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This is the scary bit, but do not fear 'cos Little Gerry is here!

What you want to do is present your results in a meaningful way, and then make some sense of them in the light of your null hypothesis. To do this we use some descriptive statistics and an inferential statistic called the t-test. Before you do anything though, you need to make up and complete a Raw Data table like the one below.


Raw Data Table

Participant Gender
Male / Female
Condition A
IQ Estimate Mother
Condition B
IQ Estimate Father
1 Male 102 106
2 Female etc. 100 110 etc.
3      
4      
5 etc.      


Make sure in any study you include a completed raw data table as an appendix.

When you have filled this in you can then use statistics to make sense of it. You could for example work out

1 the mean and median values of IQ estimate in each condition.

2 construct a histogram and a line graph for each participant's estimate for each parent. Individual participants go from 1-XX along your x-axis while IQ estimates go along the y-axis. With a histogram two 'bars' are allocated to each participant's estimates - one for the mother, and one for the father. Make sure axes are labelled; the diagram is given a name, and a fig. Number etc

3 You could also do the same thing with all female, and then male, estimates of each/both parents IQ. This may throw up some interesting patterns.

4 You may also want to use an inferential statistic called the related t-test that will allow you to accept/reject your null hypothesis, and consequently reject/accept your experimental.

Remember that you have a level of significance of 0.05, which means that whatever happens you accept a 1: 20 probability that your results occurred by chance or random factor.

You are allowed to us the related t-test because

  a) Your research hypothesis predicts a difference between perceived IQ scores based on a person's gender. N. B. H1: 'That gender has a significant effect on perceived intelligence.'
  b) You have interval data (estimated IQ scores)
  c) Your data is related because you are using a repeated measures design


It is always a good idea before you present a statistic in a results section to say what each statistical term means e.g. what is meant by the mean or median of anything, and why is a particular inferential statistic like the related t-test appropriate in this circumstance.

Its appropriate because our data meets the conditions for the t-test above. Say so and you'll get buckets of marks - as long as it makes sense!




This is how you use the t-test. First consult your raw data chart and construct the following.

Related t-test calculation

Put the condition you expect to be higher first!

Participant Condition B
IQ Estimate Father
Condition A
IQ Estimate Mother
d
1 106 102 4 16
2 110 100 10 100
3        
4        
5 etc.        
      sigma(d) sigma


Steps


  • Enter in your participants 1-XX in the Participants column
  • Enter in his or her estimates for each parent e.g. Participant 1 102 and 106
  • Find the difference (d) between theses scores for each participant e.g. with participant 1 the difference is 4.
  • Then square this difference (d²). With participant 1 d² is 16. Having worked out d and d² for each participant Sigmayou now need to work out two last things;
  • Find the sum of the (d) column giving you sigma.gif(d), and then
  • Find the sum of the (d²) column giving you sigma.gif



In statistics when you see the sign sigma (sigma), this means 'add up'. The t-test is as complicated as this! Now put this data into a t-test formula and work out the answer. You have everything you need to know e.g. N, {short description of image}(d), and Sigmad² : N is the number of participants who took part in your study. The related t-test formula is


t-test formula


You would have this formula in your Results section, and underneath it the answer for calculated t. The t-test calculation should be in an appendix. Direct the reader to this. Once you have worked out calculated t, you want to know if it means anything. Is your result 'significant' . To do this is quite simple. You consult a critical value table for the related t test for which you need to know three things

  a) Whether you have a one-or two-tailed hypothesis. This example is two-tailed.
  b) The level of significance set for your null hypothesis; being 0.05, and;
  c) The number of degrees of freedom you are operating at. Degrees of freedom (df) are calculated as N-1. N being the number of participants who took part in your study.


Lets say I ran this experiment with 22 participants and worked out calculated t to be 7.71. Consulting the critical value table for a two-tailed test, with a level of significance of 0.05, with 21 degrees of freedom (df = N-1, or 22-1 = 21) I find that critical (tabled) t is 2.080. The instruction at the bottom of the table should now be followed. It says that 'calculated t must EQUAL or EXCEED the table (critical) value of significance at the level shown.' My calculated t of 7.71 does indeed equal or exceed the critical, tabled value of t, being 2.080 for a two-tailed test, with a level of significance of 0.05, with 21 degrees of freedom (df = N-1). As a consequence I can say in my Results section that on this basis the null hypothesis is rejected and the Research hypothesis H1: 'That gender has a significant effect on perceived intelligence' is accepted.

The results section in using the mean, the median, histograms, line graphs and the related t-test makes statistical sense of our data. This is extremely useful in the Discussion section that now follows.




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