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Introduction To SPSS - Blog 2 On Standard Deviation

8/27/2014

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So in our previous blog we introduced the concept of Standard Deviation and how you use it in SPSS. 

Standard Deviation is a very useful concept if used with care and so I'm going to write a couple more blogs to help you understand more about how it is used in practice. The first one is how to interpret a standard deviation figure.

Probably a very useful way of interpreting a standard deviation is that, assuming that your underlying data is sampled from a Gaussian distribution (for these purposes a normal distribution), you expect approximately 68% of the values of your distribution to lie within one standard deviation of the mean of your distribution, and you expect approximately 95% of your distribution to lie within 2 standard deviations of the mean. Also by extension you can assume that 27% of your population will lie between one and 2 standard deviations from the mean, and 5% will lie more than 2 standard deviations from the mean.

So for example, imagine if your a distribution where the mean is 20 and the standard deviation is 5.

That means that the range within one standard deviation of the mean is 20 + or - 5 so between 25 and 15, and the range within 2 standard deviations of the mean is 30 to 10.

Therefore if you then take another reading the odds are 19 in 20 (95%) that the reading will be between 30 and 10.   

Similarly this also helps you understand why a lower standard deviation also implies a 'tighter' or more defined distribution. If the standard deviation of the above distribution was actually 2.5 not 5 then 95% of the values of the distribution would like between 20 + or - (2 * 2.5) = 25 to 15. This is the same range within which only 68% of the values of our original distribution would lie.

This can also be shown pictorially. The illustrations at the bottom of this post illustrate this point for you.

Don't worry I will write a follow up blog post to give you some more detail on Gaussian distributions but for these purposes we are assuming that your data is sampled from a normal distribution.

That's it for this week's SPSS blog.







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What is Standard Deviation And Where Do I Find It In SPSS

8/18/2014

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Today is another beginner's tip for people new to using SPSS. What is the standard deviation of a dataset and how do I use SPSS to calculate it.

Standard Deviation is a measure of how widely dispersed our dataset is. It is a fairer and more comprehensive way of describing a dataset than just using a simple mean, median or mode. It actually describes how widely a dataset is dispersed from its mean. This of course means that in order to be really useful, you also need to know the units that your standard deviation is in and the mean of the dataset that it refers to as well. On it's own a standard deviation figure is unlikely to be very useful. A low standard deviation figure implies a tight or little dispersed dataset and conversely a large standard deviation implies a widely dispersed dataset.

It is useful to know how standard deviation is calculated as well so here goes.

It is the square root of the mean of the square of the differences of each variable in the dataset from the datasets mean. So in order to calculate it the sum of all of the squares of each piece of data's difference from the mean of the data set is taken. To get the mean it is then divided by the number of pieces of data and the square root of that is taken.

It is probably most easily illustrated by example. Image a dataset of 3 items - 9, 8, 7, 6 , 5

The mean of this data is 7 and so the square of difference from the mean for the data is 4 (9-7)^1 , 1 (8-7)^1 , 0 , 1 , 4

So the sum of the square of the differences is 10. There are 5 items in the data set and so the mean of this figure is 2 (10/5), and the square root of it is 1.414.

So for our very simple distribution the mean is 7 and the square root is 1.414. Obviously it can be far more complicated to calculate for larger and more

In SPSS to calculate the standard deviation for a dataset it is a very simple process. Select your variables, click STATISTICS and select Standard Deviation as well as Mean and click CONTINUE. SPSS will now very quickly and simply calculate the mean and standard deviation of your data.




I will post more in my next post about standard deviation as it is an important concept in statistics and so for anyone using SPSS. 

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Calculating Mean and Median in SPSS

8/12/2014

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In SPSS it is very quick and simple to calculate the mean and median of a sampl. 
 
You simple choose ANALYSE > DESCRIPTIVE STATISTICS > EXPLORE. You will then need to ensure that in the dependent list is the quantity that we are measuring and describing and in the factor listing we put the factor or quantity that we are exploring. 

So for example the quantity might be people's ages and in the factor listing we would put where they come from. 

SPSS will then calculate the mean and median of your data set for you. 
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Back To Basics - The Difference Between Mean And Median

8/4/2014

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A quick one today. I thought we should just remind everyone of the difference between Mean and Median to avoid any confusion as the issue arose in one of our recent training classes for SPSS.

Both Mean and Median are different types of averages. The mean value is based on all of the values within the data and so will include outliers. In small datasets significant outliers can have a significant impact. It is calculated as the sum of all of the variable in the dataset divided by the number of items in the dataset.

So for example imagine our dataset is 1,11,12,13,14. The sum of these is 51, divided by 5 which gives a mean value of 10.2. As this is less than 80% of our dataset (chosen to illustrate the point!) in this case the outlier has made the mean a less useful statistic.

The Median however is the middle number in an ordered dataset. So imagine our dataset was actually 11,13,1,14,13, we would first order the data into 1,11,12,13,14 and then choose the middle number in the dataset, so 12 is our median. As you can see where you have an outlier in the data the median is a far more useful and representative figure as it removes the influence of the outlier.

The median is easy to calculate for datasets with odd numbers of pieces of data in them. For datasets with even numbers of pieces of data in them we calculate the mean of the middle 2 pieces of data. So assuming that our dataset had an additional piece of data in it, 15, our middle 2 pieces of data would be 12 and 13. Taking the mean of them would give a median of 12.5.  
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