Standard Deviation, Hypotheses, and Standard Error - Statistics Project Example

Standard Deviation, Hypotheses, and Standard Error Answers: Hurlburt (2001) defines standard deviation as a number representing how scattered or how closely bunched a set of data is around the mean. It is the most commonly used measure of variability because it is claimed as the most reliable. Mathematically speaking, it is the positive square root of the average squared deviations from the mean of the distribution. By the knowledge of standard deviation, one can describe a set of data as homogeneous (closely bunched) or heterogeneous (scattered).

Likewise, researchers use standard deviation to verify normal distribution. By the empirical rule, if a set of data is normal, about 68% of the data lie within 1 standard deviation above and below the mean, about 95% of the data lie within 2 standard deviations above and below the mean, and about 99.7% of the data set lie within 3 standard deviations above and below the mean. In the above example, if a sample of n=20 has a mean of M = 40 and standard deviation of s=5, would a score of X= 55 be considered an extreme value?

The answer is yes. By means of the empirical rule, 55 is at 3 standard deviations above the mean, that is (55-40)/5=3. Therefore, 55 lies beyond 99.7% of the samples, and thus it is considered extreme value.Null hypothesis (Ho) claims that the independent variable has no significant impact (relationship, association or effect) of the dependent variable being tested (Kanji, 2006). Example, if a cancer medicine is tested on its effect, the null hypothesis could be, “The medicine is not effective in curing cancer”.

It shows the absence of the effect or impact of the medicine to cure cancer. On the other hand, the alternative hypothesis (Ha) is the opposite of the null hypothesis. It claims that the independent variable has a significant impact on the dependent variable (Kanji, 2006). In our example, the alternative hypothesis could be, “The medicine is effective in curing cancer”. In research, if the null hypothesis is rejected, the alternative is accepted, or the reverse.Standard error is defined as the standard deviation of the sample means as referenced on the population mean.

In a population, for example, one portion of it (sample 1) is taken and found its mean. If another sample is taken, the mean could be different. And if another sample is again taken, possible, the mean would be different again. It this example, the population mean may not be estimated by one or any of the sample means because of discrepancy, thus, the standard deviation of the 3 sample means is taken, which is now called the “standard error” (Myers and Well, 2003).From the example presented, if the sample size is 16, the error is 5, and if the sample is 100, the error is 2.

It is seen that the greater the sample size, the lesser the error. In other words, as we take more samples, we are assured that we are estimating the population parameter closer to reality. Thus, a researcher should take large sample size as possible so that the result could be better and more reliable.References:Hurlburt, R. (2001) Comprehending Behavioral Statistics Brooks/Cole Publishing Company, New York, USAKanji, G (2006) 100 Statistical Tests Third Edition SAGE Publications, LondonMyers J and Well A (2003) Research Design and Statistical Analysis Lawrence Erlbaum Associates, Publishers.

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