Statistics Book

	Foreword	xii
1	Introducing Statistics	1
	Some good reasons to learn about statistics	1
	What sort of statistical questions can be asked?	2
	Can you summarize the data?	2
	Is there a significant difference between these two sets of results?	3
	Is there a close relationship between the two things under consideration?	3
	How are statistical questions investigated?	4
	Choosing and using your calculator	6
2	Some basic maths	8
	Algebra	8
	Why letters?	8
	Algebraic logic	10
	Graphs	15
	Notation	21
	(Capital) Sigma	21
	X bar	22
	Summary	23
	Comments on exercises	23
3	Graphing data	28
	Bar charts	28
	Pie charts	34
	Pictograms	36
	Histograms	36
	Stemplots	39
	Scattergraphs	42
	Time graphs	44
	Summary	44
	Comments on exercises	45
4	Choosing a suitable graph	47
	Types of data	47
	Discrete and continuous data	47
	Single and paired data	50
	Types of statistical judgement	52
	Summarizing	52
	Comparing	53
	Inter-relating	55
	Getting the right graph	56
	Bar charts and pie charts	56
	Stemplots and histograms	60
	Summary	62
	Comments on exercises	63
5	Summarizing data	65
	Introducing averages - finding a middle value	65
	Calculating and choosing averages	68
	Mode	68
	A simple mean (X)	70
	A weighted mean (X)	71
	Median (Md)	74
	Spread	76
	5-figure summary	77
	Boxplot	79
	Range	81
	Inter-quartile range (dq)	81
	Mean deviation	83
	Variance ([sigma][superscript 2]) and Standard deviation ([sigma])	84
	Summary	87
	Comments on exercises	88
6	Lies and statistics	89
	Misleading graphs	89
	Data set A	90
	Data set B	93
	Data set C	97
	Confusing percentages	99
	Inappropriate averages	104
	Summary	108
	Comments on exercises	108
7	Choosing a sample	109
	The sampling frame	110
	Random sampling	112
	Generating random numbers	115
	Using random numbers to select a sample	116
	Register of Electors	117
	Sampling variation	121
	Systematic sampling	121
	Human error and sampling error	124
	Summary	129
8	Collecting information	130
	Secondary source data	131
	Social Trends	131
	Data accuracy	133
	Primary source data	135
	Experimental design	135
	Questionnaire design	138
	Summary	142
	Comments on exercises	142
9	Reading tables of data	144
	Spreadsheets	145
	What is a spreadsheet?	145
	Why bother using a spreadsheet?	146
	Using a spreadsheet	146
	What else will a spreadsheet do?	150
	Turning the tables	151
	Reading the small print	158
	Summary	160
	Comments on exercises	160
10	Regression: describing relationships between things	164
	Paired data	164
	The 'best-fit' line	167
	Making predictions	172
	Summary	178
	Calculating the regression coefficients using the formula	179
	Comments on exercises	181
11	Correlation: measuring the strength of a relationship	187
	Scatter	187
	Product-moment correlation coefficient	191
	Rank correlation	197
	Cause and effect	202
	Summary	207
12	Chance and probability	208
	Measuring probability	208
	Odds	208
	Statistical probability	210
	Myths and misconceptions about probability	213
	Mutually exclusive outcomes and adding probabilities	215
	Independence and multiplying probabilities	218
	Summary	226
	Comments on exercises	226
13	Probability models	228
	Compared to what?	228
	The uniform distribution	229
	The Normal distribution	233
	Calculating probabilities from the Normal curve	238
	The binomial distribution	242
	The binomial expansion	247
	Linking the binomial distribution and the binomial expansion	248
	Summary	252
	Comments on exercises	252
14	Deciding on differences	254
	Picturing differences	255
	Contexts for investigating differences	260
	Some basic terminology	261
	What is a test of significance?	266
	Stage 1 Set up the hypothesis	266
	Stage 2 Calculate the test statistic, S	268
	Stage 3 Look up the critical value	268
	Stage 4 Is S [less than or equal] C?	269
	The z test	269
	The binomial test	275
	Summary	280
	Comments on exercises	281
	Appendix	286
	Choosing the right statistical technique	286