Author: Derek Rowntree
APA Style Citation
Rowntree, D. (1981). Statistics Without Fear: A Primer for Non-Mathematicians. Allyn and Bacon, New York.
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Many Introductory psychology instructors and students consider themselves social scientists rather than mathematicians and can be frightened by the statistical analysis that is inevitably a part of deriving meaning from data. Derek Rowntree attempts to make this analysis accessible for all regardless of one’s training or prior experience in mathematics. He achieves this by providing many examples and applications to real-world situations in straightforward language. Rowntree explains that gamblers use statistics all of the time when placing bets to attempt to determine their chances of winning, the same methods are employed in the analysis of all other types of data.
Rowntree begins with a description of statistics and how the term is used. Statistics may refer to the subject or discipline of statistics, the process of collecting data, the methods used to collect that data or the figures that characterize that data (mean, mode and median). Rowntree emphasizes that he sees statistics as a set of inquiry that can help decipher the importance (or lack thereof) of a data set. Descriptive statistics are those that describe observations, which have already occurred while inferential statistics are used to make predictions and observations about a situation that has not yet been observed. Inferential statistics can also potentially be used to predict the behavior or cognition of the entire population from which a sample has been selected. In order to make this generalization, the sample must be randomly selected from the population defined by the researcher.
Rowntree describes different types of data researcher come across. Nominal data represents different categories such as gender or age, this is categorical data and may be represented by a number but is not quantifiable, it is used solely for identification (males 1, females 2). Ordinal data can be placed in rank order but does not necessarily have equal spacing between the data points. If one had 20 used bicycles, they could place them in order from the best to worst condition, but this does not mean that the 1st and 2nd ranked bikes have the same differences as the bikes ranked 7th and 8th. Nominal and ordinal data are both considered categorical data for which one does not use mathematical computations. Quantifiable data does use mathematical calculations as can be discrete (number of children one has) or continuous (age). Rowntree goes on to discuss the types of tables that are appropriate for each type of data sets.
Once the data has been collected, descriptive data analysis can begin by examining the mean, mode, and median. Rowntree acknowledges the frequent use of the mean but notes that the median is preferable in distributions in which there are extreme scores, because these outliers may distort the mean while the median is less susceptible to these extreme scores. The range is dependent only on two values (the highest and lowest) and therefore does not tell us much about the sample in general. The inter-quartile breakdown can be quite helpful, and students may relate to this idea as they find out their results on standardized exams, which often report the student’s percentile rank to indicate their performance relative to others who took the same exam. Standard deviation is also a useful descriptive tool because it describes the average distance from the mean for a set of scores. The standard deviation can be used to show students where they score compared to others on a certain measure and is less subject to large fluctuations due to extreme scores as is the mean (on pages 54-55 Rowntree also walk through a very simple step-by-step procedure to mathematically find the standard deviation for a set of scores).
Skewed distributions are described as well as normal distributions with many pictures and examples along with a description of what happens to the measures of central tendency in each of these respective distributions. For those who might be new to teaching introductory Psychology, reading the roughly ten pages on the normal distribution will go a long way toward understanding the information one needs to work with data in a normal distribution and how to compute percentile rank for scores in a normal distribution, this is time well spent.
Rowntree explains that the larger the sample (if it is random), the more it should reflect the population from which it is drawn, and while there is always the possibility of sampling error or bias, this can generally is reduced as the sample size increases. Researchers can never report with one hundred percent certainty the results of the findings because there is always the potential for sampling error or design flaws. Even studies that have been replicated often can only at best approach levels of significance (p-scores) that are close to zero. P-scores of equal to or less than .05 are considered statistically significant in the field of psychology and which point the researchers can be assured that the results of their study are unlikely due to chance. Later chapters explore a comparison between sampling, which would be helpful to review prior to the testing and individual differences unit as one could compare the results of Intelligence scores in 2 different populations and compare the results. There are also many examples that could be used in a classroom setting to allow students to work with real data sets. The chapter on significance testing would be helpful for those who are taking students through analysis of a data set, and Rowntree makes clear connections back to a discussion of the null hypothesis, which students should understand, from their research unit.
Nonparametric tests such as the Mann Whitney test are used when there is no assumption that the data has been distributed normally. One-tailed p tests are those in which data can move only one way as in measurements of weights (it can only go up from zero) or two-tailed in which data can move either up or down (blood pressure). These are discussed in terms of the parameters one must reach in order to reject the null hypothesis. Regardless of one’s level of knowledge with statistics, this book makes statistics accessible and connects concepts to realistic data. Statistics without Fear is a book to keep on the shelf and refer to year after year to make sure that as social scientists we are still getting our data analysis right.
Other Related Resources
BBC Documentary The Joy of Stats
Hans Rosling’s hour-long BBC documentary on statistical methods
Hans Rosling's 200 Countries, 200 Years, 4 Minutes
Short clip from Hans Rosling’s BBC documentary, The Joy of Stats that powerfully demonstrates correlational data
Not Awful and Boring Ideas for Teaching Statistics
Blog with current examples from real life to enliven the teaching of statistical methods that is updated weekly.
Against All Odds: Inside Statistics
Annenberg Learning website with numerous helpful videos on statistical concepts
Stats is Fun Blog
A blog offering current examples and activities related to teaching statistics created by Jessica Hartnett, Ph.D. She is an associate professor in Gannon University’s Department of Psychology and Counseling.
Psychological Figures and Concepts
Measures of central tendency
Probability of error
Skewed distribution (positive and negative)
Type 1 error
Type 2 error