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Most of the issues associated with statistical significance and hypothesis testing can be cook-booked. You do not have to understand probablity theory etc. to interpret or report statistical tests. In fact, there are so many mistakes in expressing significance in the published literature that it is clear many people who should know all about it, don't know.
The starting point - the null hypothesis Ho.
Research Hypothesis H1
Logically, what you must do is to reject the contrary hypothesis(Ho). This then says that there is some support for your research hypothesis (h1).
More technically, if you find an instance which is contrary to your research hypothesis, then you have to reject your research hypothesis.
I do not intend to get into research paradigms, logical positivism versus phenomonology, and all that. If you are interested then you need to find some well-argued books on the topic.
The basic point is that at any time, any seemingly clear theory about the world might be disproved. Man is a fallible animal.
A logically weak, but intuitively acceptable, position is that we can have some verification of an hypothesis through continued findings which fail to force us to reject our research hypothesis. That is, we carry out studies and we are able to reject the null hypothesis each time. We, then, have a research hypothesis that is holding up.
Unless you have divine inspiration, this is the best you can do.
The role of a statistical test is, basically, quite simple:
The statisticians have spent over 100 years working on various ways of establishing whether or not a given result is significant in the sense that it can be seen as a non-chance result. And, as with most things statistical, it has not been easy for the non-statistician to see what it is all about.
Let us take a simple H1
Because the data is interval or better, we can apply a t-test which is a test of the difference between means. It asks the question " were these two sets of means obtained from samples drawn from the same population or not".
So, we calculate our t-statistic using the means and standard deviations and it comes out to be:
Now you want to know what df means. It is the degrees of freedom. The easiest way to deal with df is to cook-book it by checking how degrees of freedom are calculated for each statistic. But a stats package such as SPSS will automatically give you the appropriate dfs in the output.
We now go to our statistical table and check the value of the statistic against the degrees of freedom.
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Statistical significance and hypothesis testing
The null hypothesis is simply the opposite of your research hypothesis.
Proof, verification and all that.The performance of students on the course is directly related to their TER (or equivalent).
Null hypothesis HoThere is no relationship between TER (or equivalent) and course performance.
The issue here is one of logic. To directly test your hypothesis you suffer the fallacy of the affirmation of the consequent.
You can never prove anything.
Statistical tests
The way you test your null hypothesis is through statistical tests - chi square, t tests, f test etc.
It asks whether or not the result you obtained from your analysis might have occurred by chance.
The performance of male and female students differ in programming courses.
and its HoThere is no difference between male and female students in performance in programming courses.
Our research has collected the data on the performance of 17 male and 14 female students. t=2.8 with df=29