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What is Inferential Statistics?

If you need to collect data on a very large
population. For example, suppose you want to know the average height of all the
men in a city with a large population, it isn’t very practical to try and get
the height of each man. Inferential statistics is used instead.

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Inferential statistics makes inferences
about populations using data drawn from the population. The statistician will
collect a sample or samples from the millions of residents and make inferences
about the entire population using the sample. While carrying out Inferential
statistics upon a sample, it automatically obtains a sampling error and thus a
sample is not expected to acquire a 100% accurate representation of the
population. In addition, it is used by statisticians
to carry out estimates and test a theory by its given data.

Types of
Inferential Statistics

1) Correlation Coefficient

It shows the relationship
between two quantitative variables and is symbolized using the letter ‘r’. The
range of ‘r’ is from 1 (perfect, positive, linear relationship) to -1
(perfect, negative, linear relationship). No linear relationship is when r = 0.
The closer the coefficient is to +1, the stronger the positive relationship. The
closer the coefficient is to -1, the stronger the negative relationship. If the
coefficient is nearer 0, the variables are not linearly related to each other,
although they may be non-linearly related. A correlation coefficient of 0
represents the weakest possible relationship, although it is still possible a
non-linear relationship may exist when r = 0.

When one variable increases, the other variable
increases or decreases by giving a straight-line graph. However, if the line
increases to a certain point and then decrease, a curvilinear or non-linear
relationship would exist.

2) t-test

The Student’s t-test is a statistical test
that compares the mean and standard deviation of two samples to
see if there is a significant difference between them. In an
experiment, a t-test is used to test if there is a significant difference
between the two variables. While taking a sample from a population, an error may
be observed known as sampling error.

In any significance test,
there are two possible hypothesis:

i) Null
Hypothesis:
There is no significant difference between the two variables
and the difference is due to chance or sampling error.

ii)
Alternative Hypothesis:
There is a significant difference between the two variables
and the difference is neither due to chance nor sampling error.

3) Analysis
of Variance (ANOVA)

ANOVA is similar to the t-test, but it is used to
compare two or more means and whether there is a significance between them. They help you to figure out if you need to reject the null hypothesis or accept the alternate hypothesis.

4) Analysis
of Covariance (ANCOVA)

Analysis
of covariance (ANCOVA) is used in examining the differences in the mean values
of the dependent variables that are related to the effect of the controlled
independent variables while taking into account the influence of the
uncontrolled independent variables.

5) Chi-Square

This type of test to see if there is
a relationship between two qualitative variables, such as sex and dropping out
of school.

Importance of Inferential Statistics

Inferential
statistics enables us to make conclusions from descriptive statistics. Data obtained
from descriptive statistics are used by inferential statistics extend beyond
the immediate data. Inferential statistics are used to interpret from the
sample data what the population might think. This type of statistics can also be
used to know that if the observation is reliable and dependent or it has occurred
by chance during the experiment. 