Descriptive Statistics

Question 1

Parameter

Answer 1

Describes a population → summary of real behaviour/data present in the population

Question 2

Statistic

Answer 2

Describes a sample of data → we infer something about the population (parameters) from what we know about the sample (statistics)

Question 3

Descriptive statistics

Answer 3

Summarise patterns within the sample

• Central tendency (location)
• Dispersion (spread)

Question 4

Infererential statistics

Answer 4

Allow us to draw inferences about the population based on our sample

Question 5

Discrete variable

Answer 5

• Scores can only take on certain values e.g. 5-point Likert-type rating scale
• Usually whole numbers but e.g. UK shoe sizes are also discrete: 7, 7 1/2, 8 etc

Question 6

Continuous variable

Answer 6

• Scores can take any value
• Any level of precision
• E.g. age, time, weight etc

Question 7

Types of data

Answer 7

• Nominal: labels/names/categories e.g. gender
• Ordinal: numbers ranked or ordered by a category e.g. order of finishing in a race
• Interval: measurements are made on a scale; differences between points on the scale are equal but there is no ‘natural’ zero point (it is arbitrary) e.g. temperature scale
• Ratio: same as interval data but there is a ‘natural’ zero point e.g. height/length, weight, time etc

Question 8

Measures of central tendency

Answer 8

• Mode: the most frequently occurring score
  
  • Advantage: simple to calculate and easy to understand
  • Disadvantage: easily unrepresentative
• Median: middle score when scores ordered by size
  
  • Advantage: relatively unaffected by untypical extreme scores
  • Disadvantage: may not describe all scores in a data set
• Mean: add together scores and divide by total number of scores
  
  • Advantage: only measure which uses every single score
  • Disadvantage: easily distorted by single, extreme scores (outliers)

Question 9

Measures of dispersion

Answer 9

• Range: how far apart the highest and lowest scores are
  
  • Advantage: easy to calculate
  • Disadvantage: affected by extreme scores
• Interquartile range (IQR): ‘trimmed’ range = 75th percentile minus the 25th percentile
• Standard deviation: the average amount by which scores differ form the mean
  
  • Standard deviation takes into account all values in the data set
  • Square root of variance

Question 10

Sum of squared errors (SS)

Answer 10

The total amount that data points deviate from the mean, squared.

Question 11

Central limit theorem

Answer 11

• If we take lots of samples from a population and take the mean of each sample, these means will be nornally distributed
• The mean of all sample means will approximate the population mean
• Need sample size of at least 30

Question 12

Standard error

Answer 12

The standard deviation of sampling means = the variability in sample means around the population mean