statistical tsting and sign test

Inferential statistics

Statically tests which infer whether the results of a study are significant

Significant

When the results of a study are thought to be due to a real relationship between the variables that are being tested rather than due to chance

Statistical test

A mathematical formula used to determine whether the results of a study are significant (there are 8 different statical tests-used for different designs and levels of measurements)

Probability

The likelihood that results are due to chance- known as level of significance or p value

Steps to calculating a sign test

1. Add the signs to the sign of difference column (if there is neither a - or + difference e.g. the score stays the same, the participants data should be ignored and they should be excluded from the N value)

2. Find the least frequent sign- the number of the least frequent sign is the S value

3. Compare your calculated value (s) with the critical value (table will be given to you)

4. Using critical value table: level of significance/p-value (0.5 unless stated otherwise), N=number of participants excluding the ones whose score stayed the same, whether one (non-directional) or two (directional) tailed test

Calculated value

Result of your statistical test

Level of significance

Probability of results occurring due to chance

How to choose the right statistical test?

1. Is the research experimental(difference) or correlational (relationship)

2. If research is experimental- related (matched pairs and repeated measures) or unrelated design( independent and groups)

3. What is the level of measurement of the data collected

Type one error

We conclude our findings are significant when in fact they are not

• Incorrectly accepting an alternative hypothesis

• Incorrectly rejecting a NULL hypothesis

• More common when p value is high/more lenient

Type two error

We assume our findings are not significant when in fact they are

• Incorrectly accepting a NULL hypothesis

• Incorrectly rejecting alternate hypothesis

• More common when the p value is lower/more stringent

Why is 0.5 used for a p value?

To avoid type 1 or type 2 errors

Why might we not use a p value of 0.5 in some cases?

When there could be consequences of the results being due to chance e.g. in drug testing then we need to be more stringent and use a lower p value because the consequences of making a type 2 error are more preferable than making a type 1 error