Analyzing Quantitative Data

byProfesor Madya Dr. Mokhtar Ismail

Data analysis is a component of scientific method

Steps in scientific method

1. Defining the problem.2. Formulating hypothesis.3. Collection and analysis of data.4. Decision (rejection or retention of

hypothesis).5. Repeated verification.

What is the major role of the steps in scientific method?

• For making generalization of research findings from the sample to the population with the help of statistical theory on significance testing

Why do we need to understand the rationale of significance

testing ?

Because it helps us choosing relevant statistical tests

Lets take a look at an example of a significance testing procedure

Lets assume our Dean’s hypothesis: Our students’ GPA of

last semester was 2.75 (miu=2.75)

She can collect thousands of samples of for example 200

students for each sample and compute the mean

In research she needs only one sample to make conclusion

If she gets one sample and the mean is 2.85 (x bar= 2.85). Is it generalizable to the population?

How to make it generalizable? By the the help of CLT in order to

say the sample is representative

In other words we want to say: we are 95% confidence that the

sample represents the population

We have to make use the property of normal distribution

because of CLT

At 95% confidence interval the value of z scores are plus/minus 1.96 where the area is 2.5% at

both ends

When we get a sample we compute the mean and see

whether or not it falls within the CI

How do we do that? We use z score. Which is a deviation unit in

terms of standard error

We call this test statistic. We compare test statistic with critical

values

Whether the CI span the test statistic? If it does, we say that we are 95% confidence that the sample represent the population

Hypothesis testing is the other side of the same coin

We have the null hypothesis which says that there is no

significant difference between sample and population mean

We want to reject the null hypothesis: We want to say that

CI does not span the hypothesized value

If we can do that we can say that the sample is representative

If our Dean has GPA of each student, she does not have to do this research. She could have got

the mean by averaging from all students

Key issue is the choice of relevant test statistic for research