Section Outlines
of
“Fug’s Guide to Statistics”
Here is a list of the sections available but there will be more to follow, click to read more.
M&M&M, Data presentation
The Normal distribution
Samples and population
Confidence Intervals
Tests of Significance
Tests of significance involving two samples
Binomial Distribution and Proportion (currently being rewritten)
Linear Regression (in progress)
Chi-squared distribution (in progress)
This is the place where everyone starts so I will be no different and suggest that this section may be best read first. All different types of diagrams are shown with the same set of data indicating both the good and the bad points of each display. The typical measures of the mean, mode and median are discussed along with the measures of variation.
This section introduces the Normal distribution and explains the difference between continuous and discrete distributions. There are plenty of diagrams and templates on how to answer every type of “Normal” question. The Normal tables are shown every time a probability is calculated with full instructions on how to use them. The worked example is shown at the end in the format that the reader would write it in an examination.
The reasons why sampling is important are discussed and the sampling distribution of the mean is introduced with the aid of lots of diagrams. The Central Limit Theorem makes its debut here and will reappear in other sections but not in so much detail. Different types of examples are given concerning probabilities of average values. A few hints are given at the end of the section.
The confidence interval is the first step on the road to Statistical Inference. Once again there are many diagrams to help with understanding the interval for means and proportions. The minimum sample size for means and proportions are discussed with all the pitfalls. There is a flowchart for helping to decide when to use “t” and when to use “z”; this is useful for tests of significance as well. The Central Limit theorem and degrees of freedom are mentioned here.
Using an example of hand strengths in young children, the reader is taken through every stage of the reasoning from the hypotheses to the final conclusion. There are a variety of explanations as experience shows that not all students think alike. There are examples given of every type of hypothesis concerning the mean with detailed explanation of how that particular one was chosen. Both “z” and “t” values are used with detailed instructions on both when to use which value and how to use the tables to obtain the probability. Hints are given throughout the section and then a summary at the end particularly for revision for examinations.
Tests of significance involving two samples
Using examples of both paired and unpaired two sample tests concerning the mean, the reader is shown how to decide which test to use and why. There are reminders about the theory of tests of significance so that the reader does not have to look back to the other section. It is always nice to have an explanation on the spot rather than looking for minutes to find where the explanation is in the book. A summary of hints is given at the end of the section with usually a very non-mathematical slant.
Venn diagrams and tree diagrams are introduced and explained through examples. The formulae for the different probabilities are shown as well as related to the Venn and tree diagrams. Bayes’ Theorem is included here as some business statistics courses cover this as part of decision trees. Once again a summary of all the hints is given at the end to use when revising.
Binomial distribution and Proportions
The Binomial Distribution is given the very friendly touch of Statistica and all aspects are explained with particular attention to changing probabilities in order to use the appropriate tables. The relationship between the Binomial Distribution and the sampling distribution of the proportion is shown and then on to questions about probabilities of proportions. The dreaded tests of significance are next but they are given the usual friendly treatment of an explanation whilst going through an example. More examination hints at the end.
