# RM; Conditions for statistical tests

- Created by: mint75
- Created on: 29-04-15 14:06

## The basics

- A p value is the probability of obtaining the observed result if the null hypothesis is true. In psych, the minimum accepted stringency level is p=<.05, a 1/20 chance of the result being due to chance.
- The different types of data you can have are;
- 1) Nominal; Data that is catagorically discrete
- 2) Ordinal; Data that can be ordered, data that has a natural order. But, you can't say for certain that the differences between the values are equal. (e.g a 6th and 7th place difference is not the same as a 1st and 2nd place difference)
- 3) Interval; Similar to ordinal in that data is ordered, but unlike ordinal the differences between values is always equal, for example 1 degree and 2 degrees.
- 4) Ratio; Building on ratio, data has equal values between points BUT unlike interval, has an absolute zero, a score of zero is significant, not an absence of a score.

## Binominal test

- This is a test for NOMINAL DATA with a SINGLE dichotomy.
- The expected (usually chance, .5) and observed distribution are compared.

Conditions

- Nominal data
- A SINGLE dichotomy
- Scores are from a RANDOM sample of the population
- Independent scores, each pp contributes one data point
- The expected distribution is KNOWN

## x2 test of independence

- A test for NOMINAL data with TWO dichotomies.
- This tests for an association between two variables, the null hypothesis is that there is none.

Conditions

- Data is NOMINAL
- Scores are independent (each pp only contributes one data point)
- Scores are from a RANDOM sample of the population
- N >=40 **
- Each category has n>=5. (expected frequency) **

If ** conditions are not met, use **Fishers exact test result.**

## One way x2 test (Goodness of fit)

- This is a test for NOMINAL data, with one variable that has three + categories. It uses the same method as the x2 test of independence.

Conditions

- Data is NOMINAL
- Scores are independent, each pp contributes one data point
- N >= 5
- Scores are from a random sample of the population

**There is NO alternative test for the One way x2 goodness of fit test.

## T-tests; the basics

- The t-statistic is a ratio between between-group and within-group variance.
- A larger t-value means that there is a larger variance between between and within conditions.
- The meaningfulness of the difference between samples depends on the variability of the sample.
- So, the T is the probability that we will obtain the observed result if the null-hypothesis is true.

Conditions

- These are the main assumptions behind parametric t-tests in general.
- Data is INTERVAL or RATIO
- Data is normally distributed
- To test for this, there needs to be N of > 12
- Use visualisations of the data e.g boxplots/stem and leaf to check for skew
- You want a NON-SIGNIFICANT result on shapiro and smirnov tests, these test whether the observed distribution is abnormal.

- Homogeneity of variance (factor of 3)
- Use levenes test of equality of variance, also want a non-significant result

- No extreme outliers (z score > 3)

## Independent samples t-test

- This test compares the MEANS from two independent groups.

Conditions

- Data is INTERVAL or RATIO
- Scores are independent, each pp contributes one data point.
- Normally distributed data
- Homogeneity of variance

If these conditions are violated, use the non-parametric alternative, Mann-Whitney U test, this test uses ranks and median rather than the means.

Conditions

- Random sample of the population
- Scores are independent, one data point per participant
- Data is ORDINAL, INTERVAL or RATIO
- Approximately equal sample sizes of conditions
- At least 4 participants per condition!

## Paired-Sample t-test

- This test compares the MEANS from within the group/condition.

Conditions

- Data is INTERVAL or RATIO
- The differences between scores of the two conditions need to be normally distributed!
- N>=12.
- (T-test general assumptions)

If these assumptions are violated, use the non-para alternative, Wilcoxon-signed-ranks test. This test is based on ranks, results are ordered from low to high. The important value is W, the smallest of the 2 sums of ranks.

- At least 6 participants.
- Two data points per participant.
- Data is at least ORDINAL level.

Non-para tests are generally less powerful than para and so you are more likely to make type 2 errors. But, there are less rules and assumptions to violate.

## One-sample t-test

- This test compares the MEAN from a set of scores to a pre-determined value. (e.g speed limit)

Conditions

- Data is INTERVAL or RATIO
- Scores are independent, each pp contributes one data point
- Data is normally distributed
- The comparison value is KNOWN

If these assumptions are violated, use the non-para alternative, the One-sample Wilcoxon signed-ranks test**.** Rather than the mean, it compares the median of the set of scores to the known value.

Conditions

- One data point per pp
- ORDINAL, INTERVAL or RATIO data
- Test value is known

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