### Different Tests

#### Type 1 - Non Parametic Tests

Non Parametic Tests are tests that do not require the assumption of a normal distribution.

The tests based on the assumption of symmetrical, but not Normal data can be shown to be the more sensitive (ie powerful).

They are used when an interval scale cannot be used but the ordering of scores is justified and the sample is small.

Wold Wolfowitz Runs

Kolmogorov Smirnov

#### Type 2 - Parametic Tests

These are the most commonly used tests.

However, there can be problems if the data do not conform to the assumptions underlying the tests.

we need to estimate both the mean of the distribution and its standard deviation.

Need to make some assumptions about the shape of the distribution and the underlying probability model.

These are more sophisticated than the non parametric tests and rely on certain assumptions.

1 - the type of measure which the score represents (ie level of measurement)

2 - the distribution of scores (is it normal ?)

3 - the spread of the scores

#### Non Parametric - Sign Test

refer to the S statistic

If we want to prove that there is a difference in direction, but don't need to quantify the amount, then the Sign text can be used.

This test is designed to tell us whether two samples appear to have come from one or more sources

#### Non Parametric - Wilcoxon Test

Used on matched scores

Used when scores are paired off in some way - refer to the T statistic

This is more powerful than the Sign Test.

When we collect data which comprises of definite scores then Wilcoxon would be preferred to the Sign test.

This test is designed to tell us whether two samples appear to have come from one or more sources

#### Non Parametric - Mann-Whitney

Used on unmatched (or independent samples)

The Mann-Whitney test is equivalent to the Wilcoxon test where pairs of scores are not required

refer to the U statistic

independent samples

This test is designed to tell us whether two samples appear to have come from one or more sources

#### Parametric - F Test

Also known as **Variance Ratio** test

In Excel this is called the F-Test Two sample for variances

This can be considered a stats test in its own right and is used to decide if z-samples appear to have been drawn from one or two populations.

#### Parametric - Matched T-Test

Also known as a **Paired T -Test** or **Correlated T-Test**

In Excel this is called T:Test Paired Two sample for means

This is the equivalent of Wilcoxon but for matched samples ??

both samples must be normally distributed

the variances of the two samples must be similar

both samples comprises of scores of at least interval measurement

This test is designed to tell us whether two samples appear to have come from one or more sources

#### Parametric - Unmatched T-Test

Also known as the **Independent T-test**

In Excel there are two choices: T:Test Two sample assuming equal variances and T:Test two sample assuming unequal variances

This is the equivalent of Mann-Whitney but for matched samples ??

both samples must be normally distributed

the variances of the two samples must be similar

both samples comprises of scores of at least interval measurement

This test is designed to tell us whether two samples appear to have come from one or more sources

#### Parametric - Simple Chi-Square

#### Parametric - One-Sample Chi-Square

#### Parametric - Complex Chi-Square

#### Degrees of Freedom

This means how many items do you need to know before the remainder are fixed

The total number of items from any given sample (or samples) which have to be known.

As with the t-test you have to calculate the degrees of freedom at the end of the chi-square calculations in order to evaluate the particular X2 statistic

#### Experiments

An experiment is just a controlled test or investigation.

The results from an experiment can be one or more.

The results from an experiment can fall into two categories

**Deterministic**- Have only one possible result

These are predictable experiments

**Non Deterministic**- Have more than one result

Also called probabilistic, indeterministic

These are unpredictable experiments

We never know the exact result before hand.

An experiment whose result is unpredictable or uncertain is called a probabilistic experiment

Examples of probabilistic experiements include:

tossing a coin

rolling a nice

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