5 - Normal Distribution + Standardising Data

Standard Deviation

Measures the average amount by which all values deviate from

1. Smaller SD, the better

When Should We Change Data?

1. Return to original data

2. Error when data entered into database

3. Recode observation to ‘missing value’

4. Transform data:

   • Scale data - units

   • Standardise data - common mean

±/- Numbers to Data

1. + / - by a constant number to each value in a data set

2. Changes the mean by the amount added or subtracted

3. SD = Same

Multiplying/Dividing Data

1. Mean increases / decreases by the proportion its multiplied / divided by

2. SD Increases / decreases by the proportion its multiplied / divided by

Z Scores

Measure number of SDs an observation is from the mean

1. + Z-score - observation above mean

2. - Z-score - observation below mean

3. 0 Z-score - observation = mean

Calculating Z-Score

Rules of Z-Scores

1. Mean of all Z-scores = 0

2. SD = 1

3. Whole data set

Z-Score Indices

1. Can rank data

2. Positive measures must mean same for all variables

3. Compare Z-scores for these indicators by creating an index of all variables

Summary

Normal Curve

Properties of Normal Distribution

Areas Under the Normal Curve

Important Properties of Normal Curve

What if we don’t have a whole number Z-score?

1. Use normal tables

Normal Distribution Table

How to Use Normal Tables

Summary