# Research Methodology Sample Paper on Inferential Statistics

#### Inferential Statistics

Inferential statistics is a procedure used by researchers to draw conclusions based on data that is beyond simple description (Clayton, 2014). This method is used to make predictions from the collected data from samples and make generalizations about a population.According toPlonsky (2015),inferential statistics helps the researcher to compare sample data to other samples or to previous research using statistical models. This data is used to answer research questionsin order to make conclusions. Inferential statistics are used to make judgments that there is an observable difference between groups by determining the probability in the study. There are several types of inferential statistics that researchers can use. These methods include t-tests, analysis of variance (ANOVA), and regression analysis. T-test analysis has three basic types which include one sample t-test, independent sample t-test, and dependent sample t-test. Under the analysis of variance, there are also three basic types which include one-way analysis of variance, two-wayanalysis of variance, and factorial analysis of variance (Plonsky, 2015).

##### T-tests

The t-test is a type of statistical method that is used to compare means of two groups. It is a form of hypothesis testing used by statisticians to examine more variables and test larger sample sizes (Tae, 2015). There are several types of t-tests. They include one sample t-test, independent sample t-test, and dependent sample t-test.

##### One Sample T-test

According to Tae (2015), one sample t-test is used to compare data to the mean of a known population. This test shows a general research design of studies in which this data is selected to test hypotheses.The one-sample t-test is used in the collection of data on a single sample which is drawn from a defined population. In this design, there is only one group of subjects, and data collected from these subjects is used to compare our sample statistic to the population parameter. T-test is a type of parametric method that is used when samples satisfy the conditions of independence, equal variance, and normality (Tae, 2015).

Independent Sample T-test

Independent sample t-test is a parametric method that is used to calculate the difference between observed means in two independent samples (Abbott, 2016). This test is used to compare two groups that are independent of each other and determine whether there is a significant difference in the associated population means.This method is used to test the differences between the means of two groups, interventions and change in scores (Abbott, 2016).

##### Dependent Sample T-test

According to Tae (2015), a dependent sample t-test is a method used to test the difference between two paired results for a single sample. This indicates that a single participant is tested more than once. The researcher needs to have one dependent variable and a categorical variable which has two related groups. The difference in the results will be close to zero if there is no difference between the two paired results (Tae, 2015).

##### Analysis of Variance (ANOVA)

Analysis of variance is a statistical method used to test general differences in means for several samples by expanding the basic concepts on performing t-tests (Thomas, 2016). Analysis of variance is commonly used in advanced research methods in business and economic literature (Ostertagova&Oscar, 2013). There are four methods of testing analysis of variance. These methods are the one-way analysis of variance, two-way analysis of variance, repeated measures analysis of variance,and factorial analysis of variance.

One-Way Analysis of Variance

One way analysis of variance assesses the relative size of variance among group means in comparison with the average variance within means (Hae-Young, 2014). This method is used to determine if there is a significant difference between dependent and independent variables. It is also used when data is divided into groups according to only one factor.

##### Two-Way Analysis of Variance

Two-way analysis of variance is an analysis design that involves studying two factors that are measured by a scale (Houssein, Yongqing, Lan, Raymond &Guoyao, 2015). Two-way analysis of variance enables researchers to test the effect of two factors at the same time and investigate the simultaneous effect of two nominal.The method is an extension of variance because it has two independent variables compared to one-way analysis of variance that has an independent variable affecting a dependent variable (Housseinet al., 2015).

##### Factorial Analysis of Variance

Factorial analysis of variance is a method used to analyze differences on a continuous dependent variable between two or more independent discrete variables (Mcintosh, 2015). This method is an efficient way of conducting tests because one can test all independent variables at the same time. It is also used to examine the interaction of more than one factor because it is the only effective way to examine interaction effects (Mcintosh, 2015).

##### Repeated Measures Analysis of Variance

Repeated measures analysis of variance is a method used to test a number of minimum conditions for all members of a random sample (Sang, Dong &Junyong, 2016). There are different measurements of each sample as every sample is exposed to different conditions. Repeated measures design is used when it is difficult to recruit sample members because it is economical (Sang et al., 2016). The method is also used to collect data for the same participant under repeated conditions to eliminate individual differences and between group differences.

##### Regression Analysis

Regression analysis is a procedure used to determine the strength of the relationship between one dependent variable and a series of other changing variables (Gulden, 2013). The relationship is expressed as an equation of a line or a curve in which any coefficient of the independent variable in the equation has been determined from a sample population.There are three methods used in regression analysis. They include linear regression, multiple regressionand correlation(Conrad, 2016).

##### Linear Regression

According to Gulden (2013), linear regression is a type of regression analysis in which models are measured with one independent and one dependent variable. Linear regression finds the slope and intercepts between the dependent and independent variable explained by a straight line (Gulden, 2013).Dependent variables are differences whose value is to be predicted whereas independent variables are differences whose known value is used for prediction.

##### Multiple Regression

Multiple regression analysis is used to mean models with two or more independent variables and only one dependent variable (Gulden, 2013). This method tests the relationship between two variables by assuming that it is linear. It is used when the researcher is interested in the prediction of a continuous dependent variable from a number of dependent variables (Gulden, 2013).

##### Correlation

Correlation analysis is used to quantify the strength of the relationship between variables and to test whether two measurement variables co-vary. The analysis is done by the method of least squares to choose and fit an appropriate model to help estimate the response for the value of an independent variable (Gulden, 2013). This method is used to test the hypothesis about causes and effects on relationships, to test whether two variables are associated, and estimating the value of one variable corresponding to the other variable.

##### Conclusion

Based on data that is beyond simple description conclusions are made using methods under inferential statistics. These methods are convenient because the assumptions used are the same for all the inferential statistics tests. The analysis of variance assumes that the observations are normally and independently distributed with the same variance for each treatment or factor level. The assumptions remain the same with all designs which are normality, independence, and equality of variance. All regression analysis procedures are used to test the relationship between dependent and independent variables. Inferential statistics are used to make inferences from data to more general conditions which come from a general family of the statistical model. It is also used to test whether there is a statistical difference between variables through prediction. All these methods come from the same family introducing the researcher to data analysis in social and applied research. The lack of randomization in these designs complicates the researcher’s analysis.