Analysing Quantitative Data
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Transcript of Analysing Quantitative Data
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