Measures of central tendency What? How calculated? Strength/ weakness Mean Median Mode Measures of dispersion Range Standard Dev

Mean All scores are added together and divided by the number of scores. + Takes into account all the scores so is the most sensitive measure of central tendency - Can be distorted by a particularly high or low score in the data set (anomalous score)

+ Is not distorted by a particularly high or low score Median Put the scores in order and take the middle score. + Is not distorted by a particularly high or low score - Is less sensitive than the mean as it does not take into account all of the scores.

- Least sensitive measure and often not very representative/ useful Mode The most frequently occurring score in a set. + Easiest to calculate - Least sensitive measure and often not very representative/ useful

- Is distorted by anomalous scores & can be misleading. Range Take the lowest score form the highest score. + Easy to calculate. - Is distorted by anomalous scores & can be misleading.

- More complicated to calculate than the range. Standard deviation: The average of how far your participants’ scores ‘deviate’ (move away) from the mean. A large SD suggests that not all pp’s were affected by the IV in the same way because the data was quite widely spread. A small SD shows all data is clustered around the mean, so pp’s responded in a similar way. + Uses all the data from your set in the calculation = more sensitive measure than the range. - More complicated to calculate than the range.

Standard Deviation This is a graph of height in any given adult population: Most people fall in the middle with a few very tall people and a few very short people. The line is what we call, the bell curve. It shows a ‘normal’ distribution.

Standard Deviation This bell curve shows a large standard deviation. This bell curve shows a small standard deviation. They may show the same mean, but pp’s have performed very differently in each group. This informs us on how much we should trust our mean as a general indicator of pp performance.

Using the mean, standard deviation and a normal distribution to see the shape of your data set. Is our mean score representative of our data set? Lets draw two normal distributions for these data sets and find out … Data 1. Mean = 14 SD = 3 Data 2. Mean = 24 SD = 1 24 Mean line. Mean score. + 1 SD + 2 SD + 3 SD - 3 SD - 2 SD - 1 SD

Using the mean, standard deviation and a normal distribution to see the shape of your data set. Is our mean score representative of our data set? Lets draw two normal distributions for these data sets and find out … Data 1. Mean = 14 SD = 3 Data 2. Mean = 24 SD = 1 24 Mean line. Mean score. + 1 SD + 2 SD + 3 SD - 3 SD - 2 SD - 1 SD

Standard Deviation Remember that the standard deviation is about the spread or dispersion of data. Consider this, you are going to buy a bottle of wine. Imagine there is a scoring system for wine out of 20. Chateau Plonk Mean points score = 10 Chateau Neuf du Piddle Mean points score = 10.5  Which would you choose? The second one of course!

Standard Deviation Chateau Plonk Mean points score = 10 Standard Deviation: 0 Chateau Neuf du Piddle Mean points score = 10.5 Standard Deviation: 5.9 What does this additional information tell you?

The judges CONSISTENTLY gave Chateau Plonk 10 out of 20 Let’s look at the judge’s individual scores: Judge 1 20 Judge 2 19 Judge 3 18 Judge 4 17 Judge 5 16 Judge 6 15 Judge 7 14 Judge 8 13 Judge 9 12 Judge 10 11 Judge 1110 Judge 12 9 Judge 13 8 Judge 14 7 Judge 15 6 Judge 16 5 Judge 17 4 Judge 18 3 Judge 19 2 Judge 20 1 The judges CONSISTENTLY gave Chateau Plonk 10 out of 20 Okay so one judge gave Chateau Neuf du Piddle 20 out of 20 but another only gave it 1! The first set shows a much clearer effect – the other data could be a random spread generated by chance.

Distributions Some distributions are not normal. Its important to know if your distribution is skewed as it means you have outliers – spurious results that drag your mean up or down artificially. Most inferential tests are only reliable on data that is normally distributed, so you need to check before you do them.

Skewed distributions Normal distributions will have virtually identical mean, median & modes. Imagine an easy test – lots of people do really well and very few do badly. Note – the ‘skew’ is the tail, so this is a negative skew. Describe what’s happening to the measures of central tendency.

Skewed distributions Now imagine a really hard test… This produces a positive skew. Describe what’s happened on the test, and what’s happening to the measures of central tendency.