levels of measurement + central tendancy + dispersion

Levels of measurement

Quantitative data can be classified into different levels or types of measurement

Nominal data

• Categorical

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

• Discrete

• One item can only appear in one category

 

E.g. hair colour

Ordinal data

• Same properties as nominal data

• But has a natural order

• Does not have equal intervals between each unit

• Subjective

E.g.

Positions in a competition

Interval data

• Numerical scales with unit of equal precisely defined size

• Continuous

Ratio data is the sane - but cannot go below zero (has an absolute zero)

E.g.

Weight- ratio

Converting between levels

 only convert down the levels

 

Interval -> ordinal

• Rank order

• E.g. reaction time in seconds interval -> order from fastest to slowest

 

Ordinal -> nominal

• Create 2 or more categories

• E.g. liker scale -> 3 categories e.g. happy, neutral, s

Mean

Add up all the values and divide by number of values

Can only be used with interval (and ratio) data.

Strenght’s of the mean

Most sensitive Measure of central tendency - includes all scores in the data set

Limitations of the mean

Easily distorted by extreme values (outliers/anomalous values)

Median

• The middle value when the scores are arranged in ascending order

•  Even number of values

•  Can be used with interval and ordinal (and ratio) data.

Strengths of median

• Not affected by extreme scores (compared with mean)

•  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 data → 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 MoCT appropriate for nominal data (categorical)

Limitations of mode

• Very crude measure -> unsophisticated or basic

• Can have more than one mode (e.g. bimodal) → not very useful

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, on average, each value deviates from the mean

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