Statistical testing: The sign test

Question 1

Significance

Answer 1

The difference/association between two sets of data is greater than what would occur by chance i.e. it is a meaningful result.
To find out if the difference/association is significant we need to use a statistical test.

Question 2

Probability

Answer 2

Probability (p) is about likelihood - how likely it is that a certain event will happen if the null hypothesis were true. The accepted level of probability in psychology is 0.05 (a significance level of 5%). This is the level in which a researcher decides to accept or reject the null hypothesis. (more stringent 1% significance level may be used e.g. testing drugs).
Even though psychologists may find statistically significant differences/relationship within data, they can never find statistical certainties. This is why psychologists use phrases such as this suggests, rather than this proves.

Question 3

Calculated and critical values

Answer 3

The researcher uses a statistical test to produce a calculated value.
The calculated value is compared with a critical value to decide whether the result is significant or not.
The critical values for a particular test are given in a table of critical values.

Question 4

Finding the critical value

Answer 4

To find the critical value, need to know:
1) The significance level (usually 0.05 or 5%).
2) The number of participants in the investigation (the N value) or the degrees of freedom (df).
3) Whether the hypothesis is directional (one-tailed test) or non-directional (two-tailed test).

Question 5

What does the sign test include?

Answer 5

• Conditions of use
• Calculation
• Critical value

Question 6

Conditions of use

Answer 6

Used to analyse the difference in scores between related items e.g. the same participant is tested twice (repeated measures).
Can be used with nominal data (or better).

Question 7

Calculation

Answer 7

1) The score for condition B is subtracted from condition A to produce the sign of difference (either a plus or a minus).
2) Add up the numbers of pluses and the number of minuses.
3) Participants who achieved the same score in condition A and condition B should be disregarded, and deducted from the N value.
4) The S value is the total of the less frequent sign.

Question 8

Critical value

Answer 8

If S is equal to or less than the critical value, then S is significant and the null hypothesis is rejected and the alternative hypothesis accepted at the 5% level of certainty.