Hello,
I am just wondering how can we decide what standard deviation is accepted for a speaking test? For example, if a test-taker scores 93, 92 and 92 respectively in three test administrations, the standard deviation is 0.57, which is good. That is, the standard deviation is not far from the mean (average, 92.33), but how can we decide what standard deviation is basically accepted? and is it accepted if the standard deviation is 3.47, 3.97 or 2.86?
Thank you in advance
Hello,
Standard deviation (SD) is not to be accepted or rejected. It is to be acknowledged. In one sample it may be much higher than in the other.
Regards, Witold
Hello again,
Forgot to mention, that SD indicates variability of scores - for example, the higher value for one SD (it is useful to see the range of scores) the more scores deviate from the mean score.
Regards, Witold
Karwan -
You might be more interested in the standard error of the mean. As Witold indicated, a standard deviation is a fixed statistic of the population, like a mean, but you may want to estimate the mean, and consider its standard error. The estimate for a standard error of an estimated mean is dependent upon the population standard deviation, and your sample size. Once you have an estimate of the (fixed) standard deviation of a population, you can use that and the desired standard error, to estimate the sample size needed to obtain that estimated standard error of the estimated mean. A confidence interval may be used. If the sample was far from 'normal,' and the sample size too small for the Central Limit Theorem to be helpful, you can still, at the least, consider Chebyshev's Inequality.
Cheers - Jim
Dear Witold,
Hello,
I thank you very much for adding your answer. That was really helpful! I was not much aware of that as I am a new researcher indeed.
Peace,
Karwan.
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