InferentialStatisticsDefinitionInferential statistics targets at drawing conclusions abouta population from a sample. This is generally madethrough random sampling that leads to central tendency of a distribution. Inferential statistics offersmore accurate analyses to be performed on a survey data. This caninclude associations along variables, how well a sample represents acertain population, and cause-and-effect relationships. (Freedman, 2009;Bandyopadhyay & Forster, 2011). An example of inferentialstatistics is shown in the following figure Figure 1: The Relationbetween Potatoes Distribution and Week Days ImportanceCox(2006) points out that inferential statistics are important as it: 1.
Is effective in predicting and inferringa much larger data or population.2. Deeply analyzesthe statistical data and observations.3. Studies more details likehypothesis tests and confidence interval.4. Includesa huge range of data as the measures in inferential statistics are not alwaysexact numbers. 5.
Places the educated predictionsand guesses on the basis of the parameters of the given population, itdoes not matter how big the population is.6. Plays an important role in examiningthe relationships between variables within a sample, and then makegeneralizations or predictions about how those variables will relate within alarger population. 1. The Main Types of InferentialStatisticsThere are two main types of inferentialstatistics:1) Confidence Interval:It refers to the form of an interval that provides a rangefor the parameter of given population.
2) Hypothesis Test (Test of Significance):Bickel & Kjell (2001) believe that to conduct inferentialstatistics, it is important and necessary to conduct test of significance inorder to know whether results can be generalized to a larger population. Commontests of significance include the Chi-square and T-test. These determinethe probability that the results of statistical analysis are representative ofthe population.Besides, Freedman (2010) states that there are othertechniques that are used to examine the relationships between variables, andthereby to create inferential statistics. They include linear regression analyses, logistic regression analyses, ANOVA, correlation analyses, structural equation modeling, and survival analysis.
LinearRegression and Multiple Linear Regressions Newsom (2010)points out that linear regression is a statistical technique that is used tolearn more about the relationship between an independent (predictor) variableand a dependent (criterion) variable. If the independent variable is more thanone, this is referred to as multiple linear regressions. R-SquareR-square, also known as the coefficient of determination, is a commonly usedstatistic to evaluate the model fit of a regression equation. That is, how goodare all of independent variables at predicting dependent variable? The value ofR-square ranges from 0.
0 to 1.0 and can be multiplied by 100 to obtain apercentage of variance explained. LogisticRegressionLogistic regression is a method for modeling a binaryresponse variable, which takes values 0 and 1. The dependent variable is alwaysbinary whereas the independent, or predictor, variables can be either numericalor categorical.Analysis ofVariance (ANOVA) It clarifies thesignificant differences between means.
It is of different models: one-waybetween groups ANOVA, one-way repeated measures ANOVA, two-way between groups ANOVA, two-way repeated measures ANOVA Correlation Analysis Correlation analysis verifies the relationship between twovariables where a high, correlation means that two or more variables have astrong relationship with each other whereas a low correlation means that thevariables are hardly related. Structural Equation ModelingStructural equation modeling uses some statistical techniquesthat allow a set of relationships between one or more independent variables andone or more dependent variables to be examined. Both variables could be eithercontinuous or isolated and can be either factors or measured variables. ReferencesBandyopadhyay, P. S.; Forster, M.
R., eds.(2011), Philosophy of Statistics, Elsevier.Bickel, P.J.
;, Kjell A.(2001). Mathematical statistics: Basic and selected topics. 1 (Second (updated printing 2007)ed.). Prentice Hall.
ISBN 0-13-850363-X. MR 0443141.Cox, D. R. (2006).
Principlesof Statistical Inference, Cambridge University Press. ISBN 0-521-68567-2.Freedman, D. A.
(2009). StatisticalModels: Theory and practice (revised ed.). Cambridge University Press. pp. xiv+442 pp.
ISBN 978-0-521-74385-3. MR 2489600.Freedman, D. A.
(2010). StatisticalModels and Causal Inferences: A Dialogue with the Social Sciences (Editedby David Collier, Jasjeet S. Sekhon, and Philip B.
Stark), Cambridge University Press. Newsom.(2010).
Logistic Regressionhttp://www.upa.pdx.edu/IOA /newsom/da2/ho_logistic.pdf