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Concept Stew  Statistics for the Terrified: Glossary
Category: Mathematics and statistics > Statistics
Date & country: 13/10/2007, UK Words: 143

Active groupIn a clinical trial, the group of patients to whom the active treatment is applied and the results contrasted with a control group. See also Control group.
Alternative hypothesis (h1)Sometimes we propose an alternative to the null hypothesis, to be accepted if the null hypothesis is rejected. If the null hypothesis is that the mean is three, we reject it if the mean is not three. The alternative hypothesis may state that the mean is 3.5. Note that it is possible to reject both the null and alternative hypotheses. (The statement that the mean is not equal to three is known as the complement of the null hypothesis.)
Analysis of covarianceA technique used to detect differences between groups, which removes bias caused by a separate influential variable, and also has the advantage of increasing precision.
Analysis of variance (anova)A perversely titled technique to test whether there is a difference between a set of sample means. The simplest form of analysis of variance looks at the means classified by just one factor, eg. the factor UK nationality would produce four means: English, Irish, Scottish and Welsh. Twoway analysis of variance can handle a second factor as well, eg. Gender: male, female. This way you can look at both factors simultaneously, effectively English male, English female, Irish male, Irish female, etc. The name of the technique includes the word variance because it calculates the variation between the factor means and uses this as the basis of the test.
AntilogAntilogarithm: returns a logged number to the standard number system. See also log.
Area under the curve (auc)A single value summary of something measured repeatedly over time. It consists of a series of lines connecting adjacent points. The area underneath these lines is used as a summary of the values shown by these points. It can be calculated from the baseline established by the first measurement (usually preferable) or from zero. (The name of the technique is a misnomer, because there is no curve.)
BaselineThe initial data score of a subject before an experiment, used as a benchmark (or reference value) against which the experimental data is compared.
BiasBias is a consistent error brought about by experimental design favouring one group over another or by the investigator/data recorder favouring one group over another. In the first case it can be prevented by matching the groups, and in the second case by blinding. See also blind study.
Binary dataData that can take only one of two values, eg. Yes/no, on/off, dead/alive. See also Data types.
Biological significance (relevance)Getting statistical significance is not necessarily the end of the story. In a biological experiment you would also want to see biological significance, which is not always present. In biological terms, the statistically significant difference may be so small as to be irrelevant. Note that we may see biological significance in a sample, but we cannot conclude that this is a real effect in the population unless we also have statistical significance.
Blind studyBecause human psychology plays a big part in how we respond to things, blinding may be employed to ensure that subjects in an experiment do not know which of the treatments they are receiving. This is used to combat bias. For example, in a clinical trial people's beliefs could affect the outcome; thus nondrug treatment may appear to be more effective on advocates of alternative medicine. See also bias, blinded evaluation, double blind, single blind.
Blinded evaluationUnfortunately sometimes even investigators have biases (though they may not realise it). Therefore it is better if they do not know which treatment a particular subject received. In a blinded evaluation an investigator reviews and assesses outcome without knowing which particular treatment has been applied. This eliminates the possibility of both conscious and unconscious bias. See also bias, blind study, double blind, single blind.
Block randomisationA randomisation techique often used in multicentre clinical trials where each block contains a unique treatment allocation. The blocks are then allocated randomly in centres.
BonferroniWhen multiple testing is carried out the likelihood of finding a significant difference increases in line with the number of tests. The bonferroni correction is applied to the significance level of each test to ensure that the overall significance level (across the complete set of tests) is brought back to the required level (usually 0.05). The correction stipulates that the significance level of each test is 0.05 divided by the number of tests. See also probability, significance level.
Box and whisker plotA graphical display showing the range of the middle 50% of data within a box, with two extending lines (the whiskers) indicating the upper and lower extremes.
Carryover effectThis is a problem encountered in crossover trials. Sometimes the influence of the first treatment carries over when the second treatment is applied. Avoid this by having a long enough washout period before crossing over. The carryover effect makes crossover trials inappropriate for some disciplines. For example, you cannot test a teaching method this way, since once something has been learnt, its effect clearly carries over into the next period of the study. See also Crossover trials.
Case control studyIn a case control study, two groups are contrasted: the subjects in one share a characteristic, usually a disease (the cases), and the subjects in the other do not (the control group). See also Control group.
Categorical dataUses numbers or labels with no implied numeric value, e.g. cause of death: cancer, cardiovascular, respiratory, other. This is unlike ordinal data which has an order or hierarchy. See also Data types.
Central limit theoremAll means tend to be normal. For large sample sizes, the sample mean is normally distributed (or approximately normally distributed) irrespective of the distribution of the parent population. The larger the sample, the closer the sample mean to normality.
Chisquare statisticThe test statistic arrived at during the analysis of classification tables using the chisquare test.
Chisquare testA test used with classification tables to determine the influence (if any) of one factor (rows) on a second factor (columns) by assessing whether there is a difference in the proportion of an outcome in two or more groups. Examples of factors might be smoking (yes/no) against lung cancer (yes/no): in other words, does smoking status lead to a larger risk of lung cancer, or is it irrelevant? The chisquare test is not for use on continuous data, but specifically for counts. See also Classification table.
ciSee Confidence interval.
Classification tableThis is also known as a contingency table. Data is laid out for analysis with the chisquare or Fisher's exact tests. The rows represent different groups of subjects, and the columns different outcomes. The data consists of counts of the subjects falling into each crossclassification.
Clinical significance (relevance)Getting statistical significance is not necessarily the end of the story. In a clinical trial you would also want to see clinical significance, which is not always present. In clinical terms, the statistically significant difference may be so small as to be irrelevant. Note that we may see clinical significance in a sample, but we cannot conclude that this is a real effect in the population unless we also have statistical significance.
Clinical trialA welldefined scientific and ethical study of the effects of a particular treatment regime. Almost always, results are compared against a control group. Clinical trials are subject to very stringent regulation and codes of practice.
CodingSometimes we are interested in a quality rather than a quantity, eg. Good, bad, indifferent. The best way to get a computer to handle this kind of data is to numerically code the qualities, eg:
Deteriorated 1
Stayed the same 0
Improved 1
Alternatively we may wish to classify continuous data within categories, eg. pulse rate could be coded as:
Less than 21 1
Between 21 and 50 2
Above 50 3 See also categorical data.
Confidence interval (ci)An upper and lower limit, within which you have a stated level of confidence that the true mean lies. These are usually quoted as 95% intervals, which are constructed so that you are 95% confident that the true mean lies between the limits. To be 99% sure, you need a wider confidence interval. Increased confidence is bought at the cost of precision.
Confirmatory analysesStudies conducted specifically to confirm a particular hypothesis.
ConfoundedWhen the effects of two or more factors cannot be separated, e.g. a study recruiting old men and young women confounds age and gender effect. A welldesigned study should seek to minimise such effects.
Contingency tableAlso known as a classification table. Data is laid out for analysis with the chisquare or Fisher's exact tests. The rows represent different groups of subjects, and the columns different outcomes. The data consists of the subjects falling into each crossclassification.
Continuous dataCan take any value along a continuum (eg. body temperature: 98.4, 98.46, 99.9999997 are all valid) as opposed to discrete data which can only take integer values (eg. number of children in a family). See also Data types.
Control groupA reference group involved in a study against which the active group is compared.
CorrelationQuantifies the extent to which two variables are related to each other. it is measured in the range of +1 to 1. A correlation of +1 indicates a perfect positive relationship, ie. as one goes up, the other goes up by the same amount. A correlation of 1 indicates a perfect negative relationship, ie. as one goes up, the other goes down by the same amount. A correlation of 0 indicates that the two variables are completely independent of each other. See also Linefitting.
CountExactly as it sounds, eg. returned tablet count. See also Data types.
CovarianceThe variation in common between two related variables. See also Analysis of covariance.
CovariateA secondary variable that influences the outcome of an experiment.
Critical valueThe value at which a decision rule triggers significance.
Crossover trialA study that looks at two treatments, where each individual in the study crosses over from the first treatment to the second: particularly effective because each individual acts as his or her own control. However, it is not an appropriate technique for all disciplines. See also Carryover effect.
DataInformation (usually numeric) collected on the participants in a study and on which data analysis is performed.
Data typesAll data is not the same, and different types of data must be handled in different ways. See also Binary data, Categorical data, Continuous data, Count, Discrete data, Ordinal data.
Decision ruleA clear statement made at the outset of a study detailing how a decidion on significance is to be made.
Degrees of freedomThis crops up everywhere in statistical tests, and is used to calculate the p value. It is a fairly deep mathematical topic and we need not go fully into it here. Broadly speaking, the larger the sample size, the larger the df: the smaller the sample, the smaller the df. However, this is modified by the number of groups you have and the parameters being estimated. A small df makes it more difficult to detect significance.
Dependent variableThe term used for the outcome variable in regression analysis. A variable that depends on another variable is called the dependent variable: the variable on which it depends is called the predictor variable (sometimes the independent variable). See also Linefitting.
Descriptive statisticsSimple summary description of data carried out before a full analysis, eg. Mean, Standard error, etc.
Discrete dataData that can only take a small set of particular values, usually whole numbers. For instance, you cannot actually have 2.4 children. See also Data types.
DistributionA graph plotting probability against values. There are some typical shapes: normal, uniform, exponential. The normal distribution (bellshaped) is the most common. See also Normal distribution, population distribution, null distribution.
Double blindWhen neither subject nor evaluator knows what treatment or regime has been administered. This doubleblind approach reduces the risk of bias (psychological or otherwise) being introduced by either the investigator or the subjects of the study. Singleblind occurs when one of these two is aware of the treatment or regime administered. See also Bias, Blinded evaluation, Blind study, Single blind.
Economic significance (relevance)Getting statistical significance is not necessarily the end of the story. In an economics study you would also want to see economic significance, which is not always present. In economic terms, the statistically significant difference may be so small as to be irrelevant. Note that we may see economic significance in a sample, but we cannot conclude that this is a real effect in the population unless we also have statistical significance. A new management practice that increases profits by 38p per year has no economic value.
Educational significanceGetting statistical significance is not necessarily the end of the story. In an educational study you would also want to see educational significance, which is not always present. In educational terms, the statistically significant difference may be so small as to be irrelevant. Note that we may see educational significance in a sample, but we cannot conclude that this is a real effect in the population unless we also have statistical significance. If an expensive new teaching method increases reading ability by 0.02% in a nationwide study, it has no educational significance.
ErrorA misleading term: there is no mistake. This is actually the natural variation occurring in a sample.
EstimationA set of techniques where the value of a population parameter is inferred from sample data.
Expected valuesThe values you would expect to get in a classification table if the null hypothesis were true.
Exploratory analysesThis is a kind of gettingtoknowyourdata exercise that is carried out at the beginning of the analysis.
F distributionThe distribution of the test statistic used in analysis of variance.
F ratioThe ratio of two variances, arising from analysis of variance. A large f ratio gives rise to significant results  small ones do not.
FactorAn experiment is usually designed to investigate the effect that certain factors have on an outcome, such as sex (a twolevel factor; male, female), or UK nationality (a fourlevel factor; english, irish, scottish, welsh).
False negativeWhen our data leads us to believe something is untrue when it is in fact true.
False positiveWhen our data leads us to believe something is true when it is in fact untrue.
Field trialTrials concerned with large populations in real life situations, for example large vaccine trials. (The term derives from agricultural experiments carried out by R.A. Fisher.)
Fisher's exact testUsed in place of the chisquare test (in a classification table scenario) when the expected value of at least once cell is less than five.
Gaussian distributionAnother name for the normal distribution, after its discoverer Gauss. See also Normal distribution.
GradientAlso called slope. The gradient indicates how steeply a line slopes. You will come across this when using the linefitting technique. A line is described by its gradient and intercept, the point at which the line crosses the yaxis. See also Linefitting.
H0 (null hypothesis)The null hypothesis is an aunt sally put forward to be disproved, usually stating that there is no difference or relationship between the items under study. See also H1.
H1 (alternative hypothesis)Sometimes we propose an alternative to the null hypothesis, to be accepted if the null hypothesis is rejected. If the null hypothesis is that the mean is three, we reject it if the mean is not three. The alternative hypothesis may state that the mean is 3.5. Note that it is possible to reject both the null and alternative hypotheses. (The statement that the mean is not equal to three is known as the complement of the null hypothesis. See also H0.
HistogramA histogram is a bar or column chart, showing the frequency with which certain values occur in a sample. It is analogous to the distribution of a population.
HypothesisSee also Alternative hypothesis, H0, H1, Null hypothesis.
Independent variableA term used in linefitting for the xaxis variable, also more informatively called the predictor variable.
InterceptOne of two parameters estimated when fitting a line through pairs of data (such as height and weight), the intercept is the point at which the line crosses the yaxis).
KruskalWallis testThe nonparametric equivalent of oneway analysis of variance. This test tries to find differences between three or more groups on the basis of average ranks per group.
Line of best fitThe line that best first a set of datapoints. The best fit refers to the fact that discrepancies between the points and the line are minimised. It is described by gradient and intercept. See also Linefitting.
LinefittingAlso called regression. A method that finds the best line through a set of plotted points; a simple (and economical) way of describing th relationship between predictor and outcome variables. See also Correlation, Gradient, Intercept, Multiple regression, Regression.
LogLogarithm: also called the exponent. Expresses a number as a power of 10 or e. See also Antilog.
MannWhitney testThe nonparametric equivalent of the two sample t test; essentially based on the average rank observed in each group.
MeanAn average, one of several that summarise the typical value of a set of data. The mean is the grand total divided by the number of data points.
Mean squareAppears as a column in an analysis of variance table and consists of what may loosely be called the variance between the means for each factor.
MedianThe middle value in a sample sorted into ascending order. If the sample contains an even number of values, the median is defined as the mean of the middle two.
Missing valuesThe bugbear of many statistical experiments. This one really is what it sounds like!
ModeThe most popular point of a distribution (that is, where the shape of the distribution peaks).
Multiple regressionThis is linefitting with more than the two variables used in simple regression. The techique is used to predict one variable with the assistance of two or more predictor variables. See also Linefitting.
Multiple testing (multiplicity)The more tests we do on the same data (eg. by subdividing the data into more and more subsets) the more likely we are to find a significant result in one of them. Unfortunately this is increasingly likely to be spurious because one in twenty tests on effectively identical populations will be significant due to a type I error. See also Type I error.
Mutually exclusiveAs an example, gender can be split into two mutually exclusive groups; ie. a member of one cannot at the same time be a member of the other.
Nonparametric statisticsThat branch of statistics concerned with tests that make no assumptions about the distribution of the data  for this reason also called distributionfree statistics. Because there is no distribution, there are no parameters to estimate. The MannWhitney and Wilcoxon tests are examples. See also Parametric statistics.
Normal distributionThe most common distribution, when extreme values are much less likely to occur than the values in the middle. This distribution is symmetrical about the mean and has a bell shape. Height and weight are good examples of variables that are normally distributed. Many naturally occurring physical measurements follow the normal distribution, which was discovered by the German philosopher Gauss. See also Distribution.
Null distributionThe distribution of the test statistic when the null hypothesis is true. See also Distribution, Null hypothesis.
Null hypothesis (h0)The null hypothesis is an aunt sally put forward to be disproved, usually stating that there is no difference or relationship between the items under study. See also Null distribution.
OddsThe odds of an event happening is the ratio of the number of times the event happens divided by the number of times it does not happen.
Odds ratio (or)The odds ratio (or) is the ratio of the odds in one group to the odds in another.
Oneway analysis of varianceA generalisation of the two sample t test which tests for differences between three or more group means. The test calculates, amongst other things, the 'variance' between the group means  hence its name. See also Analysis of variance, Twoway analysis of variance.
Ordinal dataWhen categories have a natural order to them (a hierarchy), eg. improved, stayed the same, deteriorated. This is unlike categorical data where there is no natural ordering, eg. preferred colour of car; black, green, silver. See also Data types.
OutliersA value in a sample that is so extreme as to throw question on its validity.
p valueHandinhand with the test statistic is the p value which indicates the probability of getting the characteristics observed in a sample if the null hypothesis were true.
Paired t testA test on the change that occurs in a measurement carried out on the same subject under two different conditions, eg. before and after a therapeutic treatment.
ParametersVariables not in the data, but in the model (eg. distribution, line of best fit) which describes it, eg. mean, gradient, standard deviation.
Parametric statisticsThat branch of statistics based on the estimation and testing of parameters (usually normally distributed data). See also Nonparametric statistics, Parameters.
PercentileA 10 percentile is the value (of a particular variable such as weight) beneath which 10% of the population falls. A 50 percentile is the value beneath which 50% of the population falls. These could also be written as 10%ile and 50%ile.
PlaceboA nonactive treatment applied as a control in a study where psychological factors could affect the outcome. This allows the observation and quantification of any procedural effects involved in the trial that have nothing to do with any administered treatment. See also Placebo effect.
Placebo effectImprovement in outcome that is consistent but not due to any treatment or nontreatment administered. This is only a factor for human beings and possibly animals where psychology of care can affect outcome. See also Placebo.
PopulationThe set of all possible subjects from which a sample can be drawn.
Population distributionThe distribution of the population from which a sample was drawn. See also Distribution.
PowerThe ability to reject the null hypothesis when it is false.