# Dealing with Data

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## Inferential test

Procedures for drawing logical conclusions about the target population from which samples are drawn

Inferential tests are classed as parametric or non-parametric. To use a parametric inferential test the data must be:

• interval/ratio
• drawn from a population with normal distribution
• from groups with similar variances

Parametric tests are more powerful, which means that is a non-parametric test does not find a significant difference/correlation, a parametric test may do so because it is more sensitive

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## Observed value

The number produced after applying an inferential test formula

This is sometimes called the calculated value because the researcher calculates it.

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## Probability

A measure of the likelihood that an event may occur. Probability is given as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty.)

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## Significance

A statistical term indicating that the research results are sufficiently strong to enable a researcher to reject the null hypothesis under test and accept the alternative hypothesis

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## Significance level

The level of probabililty at which it has been agreed to reject the null hypothesis. Psychologists usually use a probability of 0.05 (5%)

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## Table of critical values

A list of numbers that inform you whether an observed value is significant or not. There is a different table for each inferential test.

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## The Binomal Sign Test

Step 1: State the alternative hypothesis

Systolic blood pressure (measured after the stress management programme) is lower than before the programme

This is a one tailed (directional) hypothesis and the data is related

Step 2: Place raw data in table

In this case the raw data are the blood pressure readings (interval data)

Step 3: Work out signs

Record a (+) if the number in column A is bigger than in the number in column B. Otherwise record  a (-) or a 0.

Step 4: Find observed value of S

S is the symbol for the test statistic we are calculating. You add up the + and - and select the smaller value.

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## The Binomal Sign Test continued

Step 5: Is the result in the right direction?

If the hypothesis is directional we have to check that the result is in the expected direction (blood pressure lower afterwards)

The hypothesis was directional and the results are in the expected direction - otherwise accept null hypothesis.

Step 6: Find critical value of S

• Level of significance
• Kind of hypothesis: one-tailed
• N value (total number of scores ignoring 0 values)

In the table of critical values locate the row tha begins with our N value

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## The Binomal Sign Test continued

Step 7: Report the conclusion

If the observed value is equal to or less than the critical value of our result is significant. In this case it is nor significant.

As the observed value is not significant  (at p 0.05) we accept the null hypothesis that there is no difference in blood pressure before and after the stress management training programme

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## Wilcoxon Signed Ranks Test

Step 1:  state the alternative hypothesis

Participants have a higher test score in the morning than when taking the same test in the afternoon.

This is a one tailed (directional) hypothesis and the design in repeated measures

Step 2: Place raw data in a table

The raw data are the test scores - morning scores placed in column A and afternoon in column B

Step 3: Find the differences and rank

Calculate the difference between each pair of test scores. If the difference is 0 exclude from ranking and reduce N accordingly. Rank these differences from low to high - lowest number recieves rank of 1, next lowest of 2 etc. If two or more of same number calculate rank by working out mean.

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## Mann Whitney U Test

Step 1:

Rank all the scores as if they were one group. Give the smallest score the rank of 1. This converts the data to ordinal level.

Step 2:

Add up the ranks together for the smaller groups. If the groups are the same size use either and call this R

Step 3:

Calculate U and U2 by using:

N= the number of scores (ranks in the group smaller sample)

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## Mann - Whitney U Test continued

Nl = the number of scores (ranks in the larger sample)

R+ the sum of ranks in the smaller group (either if they are the same)

Step 4:

Choose the smaller U1 or U2 and call it U.

Step 5:

Consult the table of critical values and decide whether to take account of one-tailed or two-tailed hypothesis

Step 6:

Where your two values of Ns and Nl meet you'll find your critical value which must'nt be exceeding for a two tailed test. If you've previously decided on a significant figure level of 0.05 look at this first then if your value of U is less, check the table value at the 0.01 level to see if U is still smaller.

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## Mann Whitney U Test continued

Step 7:

Make a statement of significant and decide whether or not to reject the null hypothesis in favour of the alternative hypothesis

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## Chi-square test

Step 1:

Draw up a table like the one below. The raw data is known as frequency observed (s.f.) Each box as a cell and given a letter (a) (b) (c)

A                          B                     C                    Raw total

Bramley school                  6                          42                   15

Lord Matthew school         8                          42

Column total

Step 2:

Obtain raw totals, column totals and grand totals

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## Chi-square test

Step 3:

Calculate expected frequencies (Fe) for each cell as follows:

Step 4:

Work out the degrees of freedom by calculating (number of rows -1). In a simple 2x2 chi squared test, degrees of freedom are always 1.

Step 5:

Apply he formula:

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