¶ … scientific studies involve the use of quantitative research designs whose experiments are sometimes described as true science. In this case, the research designs employ the use of conventional mathematical and statistical procedures for measurement of conclusive results. Experimental designs used in quantitative research methods involves examining various aspects that are important in a study including F-ratio, analysis of variance, significant effects, and determining probabilistic equivalence. Generally, experimental designs in quantitative research utilize a standard format in order to generate a hypothesis that can be proved or rejected. What is an F-ratio?

An F-ratio is a beneficial test statistic that is most commonly associated with ANOVA analysis. In this case, the F-ratio is utilized to test the hypothesis whose effects are regarded as real i.e. they are significantly different from each another. In an ANOVA analysis, the sampling distribution of the F-ratio must be discussed prior to presentation of the details of the hypothesis testing. Generally, F-ratio is used to test hypotheses regarding the impact of an independent variable on a dependent variable ("Variance and the Design of Experiments," 2007). One of the technical terms in an F-ratio is numerator, which refers to the treatment variance. Secondly, denominator is another technical term in F-ratio, which refers to an error variance.

Error Variance and Its Calculation

According to Gabrenya (2003), analysis of variance is a term used to represent what the analysis is about instead of t-test since the focus of the statistical procedure is examining variances. Actually, Analysis of Variance, which is commonly known as ANOVA, is a general-purpose statistical process employed to examine a series of research designs and analyze many complex problems. When conducting variance analysis, a ratio is created between the variances in the mean of the groups and the error variance...

In essence, error variance is the variability that cannot be described through systematic variations between groups in the research design and process. The systematic difference is usually an indication of differences that could be expected by researchers in case of lack of true differences between the research groups. Error variance is calculated through the use of the sum of squared residuals where the mean square for error is divided by relevant degrees of freedom.
Need for More Levels of an Independent Variable

Independent variable is sometimes referred to as grouping variable since every group in the research process has a certain level or value of the variable. While every member of the group in the research process will obtain or engage in similar intervention, there are differences in variables for varying groups. Generally, independent variables need to have at least two levels or groups though they may have more levels. However, the researcher should not have more than five levels of independent variables.

One of the major reasons an individual may want more than two levels of independent variables is because of the need to compare more groups that vary based on only a single factor in order to attribute one variance to the differences between groups in the study. This implies that more than two levels of an independent variable are needed for the researcher to manipulate one variable and examine the impact of that manipulation on another variable. Secondly, the need for more levels in an independent variable is simply because the experiment may not involve manipulation of a variable but comparison of pre-existing groups (Wright & Lake, n.d.).

Within Groups Variance vs. Between Groups Variance

ANOVA usually reports the variance within groups and calculates how these differences would contribute to variations between groups in consideration of the number of groups involved in the…