Psychological research often requires a numerical and quantitative organization of results that they get from their findings – the results in question is called ‘raw data’. To categorize large findings in these scenarios, it is often mathematically simplified and visually represented via graphs.
The numerical results collected by psychologists is known as ‘quantitative data’, the data which is detailed and descriptive is called ‘qualitative data’. Quantitative data indicates the quantity of the psychological measure I.e. the strength or amount of a response and tends to be measured on scales, such as time, or as numeric score on tests such as Personality, IQ and T-maze tests.
Quantitative data is associated with experiments and correlations which use numeric scales but it is also possible to collect quantitative data from observations and interviews.
Measures of central tendency:
A set of quantitative results can be boiled down to represent the middle score and an aggregate – this is known as measures of central tendency.
The mode is most the frequently repeated score, number in a data set. There can be more than 2 modes. It is unaffected by extreme scores and it is useful to observe repetitive behavioural patterns. An example of this would be Milgram’s study where there was a modal value of the voltage scale that was frequented on participants.
Limitations of using this measure is that it offers no insight about the other scores, it isn’t very ‘central’, it is also very fluctuating from one sample to another.
545350,8,7,7,7,7,0. - the mode is 7.
Unlike the mode, the median cannot be used with data indiscrete categories as it is only used with numerical data on a linear scale. To find the median, all the scores in the data set are put in a list from smallest to the largest. The middle one in the list is called the ‘median’. To configure this, all scores are arranged from ascending order – the middle number in this is the median value. If there are an even number of participants, in which case there are two numbers in the middle, these are added together and then divide by 2.
In essence, the median value is the halfway point that separates the lower quartile from the upper quartile. It is unaffected by extremes, in the sense that there is no distortion of results. It however can be misleading when there are only a few scores and doesn’t take into account most of them.
Score set: 3,4,7,8,9,0,2,2,6 – median being 9.
Score set: 2,6,8,10,13,16 – median being = 8+10/2 = 9.
The mean is the measure of central tendency that we usually call the ‘average’. It can only be used with numerical data from linear scales. The mean is worked out by adding up all the scores in the data set and dividing them by the total number of scores. It is the most thorough and informative measure of central tendency as it takes into account all scores. There is however the probability of it giving a distorted result if there are any anomalous scores.
It is done by adding up all the values to find a total, dividing the value by the number of values added together that were present.
2+4+6+8+10+12/6= 7 – the mean value.
Measures of Spread
This indicates how far spread, dispersed and varied data is within a set. If two data sets are the same size, with the same mean, they could still avry in terms of how close the majority of data points were to that average. Differences such as this are described by measures of spread: the range and the standard deviation.
It is the simplest measure of spread.
1. Find the largest and smallest value in the set of data.
2. Subtract the smallest value from the largest value and add 1.
Conventionally, the addition of 1 is not done. In psychological research this is done so that we measure the gaps between points, not the points themselves.
The Standard Deviation:
In the same way that the mean can tell us more than the mode, a measure of spread called the standard deviation can tell us more than the range. Range than looking only at the extremes of the data set, the standard deviation takes into account the difference between each data point and the mean – this is known as deviation from the standard.
As the standard deviation tells us the spread of a group, groups with scores that are more widely dispersed have a larger standard deviation. When the standard deviations of two groups are similar, this indicates they have a similar variation around the mean/average.