent
expected frequencies are computed how for Chi-Square as a test of independence
as if the 2 variables were independent
how to calculate df of Chi-Square
df = (a − 1)(b − 1)
If the observed value of χ2 is greater than or equal to the critical value with df = (a − 1)(b − 1) at α = .05, we may______ the null hypothesis of independence2
reject
Alternatively, if the p-value of the observed value of χ2 is less than or equal to α, we may_____ the null hypothesis
reject
