Statistics, an Intuitive Introduction

Introduction

The Summation Sign

Rounding

Central Tendency

Variability

Boxplots and Histograms

Standard Deviation

Normal Distribution

Sampling

Reliability and Standard Errors

Confidence Intervals and Student's t Distribution

Column Charts and Tables

Hypothesis Testing and One-Sample t-Test

Two-Sample t-Test

F-Test

ANOVA I

ANOVA II

Scatterplots

Scatterplots with Many Dimensions

Paired Samples t-Test

Correlation (Pearson's)

Assessing Correlations

Spearman's Rank Correlation

Regression I - Partitioning the Variation

Regression II - the Regression Line

Regression III - Model Checking

Chi Square

Statistics, an Intuitive Introduction

Hypothesis Testing

Standard normal distribution, Z-scores, area under the curve, six sigma, probability calculations.

http://www.nottingham.ac.uk/toolkits/play_508

Getting Started

Developed by Claire Chambers (School of Geography), Sue Cobb (Faculty of Engineering), Richard Field (School of Geography), Sandra Hill (School of Biosciences) and John Horton (Information Services)

Prezi menu by David Coast

Written by Richard Field and John Horton

Randomisation, types of error, sampling error, replication, pseudoreplication, how to sample randomly, sources of bias.

http://www.nottingham.ac.uk/toolkits/play_2267

Sampling distributions, evidence for Central Limit Theorem, confidence, unreliability, standard errors.

Things you need to know before starting this course.

http://www.nottingham.ac.uk/toolkits/play_245

http://www.nottingham.ac.uk/toolkits/play_2268

Confidence intervals (95% and 99%), Student's t distribution, Student's t statistic, critical t-values, calculating confidence intervals.

Understanding the Summation Sign.

http://www.nottingham.ac.uk/toolkits/play_2308

http://www.nottingham.ac.uk/toolkits/play_232

Occam's Razor, type I and II errors, statistical significance, P-values, t values, one-sample t-test, statistical power, pilot studies, assumptions of hypothesis tests.

http://www.nottingham.ac.uk/toolkits/play_2689

How do we round numbers? Why do we round numbers? Decimal Places, Significant figures.

http://www.nottingham.ac.uk/toolkits/play_2275

Presenting Data

Graphical display – boxplots and their whiskers, bins and histograms, distributions, normal distribution, Poisson distribution.

http://www.nottingham.ac.uk/toolkits/play_506

Relationships between Variables

Comparing Means and Counts

Principles of data display, error bars, annotation, captions, simple column charts, clustered column charts, tables.

http://www.nottingham.ac.uk/toolkits/play_2363

Descriptive Statistics

Correlation coefficients, four quadrants on a scatterplot, contribution of each point to the correlation, standardising the measure, determining significance, worked examples.

Choosing how to display data, principles of data display, basic scatterplots, scatterplot variants and enhancements (including jitter, Cleveland dotplots, best-fit lines, distinguishing categories, use of colour).

http://www.nottingham.ac.uk/toolkits/play_2612

http://www.nottingham.ac.uk/toolkits/play_2634

Differences measured as t-values, degrees of freedom, significance of a difference between two means, equal and unequal variances.

http://www.nottingham.ac.uk/toolkits/play_2639

Correlation assumptions, non-linear relationships, testing the assumptions, what to do if assumptions are violated.

http://www.nottingham.ac.uk/toolkits/play_2623

Comparing variances, differences as ratios, the F statistic, assumptions of t- and F-tests, non-parametric tests.

http://www.nottingham.ac.uk/toolkits/play_2641

Mean, median, mode, continuous and ratio data, ranks and categories.

http://www.nottingham.ac.uk/toolkits/play_196

Scatterplot matrices, 3-D scatterplots and alternatives, maps, panelled plots, conditioning plots, contingency tables, graphical data exploration, matching chart types with analysis types.

http://www.nottingham.ac.uk/toolkits/play_2694

Converting to ranks, doing Pearson's correlation on the ranked data, worked examples, comparison of Spearman and Pearson in different scenarios, including the presence of unusual points.

http://www.nottingham.ac.uk/toolkits/play_2628

Problem of multiple tests, comparing means by analysing variance, null and alternative hypothesis, models and null models, observed and fitted / predicted values, residuals, sums of squares of model and error, coefficient of determination.

http://www.nottingham.ac.uk/toolkits/play_2700

Range, quartiles, inter-quartile range; also the concept of inferring from samples.

http://www.nottingham.ac.uk/toolkits/play_505

ANOVA table, using F to calculate significance, model complexity, ANOVA assumptions, 'accounting for' vs. 'explaining'.

http://www.nottingham.ac.uk/toolkits/play_2701

Deviations, sums of squares, mean deviation, variance of the population, standard deviation of the population, degrees of freedom, variance (of the sample), standard deviation (of the sample).

Causality, effect of one variable on another, the regression line, comparison with ANOVA, contributions of each point to total, error and model sums of squares, coefficient of determination and link with correlation.

http://www.nottingham.ac.uk/toolkits/play_507

http://www.nottingham.ac.uk/toolkits/play_2594

Slope and intercept, least-squares best-fit, OLS regression, DF and variance calculation, regression's ANOVA table, SE of the estimate, SE of slope and intercept, regression coefficients, the origin, extrapolation beyond the range of the data.

Paired data, within-pair differences, comparing the average difference with a test value, choosing the right test, assumptions, Wilcoxon's matched pairs, influence of correlation.

http://www.nottingham.ac.uk/toolkits/play_2595

http://www.nottingham.ac.uk/toolkits/play_2607

Contingency tables, null hypothesis, expected counts, calculating chi square, continuity correction, χchi square distribution, DF, residuals, χchi square goodness of fit test, χchi square test for independence, adjusted residuals, assumptions.

http://www.nottingham.ac.uk/toolkits/play_2876

Regression assumptions including homoscedasticity and normality of residuals, linearity, patterning in residuals including spatial patterning, comparison with correlation.

http://www.nottingham.ac.uk/toolkits/play_2874