SG 10 Flashcards
require a number of assumptions about one or more population parameters
Parametric methods
distribution-free methods
nonparametric
ADVANTAGES OF NONPARAMETRIC METHODS
- When the underlying probability distribution is unknown or is known to be different from what a parametric method requires.
- When the level of measurement falls below what is required by a parametric technique.
- When there is no suitable parametric technique.
In Chi-square, the distribution tends to shift to the ____ and become more spread out with____df values.
right
larger
Chi-square
test for independence
The degree of skewness also decreases with increasing df such that the chi-square distribution approaches a normal distribution. t or f
t
Chi-square cannot be negative since it sums squared differences divided by ______
positive expected frequencies
properties of chi-square
- It cannot be negative since it sums squared differences divided by positive expected frequencies
- It is skewed to the right.
Two variables are______ if, for all cases, the classification of a case to a particular category of one variable has no effect on the probability that the case will fall into any particular category of the second variable.
independent
- it means having a particular attribute will have no effect on having another attribute
Independence
test for independence (chi-square) 3 assumptions
Independent random samples
Nominal variables
Data must be organized in a contingency table
displays the scores on two or more variables at the same time
Contingency table
3 Limitations of the Chi-square Test
- Data must be in the form of frequencies (i.e. counted data within categories).
The contingency tables = at least two columns.
Expected frequencies of any cell should not be less than 5 (although it is permissible for 20% of cells if the contingency table is larger than 2x2)
the absolute value of the difference between the observed and expected frequencies for each cell
Yates’ Continuity Correction
- corrected chi-square
- the absolute value of the difference between the observed and expected frequencies for each cell
Note: For larger tables, there is no correction formula for computing chi-square
Yates’ Continuity Correction
Used to determine if the observed frequencies differ significantly from an even distribution. In other words, it determines whether the sample data is consistent with a hypothesized distribution
Chi-square test
______ is applicable for one categorical variables from a single population.
Chi-square test
Chi-Square Test: Goodness-of-Fit-Test
if the observed and expected frequencies are similar, it is said that there is a “good fit”
Chi-square test 2 assumptions
Independent random samples
The expected frequency of each category must be at least 5
- It is useful when there are cell frequencies less than 5.
- It is therefore useful in the same situation as the chi-square test.
- It avoids the main limitation of the chi-square, which is sufficient observations within each cell. It circumvents this limitation by comparing cumulative frequencies rather than cell frequencies.
K-S T-S T
- This test determines if there is statistical difference between two independent samples.
- more than 2 groups
Kolmogorov-Smirnov Two-Sample Test
Kolmogorov-Smirnov Two-Sample Test 3 Assumptions
Assumptions:
Unless sample sizes are equal, this can only be used if both samples sizes > 40
Independent random samples
At least ordinal-scale categories
- It can be applied to small samples and is useful for samples with unequal sizes.
mann-whitney U test
- It is also called the Wilcoxon Rank-Sum Test.
- It is a test of equality between two independent samples.
- It can be applied to small samples and is useful for samples with unequal sizes.
- <20 samples
Mann-Whitney U Test
test of independence =
test of equality (small/unequal sample) =
test of statistical difference of 2 samples (less than 5 frequency) =
test of equality 2 or more using variance =
test for medians =
statistical difference when HO is rejected =
abs value of the diff between O and E frequency =
chi-square test
mann-whitney U test
k-s t-s t
anova
kw h test
flsdt
yates’ cc