6 - DATA HANDLING AND ANALYSIS [RM3]

what are statistics

a method of summarising and analysing data for the purpose of drawing conclusions about that data

compare descriptive vs inferential statistics

* descriptive - allows us to summarise the data e.g. mean, median, mode, range, standard deviation
* inferential - allow us to say whether the results are significant (whether the results are due to chance/happen or not)

measures of the central tendency

a descriptive summary of data set through a single value that reflects the centre of data

examples of measures of central tendency

mean, median and mode

mean (average)

* add up all the numbers and divide by the total number of numbers in the data set
* e.g. 1 + 2 + 3 + 4 + 5 = 15 / 5 = 3

limitations of mean; can be distorted by an outlying number

* can be distorted by extreme scores/values (outlier).
* it can be used with ordinal and interval data but not with nominal data
* if we replace 1 in the data set with 98, the mean becomes 108 which does not really represent the data overall

strengths of mean; more representative of data

* its more representative of data
* why? - it takes into account all the data and includes all the scores/values in the data set, making it more representative as a whole

median (middle)

* arrange scores in ascending order and find the middle value
* e.g. 1, 1, 3, 4, 5, 6, 9, 27 = 4.5

strengths of median; median can't be skewed by an outlying number

* the median does not take all scores into account, so it can't be skewed by an outlier.
* so, extreme scores do not affect the median so whether we replace 27 with 98 in the data set, the median is still 4.5

strengths of median; easy to calculate

it's easy to calculate once you've arranged the numbers in ascending order

limitations of median; less representative of data than mean

* it does not represent all the data.
* it can't be used with nominal data.
* it's less sensitive than mean as the actual values of lower and higher numbers are ignored and extreme values may be important.
* extreme values may be important but median ignores the values of higher or lower numbers

mode (frequency)

* it's the score which occurs most frequently in a data set
* e.g. 1, 1, 1, 2, 2, 3, 4, 5 = 1

strengths of mode; can't be skewed by outlying number

* it isn't distorted by extreme scores e.g. the number of people who chose ice cream as their favourite dessert will be the modal group as they were the majority of the data set
* this is good because mode is the only method you can use e.g. if you asked your class to list their favourite dessert the only way to identify the most typical/average value would be to select the modal group

limitations of mode; less representative than mean

* can't be used with all types of data so it's not representative of the whole data se as it only focuses on the numbers that are most frequent in the data set
* this is bad because it may not useful if there are several modes

modes of dispersion

dispersion is how dispersed or spread out the data is

examples of modes of dispersion

range and standard deviation

range

* the range is the measure of the spread of the data set of scores. it is the difference between the highest value and the lowest.
* i.e. highest value - lowest value + 1
* e.g 1, 7, 2, 8, 9, 27 = 27 - 1 + 1 = 27

strengths of range; easy to calculate

it's easy to calculate because it shows the extreme values

limitations of range; not representative of data

* it's affected by extreme values and doesn't take into account the number of observations in the data set
* it does not give info on whether the scores are clustered around the mean of spread out

standard deviation

* the measure of the spread of data around the mean.
* the bigger the number the more spread out the data is, meaning it deviates more from the standard (mean) as data collected was less consistent

strengths of standard deviation; representative of all data

* it's a more precise measure of the spread of data because all values are taken into account
* this is good because it provides greater accuracy - less affected by anomalies and values (all) are taken into account

strengths of standard deviation; not easily distorted by extreme scores as range

not distorted by extreme values because it's a more sophisticated calculation

limitations of standard deviation; can still be skewed by outliers

* standard deviation can still be skewed by outliers because it uses all of the data
* so can be unrepresentative if one piece of data is very high or low