Null and Alternative Hypothesis

Statistical Terms The author of this report has been asked to answer three broad questions about certain statistical terms and concepts. The first one of those will be standard deviation. The second of the three will be hypothesis testing. The final question will center on standard error and what it means. While statistics may be daunting and intimidating, the concepts and terms used in statistics parlance are not hard to understand or comprehend so long as they are explained and quantified carefully.

The first overall question is what precisely standard deviation happens to be. To put it simply, standard deviation is how dispersed a set of numbers are. For example, the numbers 1, 2 and 3 are very close together so the standard deviation value would be rather small. However, the numbers 1, 1000 and 1,000,000 would have a very large standard deviation because the overall range of the numbers is much wider. The formula for standard deviation is the square root of the variance.

The variance is the average of the squared differences from the mean (Math Is Fun, 2015). The author is then ask to consider a sample where the number of figures in the sample is twenty, the mean is forty and the standard deviation is five. The author is then asked whether a score of fifty-five would be an "extreme value." Since the mean is forty and the standard deviation is five, that would mean that fifty-five would be three standard deviations from the average.

While that is a bit of a difference, the author of this report would not consider fifty-five to be an "extreme" value. The author is now going to, as requested by the assignment, define the terms null hypothesis and alternative hypothesis. A null hypothesis is just another way of saying that there is no significant difference between populations based on whichever variables are being looked at.

Further, it is asserted with a null hypothesis that any differences that do exist are due to sampling or other errors and not because a true difference exists due to the variables in question (Investopedia, 2015). On the other hand, an alternative hypothesis is an outcome whereby sample observations are clearly influenced by some non-random cause. It may or may not be what the researcher is looking for and/or using as a variable.

However, if the experiment is done right, it absolutely should be because of the variables that are compared and contrasted. Null and alternative hypothesis are basically defined for each research study as a means to define what possible outcomes might happen. In other words, either the variables studied will have an effect or they will not is the usual question (Stat Trek, 2015). Finally, the author comes to standard error. The term refers to the standard deviation of the sampling distribution of a statistic.

The smaller the standard error, the more representative of a population the actual results will be. The author is presented with two pools where a sample of 16 has a standard error of five points while a sample of one hundred only has a standard error of two points. The likely cause for the smaller standard error with the second group is the larger.