# Data Analysis

**Data Analysis**

Data can be grouped for presentation in a number of ways:

– Data is put into named groups**Nominal**– Data is put into ascending or descending order**Ordinal**– Intervals are measured and differences between them measured / counted. E.g. height: 5’1″ – 5’6″, 5’7″ – 6’0″.**Interval Ratio**– Difference between lowest and highest values. E.g. range of 1 3 5 5 6 9 9 9 10 is 10-1 = 9.**Range**

Measures of central tendency (averages): e.g. 1, 3, 5, 5, 6, 9, 9, 9, 10

**Mean**The calculated average: total of items divided by number of items = mean

E.g. 1+3+5+5+6+9+9+9+10 = 57

57 ( 9 = 6.33

Mean = 6.33

**Median**The “middle” value when numbers are put into order.

E.g. 1 3 5 5 6 9 9 9 10

Median = 6

**Mode**The modal value is the most frequently occurring number.

E.g. 1 3 3 5 6 9 9 9 10

Mode = 9

### Normal Distribution Curve

The normal distribution curve is a bell shaped curve that is symmetrical about its mean value, which occurs at the central point of distribution. The mean is also the mode and median.

The outer extremities of the distribution never touch the x-axis.

The properties about this distribution mean that certain statements about probability can be made – important when a researcher wishes to express clearly the relationship between sample data and data from the population which the sample represents.

In theory, a normal distribution curve should result when a large random sample of measurements is taken from an appropriate population. In practice, it is very rare for a distribution to fit a normal distribution curve precisely.

### Standard Deviation

- 68.26% of all values lie within one standard deviation either side of the mean
- 95.44% of all values lie within two standard deviations either side of the mean
- 99.74% of all values lie within three standard deviations either side of the mean

### Normal Distribution

Work out the mean, median and mode. If they are similar, you have a normal distribution

### Homogeneity of Variance

Look at the range and see how the scores vary. If the ranges are similar for the two conditions, you have homogeneity.

### Correlations Coefficient

-1 is perfect negative correlation (one up, one down), +1 is perfect positive correlation (one up, one up), 0 is no correlation

There can be unlimited points on this scale: -0.5, +0.3 etc. The higher the correlation coefficient, the more perfect the correlation, the lower the correlation coefficient, the less perfect the correlation. This test does not tell you if your results are significant (P<0.05).

### Statistics

Did it happen by chance? How likely is it that it happened by chance? There are 7 tests but when should we use them and why?

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