Descriptives

Types of data: measurement (quantitative) and categorical (qualitative) 

Types of scales:  

Nominal – categorical data reflect label for categories 

Ordinal – orders people/objects/events along some continuum (various rankings). No information is given about differences between points on the scale  

Interval – equal intervals between objects represent equal differences 

Ratio scales – have a true zero point. A true zero point corresponds to the absense of the thing being measured. 

• Descriptive statistics: 

  • Goal to characterise 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, mode 

  Measures of central tendency descrube the typical value 

   

  Sample statisitcs are in english letters and population is in greek letters 

   

  The mean is an inaccurate description, extreme scores can influence the mean 

   

  A histogram can tell us if the data is symmetrical and whether the mean is approapriate to describe the sample 

   

  The median – the score in the middle when all scores arranged in order from smallest to largest. Not affected by extreme scores 

   

  The mode – the value of the most frequent score. 

  For two adjacent scores with common frequency, average the middle scores eg; 4 and 5 so 4.5 

  Two non-adjacent scores with common frequency eg 4 and 7 – report both scores (bimodal distribution) 

  

Measures of variability describe the degree to which values vary.  

Range, interquartile range, variance, standard deviation 

Range is the difference between maximum and minimum scores 

Straightforward to calculate and easy to interpret but unstable across different samples 

Interquartile range uses percentiles.  

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

Variance a measure of how much the scores vary given in terms of the distance from the mean  

The average of each score’s squared deviation from the mean score 

Use the population formula (divide by n) when you have the whole population. Use the sample formula (divide by n-1) when you have a smaple and from this sample you want to generalise to the wider population and therefore want to estimate the variance for the population 

the square root of the ‘average’ of each score’  standard deviation from the mean score = the square root of variance 

Standard deviation is the estimate of average variability and is the square root of the varaince.  

It is a measure of how well the mean represents the data 

• Inferential statistics: 

  • Goal to infer the characteristics of the whole from those of a part  

  • Going beyond the information given to make likely assertions, rather than certain ones