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Confidence interval and research terminology

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Confidence interval and research terminology

Postby » Mon Apr 07, 2014 8:33 am


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. ... 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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