Stats level 2 final exam, NON - Parametric statistics

When are these statistical procedures used?

Nominal (Categorical) & Ordinal (ranked)

Common parametric procedural assumptions

1: Interval or ratio data

2:Normal distribution (0,1)

3: Homogeneity of variance

Parametric procedures can tolerate some violations

Robust

Severe violations

1: Highly skewed distributions

2: Increased probability of committing a type 1 error

What if the data are interval or ratio

1: Highly skewed

2: Outlier pulling the group mean in one direction

3: Convert raw data to ranks

Advantages of putting non - parametric procedures in interval or ratios

1: Eliminates large differences between individual scores

2: Maintains a nominal type 1 error rate

Chi - square

1: Inferential procedure

2: Used with nominal data

General procedure of chi - square

1: Categorize research participants

2: Count the number of students in each category

3: No inherent value between categories

1 IV (Or factor) - 1 way chi - square

There is only one independent variable or factor,

2 IV (or factor) - 2 way chi - square

2 independent variables that can be examined simultaneously

Assumptions regarding the one way chi - square approach

1: You must have 2 or more categories

2: The categories are mutually exclusive

3: The categories are independent of each other

4: All the responses must be included in the analysis

5: The expected frequency must be at least five in each category

Participants belong to different levels of 1 variable

One way chi square

What is the fundamental question of one way chi square

As the categories change, do the frequencies change

What is the first step in one way chi - square

1: To create a model of the relationship

2: What is the expected frequency in the relationship? Create a null hypothesis (H₀)

3: Describe the distribution of frequency in the population if the predicted relationship does not exist

4: Goodness of fit, between sample data and H₀

How many tails do we use in a one way chi - square

2 tailed hypotheses only, no directionality

If there is no difference between frequencies in a one way chi - square

Then there is no relationship

What is step 2 in the one way chi - square

Translate H₀ into expected frequencies for each category

f_E

expected frequency

In one way chi - square, if the larger the difference between f_O and f_E

The lower the chance the difference is due to sampling error

f_O

The frequency observed

What is the degrees of freedom in one way chi - square

k - 1

Two independent variables and counting the frequencies along 2 variables with the same assumptions

Two way chi - square

The two way chi - square is often referred to as the

Test of independence

What does perfectly independent relationship mean

No pattern

What does perfectly dependent relationship mean

Clear pattern

what is the null hypothesis of two way chi - square

Category membership on one variable is independent of category membership on the other variable

What is the alternative hypothesis for the two way chi - square

Category membership on the 2 variables is dependent

Non Parametric procedures Includes

Mann - whitney u test

-2 independent samples of ranks

What is the 1st step in the Mann Whitney U test

Assign raw scores ranks

What is the second step in the Mann Whitney U test

Compute the sum of the ranks

What is the third step in the Mann - Whitney U test

Compute 2 scores of the Mann Whitney U test

What is the 4th step of the Mann Whitney U test

1: Determine Mann Whitney U_obtained

2: 2 tailed test

3: Select the U_obtained to be the lower U - value

What is the 5th step in the Mann - Whitney U test

Find critical U - value (Mann - whitney U table)

What is step 6 of the mann whitney U test

Compare U _critical to U _Obtained

The smaller U _obtained , The more likely that H₀ is false

If the results of the Mann Whitney U test are significant

1: The samples of reaction times represent different populations

Wilcoxon T- Test

1: Used in non parametric procedures

2: Ranked data

3: Same participants evaluated twice

Step 1 in the Wilcoxon T-Test

Determine difference scores for each pair of scores

Step 2 in the Wilcoxon T-Test

Determine the N (Number) of the non - zero scores

Step 3 in the Wilcoxon T-Test

Assign ranks to the non - zero difference scores and ignore the sign of each difference

Rank = 1, to the smallest difference

Step 4 in the Wilcoxon T-Test

Separate the ranks (using the sign of the difference scores)

Step 5 in the Wilcoxon T-Test

Compute the sum of the ranks for positive and negative ranks

Step 6 in the Wilcoxon T-Test

Determine the wilcoxon T _Obtained = smallest ER, 2 tailed

could you use one tailed in the wilcoxon T test

Yes, the predictions would be whether most differences are positive or negative

Step 7 in the Wilcoxon T-Test

Find Tcritical (Wilcoxon table.......N = number of pairs, α=0.05).

Step 8 in the Wilcoxon T-Test

Compare T_Obtained to T_Critical

T_Obtained is significant if <T_Critucal

H₀ In Wilcoxon T - Test

In the population the median difference is zero

H₁ In Wilcoxon T - Test

In the population the median difference is not zero

Kruskal-Wallis H Test

Non - parametric equivalent to 1 way anova (Not repeated measure)

Kruskal-Wallis H Test H₀

There will be no difference in ranks between the treatments

Kruskal-Wallis H Test H₁

There will be a difference in ranks between the treatments