Hypothesis testing and test of significance
HYPOTHESIS TESTING & TEST OF SIGNIFICANCE
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Introduction
·
Hypothesis testing can defined as the process
of
o
Making an assumption about a population
parameter
o
Collecting the sample data
o
Calculate a sample statistic
o
By using sample statistic evaluate the
hypothesis
·
Generally hypothesis are of two types
o
Null Hypothesis (H0)
§ A theory that has been put forward either because it is
believed to be true.
§ For an example, Smoking causes lungs cancer
o
Alternative Hypothesis (HA)
§ A statement of what a statistical hypothesis test is
setup to establish.
§ For an example, a new Paracetamol derivative is better
than the current one to treat pain.
Test
of Significance
· In Statistics, tests of significance are the method of reaching a conclusion to
reject or support the claims based on sample data.
· During a statistical process, a very common as well as an
important term we come across is “significance”.
· Statistical significance is very important in research not only in
Mathematics but in several different fields such as medicine, psychology and
biology.
· There are many methods through which the significance can be
tested & these are known as significance tests.
· In short, the significance is the probability that a
relationship exists.
· Significance tests tell us about the probability that if a
relationship we found is due to random chance or not and to which level.
· This indicates about the error that would be made by us if
the relationship is assumed to exist.
Process of Significance
Testing
In the process of testing for
statistical significance, there are the following steps:
- Stating a
Hypothesis for Research
- Stating a
Null Hypothesis
- Selecting a
Probability of Error Level
- Selecting
and Computing a Statistical Significance Test
- Interpretation
of result
Error types
There are basically two types of
errors:
- Type I
- Type II
Type I Error
· The type I error occurs when the researcher finds out
that the relationship assumed through research hypothesis does exist; but in
reality, there is evidence that it does not exist.
·
In this type of
error, the researcher is supposed to reject the research hypothesis and accept
the null hypothesis, but its opposite happens.
·
The probability that
researchers commit Type I error is denoted by alpha (α).
Type II Error
· The type II error is just opposite the type I error.
·
It occurs when it is
assumed that a relationship does not exist, but in reality it does. In this
type of error, the researcher is supposed to accept the research hypothesis and
reject the null hypothesis, but he does not and the opposite happens.
·
The probability that
a type II error is committed is represented by beta (β).
Types of Statistical
Tests
One-tailed and two-tailed are two types of statistical tests that are used
alternatively for the computation of the statistical significance of some
parameter in a given set of data.
- In
research, the one-tailed test can be used when the deviations of the
estimated parameter in one direction from an assumed benchmark value are
considered theoretically possible.
- On the
other hand, the two-tailed test should be utilized when the deviations in
both directions of benchmark value are considered as theoretically
possible.
The word “tail” is used in the names on these
tests since the extreme points of the distributions in which observations tend
to reject the null hypothesis are quite small and “tail off” to zero similar to
the bell curve or normal distribution. The choice of one-tailed or two-tailed
significance test depends upon the research hypothesis.
Example
- The
one-tailed test can be utilized for the test of the null hypothesis such
as, boys will not score significantly higher marks than girls in 10
Standard. In this example, the null hypothesis does indirectly assume the
direction of the difference.
- The
two-tailed test could be utilized in the testing of the null hypotheses:
There is no significant difference in scores of boys and girls in 10
Standard.
P-Value Testing
In the context of the statistical
significance of a data, the p-value is an important terminology for hypothesis
testing.
The p-value is said to be
a function of observed sample results which is being used for testing of
statistical hypothesis.
·
A threshold value is
to be selected before the test is performed. This
value is known as the significance level that is traditionally 1% or 5%. It is
denoted by α.
· In the case when the p-value is smaller than or equal to
significance level (α), the data is said to be inconsistent for our assumption
of the null hypothesis to be true. Therefore, the null hypothesis should be
rejected and an alternative hypothesis is supposed to be accepted or assumed as
true.
· Note that the smaller the p-value is, the bigger the
significance should be as it indicates that the research hypothesis does not
adequately explain the observation. If the p-value is calculated accurately,
then such test controls type I error rate not to be greater than the
significance level (α). The use of p-values in statistical hypothesis testing
is very commonly seen in a wide variety of areas such as psychology, sociology,
science, economics, social science, biology, criminal justice etc.
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