Levels of Measurement

Levels of measurement

quantitative data can be classified into types or levels of measurement

Levels

1. Nominal

2. Ordinal

3. Interval

Nominal data

• categorical data

• The frequency count of a particular variable is recorded at this level of measurement

• Discrete

• One item can only appear in one category

Ordinal data

• same properties as nominal data- a form of categorical data

• Has a natural order

• Does not have equal intervals between each unit

• Subjective

Interval (& ratio)

• numerical scales with units of equal precisely defined size

• Continuous

• (Ratio data is the same but has an absolute zero- it can’t go below 0)

Converting between levels of measurement

can only convert down the levels

Interval→ Ordinal - rank the order

Ordinal→ Nominal- create two or more categories

Measures of central tendency

A descriptive statistic that provides information about a ‘typical’ value for a given data set

Information us about the central (or middle) value for a data set

Essentially they are averages

each one is appropriate for a different situation

Mean

Add up all the values and divide by number of values

Can only be used with interval and ration data

Strengths of mean

most sensitive

Includes all scores in the data set

More representative

Limitations of mean

easily distorted by extreme values (outliers/ anomalous data)

Median

The middle value when the scores are arranges in ascending order

Even number- sum of two central values/2

Can be used with interval and ordinal (and ration) data

Strength of median

• not affected by extreme values

• Easy to calculate

Limitations of median

Less sensitive than the mean as ignores the value of the highest and lowest values

Mode

The most frequently occurring value within a data set

Nominal→ category that has the highest frequency count

Ordinal and interval data→ the data item that occurs most frequently

Strengths of mode

• easy to calculate

• Only one appropriate for the nominal data

Limitations of mode

• very crude measure

• Can have more than one

Measures of dispersion

A descriptive statistic that provides information about the spread or variation in a set of data

Tell us how far scores vary and differ from one another

Range

the arithmetic difference between the highest and lowest values in a data set

Add 1 to correct for rounding errors

Strengths of range

• easy to calculate

• Useful for ordinal data

Limitations of range

• affected by extreme values

• Doesn’t take account of the distribution of the data

Standard deviation

precise measure of the dispersion in a set of data

Tells us by how much, an average each value deviates from the mean

High SD_ not all P’s are affected by the IV in the same way- there is a lot of data variation within the data set

Low SD- values are clustered around the mean- all the P’s may have responded in a similar way

Strengths of standard deviation

• precise measure of dispersion- takes all scores into account

• Useful for interval data

Limitations of standard deviation

• affected by extreme values

• Extreme values may be ‘hidden’ within the data