Mathematical content

Descriptive statistics

Allow us to describe and summarise quantitative data.

• Measures of central tendency - averages (‘Typical score’)

• Measures of dispersion - variability (‘spread out’)

Measures of central tendency

• Reduce a large amount of data (raw data) to a single value (one number) which is representative of that set of data

• Mean, median and mode

Mean

• Add all scores together and divide by no. Of values

+ Uses all the scores so is the most powerful and sensitive

- Can be distorted by extreme scores (some much higher or lower compared to others). These are outliers or anomalies.

Mean

• Put into rank order and find its middle score. If there is an even number add the 2 middle scores together and divide by 2

+ Unaffected by extreme values therefore would be more appropriate if data has extreme values. Easier to calculate than mean.

- Only takes into account one or two score values (middle values)

Quantitative

• Numerical data

• Involves measuring something eg. How much? How often?

• Statistical analysis can be used (central tendency/dispersion)

• Collected in experiments based research methods

Qualitative

• Non-numerical, descriptive data i.e. data in the form of words

• Involves finding out what people think and how they feel in more detail

• Often collected in case studies, unstructured observations and unstructured interviews

Range

• Often accompanies an average to allow the reader to gain a greater understanding of data sets. Illustrates highest and lowest score within a set of data

• +Easy to calculate, takes full account of extreme scores

• - Can be distorted by extreme scores

Standard deviation

• More sophisticated measure of variability, takes into account all scores and their difference from the mean value

• Larger the SD, greater spread of scores

+ Takes into account all scores, more sensitive

- Less meaningful if data not normally distributed

Calculating percentages

• Show the rate, number or amount of something within every 100

• Data shown as percentages can be displayed in many ways including pie charts and bar graphs

• Easily convert data into a percentage by multiplying them as a factor of 100

Calculating percentages increase/decrease

• Calculated using before and after scores

• First, calculate difference in numerical values

• Then divide by the original score and multiply it by 100

Ratios

• Used to compare quantities, but don’t give any info about the actual values

• Useful descriptives

• Calculated by dividing both numbers in the ratio by the same number

Graphs and tables

• Useful for summarising data, allowing psychologists to see patterns in data easily

• Different types of graph used for different types of data e.g. bar chart, histogram, pie charts, scattergrams, summary tables

Normal and skewed distributions

• When data is plotted on a histogram or bar chart, and the vertical axis is labeled frequency, the data often forms some kind of pattern that is referred to as a distribution

Normal distribution

• Revolves around the idea that with any given attribute or behaviour, most people will gain a score that centres on the mean e.g. height in cm

• With this distribution, the median, mean and mode occur at the peak of the curve

• It is symmetrical with the same number of scores above of below the mean

Negatively skewed distribution

• With lots of outliers, we get skewed distributions

• This affects the mean score more than any other average

• A negatively skewed distribution will contain significantly more high scores than low scores and can be classed as having a ceiling effect

Positively skewed distribution

• Will contain more low scores than high scores as shown by the mode

• They will also have most of the scores falling below the mean

• This can be classed as having a floor effect