According to Chesemore (2011), statistics is concerned with methods based on mathematics theory and probability, which allowed scientists to summarize many observations concisely. The first recorded use of statistics was in the 16th century; it was used by gamblers and life insurance companies. The use and development of statistical methods has greatly expanded in the 20th century. The invention of the computer simplified calculation (Chesemore, 2011). On the shoulders of statisticians of the past, we have learned a great deal. In addition to learning that statistics is used more often than I thought, I have learned the methods, calculations, the theories behind the formulas, and the ...view middle of the document...
This is the only use for a z-test (Tanner & Youssef-Morgan, 2013).
The one sample t-test accomplishes the same thing as the z-test. The calculated t from the sample is compared to a t value which is determined by degrees of freedom and alpha. The t-test can be one-tailed or two-tailed, based on what is being tested. It can be used when there are fewer than 30 items in the sample and the sample is not normally distributed. The null hypothesis is that the sample mean and population mean are statistically equal. The alternate hypothesis is that they are not equal.
If there are two independent samples to be tested, an independent samples t-test can be used. In this test, 2 samples of the same size are repeatedly drawn. The data are subtracted and the result will be a distribution of difference scores. The null hypothesis would be that the population means are equal; the alternate hypothesis would be that they are not equal.
The t-test may be limited in the number of samples one could easily analyze, but ANOVA is much better and reduces cumulative errors which would occur if the t-test was used to analyze more than two samples. The one-way ANOVA tests the variances between and within the samples; the F ratio is used to determine statistical significance. For an ANOVA problem, the null hypothesis is that the population means are equal; the alternative hypothesis is that they are not. If the null hypothesis is rejected, further testing would be required to determine which sample(s) are not part of the population. Required conditions to perform a one-way ANOVA test include testing one independent variable, the categories of the independent variable must be independent,
And the independent variable must be nominal data, the dependent variable must be interval or ratio data, and the samples must be similarly and normally distributed. Fortunately, Excel has a tool which will perform a one-way ANOVA that displays statistics about the samples including the F-ratio.
If the F-ratio is not significant, further testing is required, such as Tukey’s HSD.
If there is more than one independent variable, factorial ANOVA can be used. As with one-way and two-way ANOVA, the samples must be...