Statistics are a way of assessing the quality of information being evaluated. The types of statistical analysis primarily relied upon in this study are mathematical mean (average), standard error t-probability, and Analysis of Variation between groups (ANOVA).

The null hypothesis states that all means are equal and there is no difference between them.  Therefore the alternative hypothesis tested is that the means are unequal.  The following statistical analyses were carried out to determine if the null hypothesis should be rejected or accepted.

Mathematical mean, or mean, is the same as average. It is calculated by determining the sum of all samples, and dividing by the n variable. Mathematical mean, or average, is a valuable descriptive statistic used in the analysis of the data collection.

The standard error of a sample of sample size n is the sample's standard deviation divided by the squareroot of n. It therefore estimates the standard deviation of the sample mean based on the population mean[1]. For example, if a sample size consisted of 5 different samples, the standard error measures the variation that could fluctuate from the mean if a different sample was collected. It is written as a decimal, for example (+/-) 0.1234. The (+/-) indicates that the mean could either increase 0.1234 from the mean, or decrease 0.1234 from the mean.

T-probability can be referred to as p value or t-test. The t-Test is used to compare the means of two samples. Specifically, this can be used to determine whether or not the means in two samples are significantly different. If the outcome (p value) is less than 5%, there is statistical significance between the two groups and the null hypothesis can be rejected. If the p value is greater than 5%, there is no statistical significance between the two groups. A p value of less than 5% ensures that the outcome is not just as a result of coincidence, but is indeed as a result of the variables in the experiment.

However when a t-test is used on its own to test significance, the chance of encountering a Type I error increases. A Type I error is a false positive which shows significance where there isn’t. To avoid a possible Type I error, and since the t-test only measures differences between two groups, a more powerful approach is to analyze all the data together. The model is similar and is called a one-way ANOVA and the test statistic is the F ratio. T-tests are a special type of ANOVA: if the means of only two groups are being analyzed by ANOVA, the same results are achieved as would have been achieved conducting the analysis with a t-test[2].

ANOVA tests whether there is statistical significance among the means of more than 2 groups, i.e. it tests the variability among group means.  ANOVA uses various statistics (sum of squares, degrees of freedom and mean squares) to produce the F-ratio and the sig. value. The F-ratio is a measure of how different the means are relative to the variability between each sample. The larger this value, the greater the chance that the differences between the means are due to something other than chance alone, namely real effects. For the F-ratio to be considered statistically significant, it has to be significantly greater than 1. Like the t-test, if the significance (sig.) value is less than an alpha level of 5% the result is statistically significant and the null hypothesis can be rejected. So an ANOVA test determines whether there is a difference among the means of the groups.