Choosing a statistical test and critical value

What is a Type 1 error?

* optimist’s error
* falsely accept the alernate hypothesis and reject the null hypothesis
* when the null hypothesis is true
* fasley claim that there is a significant difference when there isn’t one

What is a Type II error?

* pessimist’s error
* falsely accept the null hypothesis
* when the alternate is true
* falsly claim that there is not a significant difference when they is one

When is the Type 1 error more likely?

significance level is too lenient/high e.g 10% or 0.1 rather than 5%

When is the Type 2 error more likely?

significance level is too stringent/low e.g 1% or 0.01

Why do psychologists favour the 5% level of significane?

Best **balances the risk of making a type 1 and type 2 error**

What is a significance level?

* the point at which researcher can claim to have discovered a large enough difference within the data to claim an effect has been found


* allows them to accept or reject the null hypothesis

Critical value

cut-off point between accepting or rejecting the alternate/null hypothesis

sign test

a satistical test of difference between related items (same participant test twice). Data should be nominal

Levels of measurement

quantitative data can be classified into levels of measurement; nominal, ordinal, interval

Spearman’s rho

test of correlation when the data is at ordinal level

Pearson’s r

a parametric test for a correlation when the data is at interval level

Wilcoxon

a test for difference between two set of score. Data should be ordinal level using a related design

Mann-whitney

a test of difference between two sets of score. should be ordinal level using an unrelated design

Related t-test

parametric test of difference between two sets of scores. Data should be interval using a related design

Unrelated t-test

parametric test of difference between two sets of scores. Data is interval using an unrelated design

Chi-squared

* test of correlation/association between two co-variables. data should be at nominal level
* test of difference between two sets of scores. data should be nominal using an unrelated design

Unrelated design?

independent group design, the 2 groups are not related

Related design?

repeated measures / matched pairs

Nominal data?

* data is in **categories**
* **discrete** data as data can only appear in one of the categories

ordinal data?

* data is ordered in some way
* ordinal data doesn’t have equal interval between each unit
* lacks precision, based on subjective opinion - a score of 8 might be viewed differently by different people

Interval data?

* data that is based on numerical scales that include units of precisely defined size
* time using seconds, temperature using degrees celsius

How do you choose a statistical test?

1. test of difference or correlation?
2. experimental design - independent / repeated measure or matched pairs?
3. level of measurement?

Which tests use the Number of participants to work out the critical value?

* Sign (N)
* Mann Whitney (2 groups, need to know Na and Nb, num of ppts in each group)
* Wilcoxon (N)
* Spearman (N)

Which tests use DEGREES OF FREEDOM to work out the critical value?

* Chi squared
* Unrelated / related t-test
* Pearson’s r

How to work out degrees of freedom for Chi squared?

(R-1)x(C-1)

* (row -1) multiplied by (column - 1)

How to work out the degrees of freedom for Unrelated t-test?

(Na + Nb) -2

How to work out the degrees of freedom for Related t-test?

N-1

How to work out degrees of freedom for Pearson’s r?

N-2