# Definition the statistical data and observations. 3. Studies more

Definition

Inferential statistics aims at drawing conclusions about
a population from a sample. This is generally done through random sampling that leads to central tendency of a distribution. Inferential statistics offers
more powerful analyses to be performed on a survey data.  This can
include associations between variables, how well a sample represents a
certain population, and cause-and-effect relationships. (Freedman, 2009;
Bandyopadhyay & Forster, 2011).  An example of inferential
statistics is shown in the following figure

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Figure 1: The Relation
between Potatoes Distribution and Week Days

Importance

Cox
(2006) points out that inferential statistics are important as it:

1.
Is effective in predicting and inferring
a much larger data or population.

2.      Deeply analyzes
the statistical data and observations.

3.
Studies more details
such as hypothesis tests and confidence interval.

4.      Covers a
wide range of data as the measures in inferential statistics are not always
exact numbers.

5.
Places the educated predictions
and guesses on the basis of the parameters of the given population, it
does not matter how big the population is.

6.
Plays an important role in examining
the relationships between variables within a sample, and then make
generalizations or predictions about how those variables will relate within a
larger population.

1.     The Main Types of Inferential
Statistics

There are two main types of inferential
statistics:

1) Confidence Interval:

It refers to the form of an interval that provides a range
for the parameter of given population.

2) Hypothesis Test (Test of Significance):

Bickel & Kjell (2001) believe that to conduct inferential
statistics, it is important and necessary to conduct test of significance in
order to know whether results can be generalized to a larger population. Common
tests of significance include the Chi-square and T-test. These determine
the probability that the results of statistical analysis are representative of
the population.

Besides, Freedman (2010) states that there are other
techniques that are used to examine the relationships between variables, and
thereby to create inferential statistics. They include linear regression analyses, logistic regression analyses, ANOVA, correlation analyses, structural equation modeling, and survival analysis.

Linear
Regression and Multiple Linear Regressions

Newsom (2010)
points out that linear regression is a statistical technique that is used to
and a dependent (criterion) variable. If the independent variable is more than
one, this is referred to as multiple linear regressions.

R-Square

R-square, also known as the coefficient of determination, is a commonly used
statistic to evaluate the model fit of a regression equation. That is, how good
are all of independent variables at predicting dependent variable? The value of
R-square ranges from 0.0 to 1.0 and can be multiplied by 100 to obtain a
percentage of variance explained.

Logistic
Regression

Logistic regression is a method for modeling a binary
response variable, which takes values 0 and 1. The dependent variable is always
binary whereas the independent, or predictor, variables can be either numerical
or categorical.

Analysis of
Variance (ANOVA)

It clarifies the
significant differences between means. It is of different models: one-way
between 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 two
variables where a high, correlation means that two or more variables have a
strong relationship with each other whereas a low correlation means that the
variables are hardly related.

Structural Equation Modeling

Structural equation modeling uses some statistical techniques
that allow a set of relationships between one or more independent variables and
one or more dependent variables to be examined. Both variables could be either
continuous or isolated and can be either factors or measured variables.