Block 4: Hypothesis testing
[Page last updated 24 October 2017]
"All the right notes, but not necessarily in the right order!" as Eric Morecambe once said to André Prévin.
4.1 Hypothesis testing
The concepts and tests to be dealt with in this section are explained in the accompanying Statistical notes. They were written by Jim Ring for the original course, in as non-technical language as possible, and were aimed at students with little or no background in mathematics or statistics. For now you are referred to my recommended SPSS textbooks and to my selection of on-line SPSS intros and tutorials by others. However, there is no shortage of literature or other materials out there, especially on Youtube, Google and Wikipedia.
My original course hand-outs are very cursory as by this point there was less formal teaching and stats were demonstrated verbally and visually. My hand-outs date from 1991-92 and await conversion and updating from WordStar4 and SPSS-X on a Vax mainframe to MS Word and SPSS for Windows on a PC.
My own materials will attempt to explain, in non-mathematical language, what the research question is, what the statistical techniques are, why they are used and how to interpret the results. There will be very few, if any, equations except when they are built up from graphic explanations of what the elements of the equations are and how and why they are calculated.
Until I get round to writing all these, users with little or no knowledge (or even fear) of statistics are invited to look at the wonderful series of introductory videos from the Statistics Learning Centre. These explain basic statistical concepts in simple non-technical language and can be easily understood, not just by the business and finance students for whom they were written, but even by students in sociology, social work and the like. Anyone who can’t follow them should perhaps not be undertaking a course at any level in any discipline, let alone one designed for postgraduates and beginning researchers in the social sciences. The narration is clear, the explanations are gentle, the graphics are helpful and vibrant, and the examples are relevant to everyone, especially if you like chocolate!
Start with:
Statistics Videos and Resources
Important statistical concepts: significance, strength, association, causation
Hypothesis tests, p-value - Statistics Help
Choosing which statistical test to use?
SPSS itself has a comprehensive set of statistics tutorials which can be accessed via the Statistics Coach but only if you have SPSS installed or are a user on a licenced site.Until I can write something of my own, I've picked out some very good tutorials available as YouTube videos.
4.2 Chi-square (for contingency tables)
4.2.1 Income differences – Statistical significance (draft only)
Demonstration, using a two-way contingency table from CROSSTABS, to test the null hypothesis that there is no difference between the earnings (from paid work) of men and women. Step-by-step procedure to produce expected cell values (E) compare them to observed values (O) and gradually build up the equation for chi-square.
Follows up exercise 3.1.4.1 Income differences work-through.
4.3 Two means (t-test)
4.4 Three means (one way anova)
There's a very good step-by-step tutorial on Statisticsfun by David Longstreet:
How to Calculate and Understand Analysis of Variance (ANOVA) F Test
Visual tutorial on how to calculate analysis of variance (ANOVA) and how to understand it too. The tutorial includes how to interpret the results of an Anova test, f test and how to look up values in the f distribution table. The Anova example is for a one way anova test. It doesn't explain why the differences have to be squared, but if you look at the example you will see that the un-squared ones total to zero.
A more detailed, but equally helpful pair of tutorials is by Brandon Folz. In Part 1 Statistics 101: One-way Analysis of Variance, A Visual Tutorial he shows the formulae before working with the raw figures, but for statistical newbies it might be better the other way round. The charts are very clear, but it's a shame he doesn't tabulate the actual differences before showing the summary distributions. He does some detailed working in Part 2 Understanding the calculation using Excel, but the intermediate raw and squared differences are not shown, which is a great pity.
4.5 Regression and correlation
4.5.1 Visual aid for regression and correlation
4.6 Association, structure and cause (modelling)
.
"All the right notes, but not necessarily in the right order!" as Eric Morecambe once said to André Prévin.
4.1 Hypothesis testing
The concepts and tests to be dealt with in this section are explained in the accompanying Statistical notes. They were written by Jim Ring for the original course, in as non-technical language as possible, and were aimed at students with little or no background in mathematics or statistics. For now you are referred to my recommended SPSS textbooks and to my selection of on-line SPSS intros and tutorials by others. However, there is no shortage of literature or other materials out there, especially on Youtube, Google and Wikipedia.
My original course hand-outs are very cursory as by this point there was less formal teaching and stats were demonstrated verbally and visually. My hand-outs date from 1991-92 and await conversion and updating from WordStar4 and SPSS-X on a Vax mainframe to MS Word and SPSS for Windows on a PC.
My own materials will attempt to explain, in non-mathematical language, what the research question is, what the statistical techniques are, why they are used and how to interpret the results. There will be very few, if any, equations except when they are built up from graphic explanations of what the elements of the equations are and how and why they are calculated.
Until I get round to writing all these, users with little or no knowledge (or even fear) of statistics are invited to look at the wonderful series of introductory videos from the Statistics Learning Centre. These explain basic statistical concepts in simple non-technical language and can be easily understood, not just by the business and finance students for whom they were written, but even by students in sociology, social work and the like. Anyone who can’t follow them should perhaps not be undertaking a course at any level in any discipline, let alone one designed for postgraduates and beginning researchers in the social sciences. The narration is clear, the explanations are gentle, the graphics are helpful and vibrant, and the examples are relevant to everyone, especially if you like chocolate!
Start with:
Statistics Videos and Resources
Important statistical concepts: significance, strength, association, causation
Hypothesis tests, p-value - Statistics Help
Choosing which statistical test to use?
SPSS itself has a comprehensive set of statistics tutorials which can be accessed via the Statistics Coach but only if you have SPSS installed or are a user on a licenced site.Until I can write something of my own, I've picked out some very good tutorials available as YouTube videos.
4.2 Chi-square (for contingency tables)
4.2.1 Income differences – Statistical significance (draft only)
Demonstration, using a two-way contingency table from CROSSTABS, to test the null hypothesis that there is no difference between the earnings (from paid work) of men and women. Step-by-step procedure to produce expected cell values (E) compare them to observed values (O) and gradually build up the equation for chi-square.
Follows up exercise 3.1.4.1 Income differences work-through.
4.3 Two means (t-test)
4.4 Three means (one way anova)
There's a very good step-by-step tutorial on Statisticsfun by David Longstreet:
How to Calculate and Understand Analysis of Variance (ANOVA) F Test
Visual tutorial on how to calculate analysis of variance (ANOVA) and how to understand it too. The tutorial includes how to interpret the results of an Anova test, f test and how to look up values in the f distribution table. The Anova example is for a one way anova test. It doesn't explain why the differences have to be squared, but if you look at the example you will see that the un-squared ones total to zero.
A more detailed, but equally helpful pair of tutorials is by Brandon Folz. In Part 1 Statistics 101: One-way Analysis of Variance, A Visual Tutorial he shows the formulae before working with the raw figures, but for statistical newbies it might be better the other way round. The charts are very clear, but it's a shame he doesn't tabulate the actual differences before showing the summary distributions. He does some detailed working in Part 2 Understanding the calculation using Excel, but the intermediate raw and squared differences are not shown, which is a great pity.
4.5 Regression and correlation
4.5.1 Visual aid for regression and correlation
4.6 Association, structure and cause (modelling)
.