StandardDeviation, Hypotheses, and Standard Error

StandardDeviation, Hypotheses, and Standard Error

Definitionof Standard Deviation

Standarddeviation alludes to the measure used that is used to find out thedegree of variation for a set of data. This means that a lower valuefor standard deviation, the data captured points towards the mean,while for higher values of standard deviation, means that there is awide spread of the data points on a range of values (Gupta, 1952).

Importanceof Standard Deviation

Knowingthe standard deviation of a given sample is significant as it helpsin the estimation of the population standard deviation.

WhatResearchers Learn about Normal Distribution

Outof the various concepts of standard deviation and informationgathered for the concept, researchers can tell the normaldistribution of values from the mean. Usually, for a normaldistribution, half of the normal distribution lies to the left of themean while the other half is to the right of the mean (Bland &Altman, 1986).

CalculatingSample

N=20

Mean=40

SD=5

X=55

Thisis an extreme value as the acceptable values for the calculation needto deviate from the mean by five on the lower or higher end. Thismeans that the lower value is 35 while, the higher value is 45. Giventhat 55 is ten points higher than the highest acceptable variation,it is treated as an extreme value.

NullHypothesis

Anull hypothesis is a hypothesis that is applied in statistics to showthat there is no statistical significance that exists between someset of observations made (Anderson, Burnham & Thompson, 2000).Through the null hypothesis, there is an indication that no variationoccurs between some variables or rather a given variable is not inany way different than zero. The hypothesis is held to be true up tothe point when the statistical calculation nullifies it and supportsthe alternative hypothesis.

Alternativehypothesis

Uponthe rejection of the null hypothesis, the alternative hypothesis isaccepted. Often, there is no testing of the alternative hypothesisgiven that testing focuses on the null hypothesis (Anderson, Burnham& Thompson, 2000).

Useof Null and Alternative Hypotheses in Hypothesis Testing

Inhypothesis testing, the null hypothesis is often treated to be trueup to the point when enough evidence exists to reject the nullhypothesis or fail to reject the null hypothesis. In hypothesistesting, if enough reasons exist to reject the null hypothesis, thenfor the alternative hypothesis, the evidence fails to reject it.Rather, it is required that it be accepted (Anderson, Burnham &Thompson, 2000).

StandardError

Thismeasure is to find out if the measure the degree of accuracy of asample as the ratio of the whole population. When using the sampledistributions, the standard error helps to tell the degree ofaccuracy of the sample distribution as representative of thepopulation distribution (Bland & Altman, 1996).

Calculation

PopulationMean = 100

Standarddeviation = 20

Thevarious errors that are between the sample means and the populationmeans are given below for different cases of sample:

Case1: n= 16 is 4

Case2: n= 100 is 2

SE_{x1-x2} =sqrt [ s^{2}_{1} /n_{1} +s^{2}_{2} /n_{2} ]

4-2= sqrt [ s^{2}/16+ s^{2}/100]

2=[s/4] + [s/10]S= 40/7

Standarddeviation for sample 1= 22.8857

Standarddeviation for sample 2= 57.142

Thisstandard error of the difference in the means of the two samplesalludes that the experimental degree of the variance of the samplemeans will be the difference in the given population means.

References

Anderson,D. R., Burnham, K. P., & Thompson, W. L. (2000). Null hypothesistesting: problems, prevalence, and an alternative. *Thejournal of wildlife management*,912-923.

Bland,J. M., & Altman, D. G. (1996). Statistics notes: measurementerror.*Bmj*, *313*(7059),744.

Bland,J. M., & Altman, D. (1986). Statistical methods for assessingagreement between two methods of clinical measurement. *Thelancet*,*327*(8476),307-310.

Gupta,A. K. (1952). Estimation of the mean and standard deviation of anormal population from a censored sample. *Biometrika*, *39*(3/4),260-273.