Descriptives

Types of data

Measurement (quantitative) and categorical (qualitative).

Types of scales:

Nominal, ordinal, interval, and ratio.

Nominal Scale

Categorical data reflecting labels for categories.

Ordinal Scale

Orders people/objects/events along a continuum without information about differences between points.

Interval Scale

Equal intervals between objects represent equal differences.

Ratio Scale

Has a true zero point that corresponds to the absence of the thing being measured.

Descriptive Statistics

• Characterizes a numerical dataset efficiently and representatively

• Condense and render meaningful a multitude of information

• minimise the inevitable error that is involved in condensing that information

Measures of Central Tendency

Mean, median, and mode. these all describe the typical value

What letters are sample and population statistics in?

Sample are in English letters

Population are in greek letters

Mean

Inaccurate when extreme scores influence its value.

A histogram can tell us if the data is…

symmetrical and whether the mean is appropriate to describe the sample

Median

The middle score when all scores are arranged from smallest to largest, unaffected by extreme scores.

Mode

The most frequent score in a dataset.

Mode: for 2 adjacent scores with common frequency…

average the middle score

mode: for 2 non-adjacent scores with common frequency

report both scores (bimodal distribution) eg 4 and 7

What do measures of variability describe?

the degree to which values vary

Range, interquartile range, variance, standard deviation

Range

The difference between maximum and minimum scores, easy to interpret but unstable across different samples

Interquartile Range

Uses percentiles

What is a percentile?

A cut-off point that divides the data into percentage chunks

Variance

Measures how much scores vary from the mean,

The square root of variance =

the square root of the ‘average’ of each scores standard deviation from the mean

When you have a whole population?

When you have a sample?

Use population formula - divide by n

Use sample formula - divide by n-1

Standard Deviation

estimating average variability and it is the square root of the variance. It is a measure of how well the mean represents the data

Inferential Statistics

Infers characteristics of a whole from those of a part. Going beyond the information given to make likely rather than certain assertions.