In this section we will cover statistics, loosely defined as ways of using numbers, tables and figures to represent the data you collect. There are two main types of statistic: descriptive and inferential. What are descriptive and inferential statistics? Well, descriptive statistics only describe what you have found. This includes means, standard deviations, and graphical representations of your data. Inferential statistics allow us to make statements about the populations. Imagine a study we set up to look at reading skill and educational placement? Well, we cannot select all of the possible children. We can only select a subset of all the deaf children in mainstream and sign bilingual schools. This subset is called our sample; all of the deaf children in mainstream and sign bilingual schools are called our population. Descriptive statistics describe our sample; inferential statistics allow us to make statements about the population from which that sample was selected.
Whatever study you choose to conduct, it will probably have a target population. The target population is the group of people who could be involved in your study. For example, if you wanted to do some research on British Sign Language learning by hearing people, then your target population would be all hearing people who are currently learning British Sign Language. Thats a lot of people! So, in practice, you will probably select a smaller group of people for you study say 3050 people in the Bristol area. These 3050 people are your sample. Maybe you test the number of learning strategies they use, and find that on average they use 3.4 strategies. This is an average, or in research terms usually called a mean. This is an example of a descriptive statistic it describes the average score for your sample. Other types of descriptive statistic include standard deviation and sample size. Standard deviation is a statistic that measures how much the scores of the sample vary. If everyone in the sample gets the same score, then the standard deviation will be 0 (zero) the more the different scores vary, the higher the standard deviation. Sample size indicates how many people there are in the sample in this example it may be 35 (indicating 35 different hearing BSL learners).
Descriptive statistics are reported in the Results section. You will not normally report all of your raw data in the Results section, including it in an Appendix instead. Often the descriptive statistics are incorporated in a Table, or presented as a Figure (such as a graph or diagram). More on this below.
Normally, you do not want to confine your findings to this sample you want to be able to generalise your findings to all hearing BSL learners (i.e. the target population). In order to be able to do this, you need two things:
Inferential statistics are beyond the scope of this short introductory course, and again you will need to discuss with your supervisor the appropriateness of using them and how to go about doing so. We will make one important point here, though. You want to minimise the chance of making a mistake when you say two groups are different. The more participants you have, the less likely you are to make a mistake. A large number of participants is good. This is not related to the size of the target population, for statistical reasons you do not need to worry about. Focus upon your sample, and try to make it as large as possible.
More now on descriptive statistics, and how to report what you find in your study. As we saw in the previous section, descriptive statistics do just what they say describe the data you have collected. In your results section, you will state the kind of data you collected and then present it in a form which the reader can understand. Merely presenting a large table with all your raw data will not help the reader. You must help them make sense of what you found. Normally this is done with a Table or a Figure.
There are 3 different types of descriptive statistic that you should report:
Make a table with 4 columns, as shown below.
In the first column, enter the scores for each participant.
Score 
Mean 
ScoreMean 
(ScoreMean)^{2} 
6 



7 



4 



5 



3 



5 



6 



8 



2 



4 



Next, calculate the mean score and enter that in column the second column.
Score 
Mean 
ScoreMean 
(ScoreMean)^{2} 
6 
5 


7 
5 


4 
5 


5 
5 


3 
5 


5 
5 


6 
5 


8 
5 


2 
5 


4 
5 


Subtract the mean from each score, and enter the differences in the third column.
Score 
Mean 
ScoreMean 
(ScoreMean)^{2} 
6 
5 
1 

7 
5 
2 

4 
5 
1 

5 
5 
0 

3 
5 
2 

5 
5 
0 

6 
5 
1 

8 
5 
3 

2 
5 
3 

4 
5 
1 

Now square each of these differences (multiply them by themselves) and enter the new value in the fourth column.
Score 
Mean 
ScoreMean 
(ScoreMean)^{2} 
6 
5 
1 
1 
7 
5 
2 
4 
4 
5 
1 
1 
5 
5 
0 
0 
3 
5 
2 
4 
5 
5 
0 
0 
6 
5 
1 
1 
8 
5 
3 
9 
2 
5 
3 
9 
4 
5 
1 
1 
Add all of the numbers in the fourth column together.
1 + 4 + 1 + 0 + 4 + 0 + 1 + 9 + 9 + 1 = 30
Finally, take the square root of this number.
_{}5.48 = standard deviation
The larger the standard deviation, the more variation there is in the group of scores. It is important to know this, as it gives you extra information about whether two groups of scores are really different. Consider the data given in the Table below:

Group A 
Group B 
Mean 
4.3 
6.4 
Standard deviation 
3.5 
4.2 
Looking at the mean alone, you may conclude that group A scored higher than group B. While this is true on average, by looking at the standard deviations we can see that the scores within each group varied a lot. This means that many members of group A will have scored more than group B, and vice versa. If we performed an inferential statistical test on this data, we would probably find that there was no real difference between the two groups as the scores varied widely for each of them.
There are commonly accepted abbreviations for the mean, standard deviation and sample size. The ones that you should use are M (mean), SD (standard deviation) and N (sample size).
Generalisability of Research Data http://trochim.human.cornell.edu/tutorial/ward/tutorial.htm
Central Tendency & Dispersion http://www.psychstat.smsu.edu/introbook/sbk13.htm
Statistics Every Writer Should Know http://nilesonline.com/stats/