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#### Dissertation Statistics - A Comprehensive Guide

Your dissertation marks the end of your degree and is the most important aspect of your entire programme. Getting the grade that you need can depend on the score that you are awarded for this piece of work.

The issue? Dissertation Statistics! The data analysis aspect of your dissertation carries significant weight on your overall grade but most people do not know where to start.

This guide provides a comprehensive guide to the things that you need to know in order to ace the analytical part of your dissertation. We will talk you through hypothesis testing, outliers and many of the misconceptions in the field of statistics. Statistics is like a bikini, what they reveal is suggestive, but what they conceal is vital

#### Statistical Misconceptions - Hypothesis Testing

Statistics are used much like a drunk uses a lamppost: for support, not illumination

The first thing you will need to do is to construct a null and alternative hypothesis.

Typically, the null hypothesis will assume that means between two different samples are equal: Ho: µ1 = µ2

The alternative hypothesis will assume that the means between samples are not equal: Ha: µ1 ≠ µ2

It is the researcher’s task to find evidence to determine whether the data provides evidence in support of the null hypothesis or not.

Should the data prove that sample means are equal then the researcher will conclude that “we fail to reject the null hypothesis” – note, we do NOT accept the null, we simply fail to reject it.

Statistical analysis is able to disprove a theory but never to prove one

When testing for equality in means, we want to establish if any difference is statistically significant. We expect so see some sort of difference between means due to variation but a hypothesis test will need to ascertain if the difference is statistically significant.

For instance, if one was conducting research on the weight of French Bulldogs – the researcher could construct a hypothesis that no French Bulldog can weigh in excess of 15kg. This notion is absolutely vital to hypothesis testing in your dissertation.

If they collected a sample of 50 dogs and one of the dogs weighs 15.2kg then statistics can disprove the null hypothesis, since we have seen in our sample a dog that weighs in excess of 15kg. We can prove that the theory is wrong.

However, if all dogs weigh less than 15kg we cannot prove that all French Bulldogs weigh less than 15kg, we simply state that we have found evidence to suggest that French Bulldogs may not exceed 15kg in weight.

If you are struggling to understand, think of this: every French Bulldog in the world is referred to as a “population“. We cannot examine EVERY one of them so we select a “sample“.

This would be our 50 dogs. Statistically speaking we would say we have a sample of size 50

How confident can we be that the 50 dogs that were sampled are a true representation of all French Bulldogs?

Even so, because results from our study of 50 dogs exhibits a certain trait – we cannot assume that the same trait applies to dogs that we have not examined.

But by “accepting our null hypothesis – that is exactly what we are trying to do

A very simplistic potential hypothesis for the above mentioned survey would be:

Ho: No French Bulldog will exceed 15kg in weight

Ha: A French Bulldog exceeds 15kg in weight

How do we test for statistically significant mean inequalities?

Its all in is the P-value

A statistician can have his head in an oven and his feet in ice, and he will say that on average he feels fine

100% of divorces are caused by marriage

If 4 out of 5 people suffer with diarrhea does one enjoy it?

#### Statistical Misconceptions - Hypothesis Testing

The significant probability is typically referred to as the p value. The p value is the probability, assuming the null hypothesis is true, that an event as extreme than that observed will occur.

The smaller the p value – the less likely it is that under the null hypothesis (i.e if Ho were true) that we would have achieved the results that we did.

A small p value is likely to mean that Ho is not true in which case we would prefer Ha.