Hypothesis Testing

Hypothesis Testing

It is a procedure of testing in which statements with respect to a feature about a population or populations are tested based on sample evidence and probability.

We usually like to make a new statement about a feature of a population or populations with an original statement. However, we have no idea that these statements are true or false unless we find evidence, from the sample data, that will support our new statement or reject our original statement. The evidence is then analyzed by using some statistical calculation methods to test the logic of our statements.

The first step in testing a statistical hypothesis is to know the probability model of the population under study. Then, we need to know the feature of the population about which the hypothesis is made. For example, the features of a normal probability model are mean μ and standard deviation σ. Statistically we call a feature of a probability model parameter.

Then, we will make our hypothesis about a feature or also called a parameter. That is actually we are making a proposed value of a mean or a standard deviation suppose the probability model is a normal probability model. This proposed value is not a true value. Thus the true value of the parameter, which we are forming hypothesized value, is unknown.

Parameter: a numerical characteristic of a population

Statistic: a numerical characteristic of a sample

Simple Random Sample: a sample obtained through a simple random sampling process

Simple random sampling: a process of selecting individuals to be included in a sample from a population using chance of occurring that is equally likely for each of the individual in the sample.

At least: greater than or equal to or no less than (≥)

Exactly: equal or is (=)

No more than: at most or less than or equal to (≤)

Fewer then: less than (<)

More than: greater than (>)

Sampling distribution: the probability shared among all possible values of data computed from a sample of size n

Sampling distribution of the sample mean: the probability distribution of all viable values of the sample mean computed from a sample of size n from a population with mean μ and sample standard deviation σ.

Hypothesis: a proposed statement about a feature of a population or populations.

Hypothesis Testing

DNA Pot (c) 2009 - Current

Then, we collect the sample data from the population, and run the hypothesis testing of the hypothesis we have just made with a hypothesized value of a parameter of the population. So then, what is the true value of the parameter under study and the question of - is the hypothesized value closer to that true value - is what we are trying to find out by doing hypothesis testing.

Suppose there is a population of with a mean of existing value μ0. This mean is accepted to be true but it is actually a hypothesized value proved before to be closer to the true mean μ. The true mean is one that is unknown to us. We just don’t know the exact value of mean of this population. The μ0 is therefore a hypothesized accepted value which we now call the mean from null hypothesis, H0, which is an existing and accepted value at the moment. The null hypothesis, H0, is someone’s calculation or proposed statement about the mean of the population under study.

Now, we are facing there is a need to challenge this existing mean according to the changes happening in the population and we come up with a new hypothesis about the mean and state that the alternative mean could be μa, alternative mean. This statement is made based on the new information obtained about the population and is called research hypothesis or alternative hypothesis, Ha or H1.

Then, we study the sample data that is collected and based on that information, we either continue to accept the null hypothesis H0 with currently accepted mean value μ0, or we get rid of the null hypothesis, H0, and accept the alternative hypothesis, Ha, because the calculation from the sample data show strong evidence that the alternative mean, μa, should be accepted.

This procedure of rejecting or not rejecting the existing null hypothesis H0 is called the testing of the statistical hypothesis.

Null Hypothesis H0 (currently accepted one)

Alternative Hypothesis

Ha or H1

There is a need to Test this hypothesis

because of new information arise

The hypothesis is about a parameter of a population

Examples of parameters are mean, standard deviation, etc.

if evidence from the sample data supports the alternative hypothesis

Collect the sample data about this parameter

Reject the

Null Hypothesis H0

if evidence from the sample data does not support the alternative hypothesis

Do not Reject the

Null Hypothesis H0