Inferential statistics: degrees of freedom, significance testing, and assumptions

Inferential Statistics and Their Discontents

The notion of conducting statistical testing is increasingly important because of the significance testing is the basis of statistics. Inferential statistics is an important part of this process despite the necessity of descriptive statistics, which help in data exploration and interpretation. Actually, one of the most important aspects of inferential statistics is significance testing largely because this is what statistics are centered on. Generally, inferential statistics mainly focus on statistical concepts and thinking. There are several components to consider when examining inferential statistics including degrees of freedom, what to infer, General Linear Model, parametric and non-parametric statistics, and assumptions of the statistical test.

Degrees of Freedom and How they are Calculated

Degree of freedom is a term that is commonly used to refer to mathematical equation utilized in statistics as well as other fields like chemistry, physics, and mechanics. However, many researchers seemingly struggle to understand this concept because of reluctance to understand its importance in statistical testing. This concept is defined as the number of scores in any sample that can change in a free and easy way. Given the broad nature of degrees of freedom, calculating them is increasingly important because the number of degrees enables an individual to know the number of values in the final calculation that is permitted to differ (Lawrence, n.d.).

Degrees of freedom are calculated using different steps beginning with determination of the type of statistical testing to be carried out. This is followed by identifying the number of independent variables in the population or sample. The third step in calculating degrees of freedom is identifying important values for the equation using a critical value table in order to determine the statistical importance of results.

Inference in Inferential Statistics

Statistical significance testing in inferential statistics has been increasingly relied upon to provide equivalent information though it has come under considerable attack in recent decades because of researchers' fantasies (Carver, 1978). The increased dependence on statistical significance testing is primarily because inferential statistics allow a researcher to infer certain elements in the study. Inferential statistics allow the researcher to infer what he/she can report or state regarding a population. However, these statements must be based on the conclusions or findings in a research on a representative sample of the population. The research study on a representative sample of the population must in turn comply with certain statistical and sampling processes or procedures.

General Linear Model and its Significance

The General Linear Model (GLM) is an ANOVA process that entails performing calculations through a least squares regression mechanism. This procedure is geared towards explaining the statistical link between at least one indicator and a constant response variable. Consequently, the general linear model combines different statistical frameworks into a dynamic simplification of linear regression. The combination of these statistical models is carried out in a way that response variables seemingly differ from normally distributed variables. The predictors whose statistical relationship with constant response variable is evaluated in general linear model can either be factors or covariates in the study. If these predictors are covariates, the covariates may be crossed and intertwined with one another or with factors. In some cases, these covariates may as well be nested within factors instead of being crossed. As a result, the subsequent design from crossing or nesting covariates can either be balanced or unbalanced. The general linear model can carry out several comparisons between means of factor level in order to determine considerable differences ("What is a General Linear Model?" n.d.).

Given the various processes involved in the general linear model, this ANOVA process matters for several reasons. First, the general linear model matters because it helps in accurate summary or description of events that are taking place in the data. This process achieves this through enhancing the ability of data analysis procedures. Secondly, the general linear model promotes the discovery of advanced models for statistical tools, which help in improving statistical testing. This is primarily because this model effectively combines incongruent statistical tools into a single model or technique.

Importance of Assumptions of the Statistical Test

Statistical procedures including parametric and non-parametric tests have underlying assumptions that are stringent in some cases. The violation of these assumptions can either alter substantive research findings/conclusions or undermine meaningful research. The assumptions in parametric statistical tests are the interval level of evaluation and homogeneity of variances when comparing at least two samples. On the contrary, non-parametric tests do not have assumptions relating to a certain or specific distribution of data (Garson, 2012). Since all statistical procedures have some underlying assumptions, it is increasingly important to pay attention to the assumptions of the statistical test. This is largely because assumptions made regarding some aspects of the problem under evaluation determine the validity of the statistical process. Moreover, it is important to pay attention to assumptions of the statistical tests, especially parametric tests, because failure to do so may lead to inaccurate, wrong, and misleading results. If dependent variable scores are not normally distributed, a t-test parametric analysis or non-parametric statistical test can be conducted if the variable scores are bell-shaped or not bell-shaped respectively.

In conclusion, statistical tests and procedures are carried out using different techniques depending on the nature of the study and variables in the tests. While there are different statistical techniques and tests such as parametric and non-parametric statistics, all statistical procedures are based on some underlying assumptions.