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Confidence interval and research terminology

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Confidence interval and research terminology

Postby sarah.pl.a8144 » Mon Apr 07, 2014 8:33 am

Hi,

Can anyone suggest a good text/article/website that explains terms such as confidence interval, standard deviation and other statistical terminology and it's meaning please ?

Struggling to interpret statistics.

Many thanks,
sarah :)
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Re: Confidence interval and research terminology

Postby goldstanda3269 » Wed Apr 09, 2014 6:23 pm

When I first looked at your question, I thought I could get you an easy online summary. University or College stats summary? Way too much detail for the GAMSAT. So I looked for a high school stats summaries. Yikes, still too much detail for GAMSAT!

OK, so we are a GAMSAT prep website, I hope to teach you the meaning of confidence interval and standard deviation while discussing the GAMSAT.

Please look at Figure 1.

http://www.gamsat-prep.com/GAMSAT-score ... HighScores

First notice that the curve of the distribution of GAMSAT scores follow the bell curve (as an aside: ACER would not describe the results of the GAMSAT as being bell curved; however, evaluating the results of annual GAMSAT tests over the years has a similar result to evaluating the height, weight or intelligence of populations: a normal bell curve).

Notice the mean or average GAMSAT score in the curve: 57. Sometimes it is 56 but 57 is the best average over the years. Notice that in the bell curve, there are the numbers 68% and 95%. This is not special for the GAMSAT, it is the way all bell curves operate. Plus or minus 34% (i.e. a total of 68%) represents plus or minus 1 SD (standard deviation). This is by mathematical definition. Likewise, within 2 SD covers 95%, and 3 SD covers 99%. Definitions. None of these numbers need to be memorized, I'm just giving you the background information.

So, for GAMSAT Scores, what exactly is 1 SD? It is 8 points out of 100. How can we read this from the graph? Because 68% of students get scores between 49 and 65 (notice that this means an average of 57 plus or minus 8 since 8 = 1 SD).

2 SD's? That means that 95% of students score between 41 and 73 (notice that this means an average of 57 plus or minus 2 SD = 2 x 8 = 16). And so on for 3 SD's, 99% of students.

If a corresponding hypothesis is performed, the confidence level is the complement of respective level of significance, i.e. a 95% confidence interval reflects a significance level (p) of 0.05.

Example: a random GAMSAT student is chosen. What is the 99% confidence level for the range of possible scores that the student could have? Answer from the graph and/or by remembering that the mean is 57 and 1 SD is 8 (i.e. 3 SD = 3 x 8 = 24): 33 to 81.

Certain factors may affect the confidence interval size including the size of the sample and the population variability. A larger sample size normally will lead to a better estimate of the population parameter (i.e. GAMSAT score).

btw, the next edition of the GS book will have a stats section.
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