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Block 4: Hypothesis testing
[Page last updated 4 September 2015]
"I'm playing all the right notes, but not necessarily in the right order!" as Eric Morecambe declared to André Prévin in the brilliant 1971 sketch Greig's Piano Concerto .
4.1 Hypothesis testing
My original hand-outs for statistical calculations are cursory to non-existent: by this point in the course there was less formal teaching and stats were demonstrated verbally and visually with transparencies and with work-throughs on the chalk-board. Examples are 4.2.1 and 4.5.1 below.
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.
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.
The Methodological Institute at the London School of Economics and Political Science (LSE) has produced an excellent set of On-line software tutorials:
Videos on SPSS (uses GUI rather than syntax, but the syntax is printed in the output.)
Videos on Stata
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 (see 4.2.1 below).
Until I get round to writing these, users with little or no knowledge (or even fear) of statistics are should 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, finance, maths, stats) secondary school 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?
Why not just watch the entire set: enjoy!
Another helpful set of video tutorials is contained in Statisticsfun by David Longstreet
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.
See also the LSE Methodology tutorials:
Two‐way contingency table and chi-squared test (two categorical variables)
Three‐way contingency table and chi-squared tests: (two categorical variables controlling for third test variable)
4.3 Two means (t-test)
Independent samples t‐test (continuous dependent variable, dichotomous independent variable) from LSE
Two Populations, t-test with Hypothesis is a video tutorial by Brandon Folz. It uses orange juice as an example and is quite mathematical, but the animated diagrams demonstrate clearly what the test is trying to do.
4.4 Three means (one way anova)
How to Calculate and Understand Analysis of Variance (ANOVA) F Test is a very good step-by-step tutorial on Statisticsfun by David Longstreet. It shows how to calculate analysis of variance (ANOVA) and how to understand it. It explains 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 raw 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
Best intros are:
Regression, part 1 and Regression in Excel from Statistics Learning Centre. They use Excel, not SPSS.
See also 4.5.1 Visual aid for regression and correlation (Idiosyncratic idea by John Hall)
LSE tutorial Simple linear regression: (continuous dependent variable, continuous independent variable)
4.6 Association, structure and cause (modelling)
I currently have no tutorials of my own on these topics, but they would include:
Cluster Analysis
Discriminant Function Analysis
Factor Analysis
Multiple Regression
.
"I'm playing all the right notes, but not necessarily in the right order!" as Eric Morecambe declared to André Prévin in the brilliant 1971 sketch Greig's Piano Concerto .
4.1 Hypothesis testing
My original hand-outs for statistical calculations are cursory to non-existent: by this point in the course there was less formal teaching and stats were demonstrated verbally and visually with transparencies and with work-throughs on the chalk-board. Examples are 4.2.1 and 4.5.1 below.
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.
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.
The Methodological Institute at the London School of Economics and Political Science (LSE) has produced an excellent set of On-line software tutorials:
Videos on SPSS (uses GUI rather than syntax, but the syntax is printed in the output.)
Videos on Stata
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 (see 4.2.1 below).
Until I get round to writing these, users with little or no knowledge (or even fear) of statistics are should 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, finance, maths, stats) secondary school 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?
Why not just watch the entire set: enjoy!
Another helpful set of video tutorials is contained in Statisticsfun by David Longstreet
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.
See also the LSE Methodology tutorials:
Two‐way contingency table and chi-squared test (two categorical variables)
Three‐way contingency table and chi-squared tests: (two categorical variables controlling for third test variable)
4.3 Two means (t-test)
Independent samples t‐test (continuous dependent variable, dichotomous independent variable) from LSE
Two Populations, t-test with Hypothesis is a video tutorial by Brandon Folz. It uses orange juice as an example and is quite mathematical, but the animated diagrams demonstrate clearly what the test is trying to do.
4.4 Three means (one way anova)
How to Calculate and Understand Analysis of Variance (ANOVA) F Test is a very good step-by-step tutorial on Statisticsfun by David Longstreet. It shows how to calculate analysis of variance (ANOVA) and how to understand it. It explains 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 raw 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
Best intros are:
Regression, part 1 and Regression in Excel from Statistics Learning Centre. They use Excel, not SPSS.
See also 4.5.1 Visual aid for regression and correlation (Idiosyncratic idea by John Hall)
LSE tutorial Simple linear regression: (continuous dependent variable, continuous independent variable)
4.6 Association, structure and cause (modelling)
I currently have no tutorials of my own on these topics, but they would include:
Cluster Analysis
Discriminant Function Analysis
Factor Analysis
Multiple Regression
.
