A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
A [top]
Absolute Risk Reduction (AAR)
The absolute arithmetic difference in the rate of adverse outcomes between experimental and control participants in a trial.
Alpha error
(see type I error)
Alpha Level
Threshold of statistical significance established by the researcher (p<0.005 by convention).
Alpha Value
The level of alpha (a) selected in a hypothesis test.
Alternative Hypothesis
The opposite of the null hypothesis. It is the conclusion when the null hypothesis is rejected.
Analysis of Covariance (ANCOVA)
A special type of analysis of variance or regression used to control
for the effect of a possible confounding factor.
Analysis of Variance (ANOVA)
A statistical procedure that determines whether or not there are any differences among two or more groups of subjects on one or more factors. The F test is used in ANOVA.
B [top]
Bar Chart or Bar Graph
A chart or graph used with nominal characteristics to display the numbers or percentages of observations with the characteristic of interest.
Bell-Shaped Distribution
A term used to describe the shape of the normal (Gaussian) distribution.
Beta Error
(see type II error)
Bias
The error related to the ways the targeted and sampled populations differ; also called measurement
error, it threatens the validity of a study.
Binary Observation
A nominal measure that has only two outcomes (examples are gender
male or female; survival
yes or no).
Binomial Distribution
The probability distribution that describes the number of successes X observed in
n independent trials, each with the same probability of occurrence.
Blinding
A method to decrease bias in which the subject or investigator (single blinding) or both
(double blinding) are unaware of the subject's assignment to interventional or control samples.
Blind Study
An experimental study in which subjects do not know the treatment they are receiving; investigators may also be blind to the treatment subjects are receiving; see also double blind.
Block Design (In analysis of variance)
A design in which subjects within each block (or stratum) are assigned to a different treatment.
C [top]
Case-Control Study
An observational study that begins with patient cases who have the outcome or disease being investigated and control subjects who do not have the outcome or disease and then looks backward to identify possible precursors or risk factors.
Case-Series Study
A simple descriptive account of interesting or intriguing characteristics observed in a group of subjects.
Categorical Observation
A variable whose values are categories (an example is type of anemia). See also nominal scale.
Cause-Specific Mortality Rate
The mortality rate from a specific disease.
Cell
A category of counts or value in a contingency table.
Censored Data
In survivorship analysis, an outcome that is known because the patient has not had the event of interest or is no longer being followed.
Central Limit Theorem
A theorem that states that the distribution of means is approximately normal if the sample size is large enough (n > 30), regardless of the underlying distribution of the original measurements.
Chance Agreement
A measure of the proportion of times two or more raters would agree in their measurement or assessment of a phenomenon.
Chi-Square (X2) Distribution
The distribution used to analyze counts in frequency tables.
Chi-Square (X2) Test
The statistical test used to test the null hypothesis that proportions are equal or, equivalently, that factors or characteristics are independent or not associated.
Clinical Practice Guideline (CPG)
A systematically developed, evidence-based statement designed to standardize the process of care and optimize the outcome of care under specified clinical circumstances.
Clinical Trial
An experimental study of a drug or procedure in which the subjects are humans.
Cluster Random Sample
A two-stage sampling process in which the population is divided into clusters, a random sample of clusters is chosen, and then random samples of subjects within the clusters are selected.
Coefficient of Determination (r2)
The square of the correlation coefficient. It is interpreted as the amount of variance in one variable that is accounted for by knowing the second variable.
Cohort
A group of subjects who remain together in the same study over a period of time.
Cohort Study
An observational study that begins with a set of subjects who have a risk factor (or have been exposed to an agent) and a second set of subjects who do not have the risk factor or exposure. Both sets are followed prospectively through time to learn how many in each set develop the outcome or consequences of interest.
Collinear
In multivariable analysis, two or more independent variables that are not independent of each other.
Concurrent Controls
Control subjects assigned to a placebo or control condition during the same period of time that an experimental treatment or procedure is being evaluated.
Conditional Probability
The probability of one event given the occurrence of another event.
Confidence Interval (CI)
The interval computed from sample data that has a given probability that the unknown parameter, such as the mean or proportion, is contained within the interval. Common confidence intervals are 90%, 95%, and 99%.
Confidence Limits
The limits of a confidence interval. These limits are computed from sample data and have a given probability that the unknown parameter is located between them.
Confounded
A term used to describe a study observation that has one or more nuisance variables present that may lead to incorrect interpretations.
Confounding Variable
A variable more likely be present in one group of subjects than another that is related to the outcome of interest and thus potentially confuses, or "confounds," the results.
Construct Validity
Psychometric property of an outcome instrument assessing whether the instrument follows accepted hypotheses (constructs).
Content Validity
A measure of the degree to which the items on a test or measurement scale are representative of the characteristic being measured.
Contingency Table
A table used to display counts or frequencies for two or more nominal or quantitative variables.
Continuous Scale
A scale used to measure a numerical characteristic with values that occur on a continuum (an example is age).
Controlled For
A term used to describe a confounding variable that is taken into consideration in the design or the analysis of the study.
Controlled Trial
A trial in which subjects are assigned to a control condition as well as to an experimental condition.
Control Subjects
In a clinical trial, subjects assigned to the placebo or control condition; in a case-control study, subjects without the disease or outcome.
Correlation Coefficient r
(Pearson product moment) a measure of the linear relationship between two numerical measurements made on the same set of subjects. It ranges from -I to +1, with zero indicating no relationship.
Covariate
The potentially confounding variable controlled for in analysis of covariance.
Criterion Validity
An indication of how well a test or scale predicts another related characteristic, ideally a "gold standard" if one exists.
Critical Value
The value that a test statistic must exceed (in a absolute value sense) in order for the null hypothesis to be rejected.
Crossover Study
A clinical trial in which each group of subjects receives two or more treatments but in different sequences.
Cross-Product Ratio
(see relative risk)
Cross-Sectional Study
An observational study that examines a characteristic (or set of characteristics) in a set of subjects at one point in time; a "snap-shot" of a characteristic or condition of interest; also called survey or poll.
Cumulative Frequency or Percentage
In a frequency table, the frequency (or percentage) of observations having a given value plus all lower values.
D [top]
Decision Analysis
A formal model for describing and analyzing a decision; also called medical decision-making.
Decision Tree
A diagram of a set of possible actions, with their probabilities and the values of the outcomes listed. It is used to analyze a decision process.
Degree of Freedom
A parameter in some commonly used probability distributions; e.g., the t distribution and the chi-square distribution.
Dependent Groups or Samples
Samples in which the values in on group can be predicted from the values in the other group.
Dependent Variable
The variable whose values are the outcomes in a study; also called response or criterion variable.
Descriptive Statistics
Statistics such as the mean, the standard deviation, the proportion, and the rate used to describe attributes of a set of data.
Dichotomous Observation
A nominal measure that has only two outcomes (examples are gender
male or female; survival
yes or no); also called binary.
Directional Test
(see one-tailed test)
Discrete Scale
A scale used to measure a numerical characteristic that has integer values
(an example is number of pregnancies).
Discriminant Analysis
A regression technique for predicting a nominal outcome that has more than two
values; a method used to classify subjects or objects into groups; also called discriminant function analysis.
Distribution (population)
The values of a characteristic or variable along with the frequency of their occurrence. Distributions may be based on empirical observations or may be theoretical probability distributions (e.g., normal, binomial, chi-square).
Double-Blind Trial
A clinical trial in which neither the subjects nor the investigator(s) know which treatment subjects
have received.
E [top]
Effect or Effect Size
The magnitude of a difference or relationship. It is used for determining sample sizes and for combining results across studies in meta-analysis.
Estimation
The process of using information from a sample to draw conclusions about the values of parameters in a population.
Event
A single outcome (or set of outcomes) from an experiment.
Evidence-Based Medicine
Conscientious, explicit, and judicious use of current best evidence to make decisions about the care of individual patients.
Expected Frequencies
In contingency tables, the frequencies observed if the null hypothesis is true.
Experimental Study
A comparative study involving an intervention or manipulation. It is called a trial when human subjects
are involved.
Explanatory Variable
(see independent variable)
F [top]
Factor
A characteristic that is the focus of inquiry in a study; used in analysis of variance.
Factor Analysis
An advanced statistical method for analyzing the relationships among a set of items or indicators to determine the factors or dimensions that underlie them.
False-Negative
A test result that is negative in a person who has the disease.
False-Positive
A test result that is positive in a person who does not have the disease.
First Quartile
The 25th percentile.
Fisher's Exact Test
An exact test for 2 x 2 contingency tables. It is used when the sample size is too small to use the
chi-square test.
Frequency
The number of times a given value of an observation occurs. It is also called counts.
Frequency Distribution
In a set of numerical observations, the list of values that occur along with the
frequency of their occurrence. It may be set up as a frequency table or as a graph.
Frequency Table
A table showing the number or percentage of observations occurring at different values (or ranges of values) of a characteristic or variable.
G [top]
Gaussian Distribution
(see normal distribution)
Gold Standard
In diagnostic testing, a procedure that always identifies the true condition-diseased or disease-free-of a patient.
H [top]
Histogram
A graph of a frequency distribution of numerical observations.
Historical Cohort Study
A cohort study that uses existing records or historical data to determine the effect of a risk factor or exposure on a group of patients.
Historical Controls
In clinical trials, previously collected observations on patients used as the control values against which the treatment is compared.
Homogeneity
The situation in which the standard deviation of the dependent (Y) variable is the same, regardless of the value of the independent (X) variable; an assumption in ANOVA and regression.
Hypothesis Test
An approach to statistical inference resulting in a decision to reject or not to reject the null hypothesis.
I [top]
Incidence
a rate giving the proportion of people who develop a given disease or condition within a specified period of time.
Independent Events
Events whose occurrence or outcome has no effect on the probability of each other.
Independent Groups or Samples
Samples for which the values in one group cannot be predicted from the values in the
other group.
Independent Observations
Observations determined at different times or by different individuals without the knowledge of the value of the first observation.
Independent Variable
The explanatory or predictor variable in a study.
Inference (statistical)
The process of drawing conclusions about a population of observations from a sample of observations.
Interaction
A relationship between two independent variables such that they have a different effect on the dependent variable; i.e., the effect of one level of a factor A depends on the level of factor B.
Intercept
In a regression equation, the predicted value of Y when X is equal to zero.
Internal Consistency
Psychometric property of an outcome instrument regarding the degree to which individual items are related to each other.
Interobserver Reliability
Reliability between measurements made by two observers.
Interquartile Range
The difference between the 25th percentile and the 75th percentile.
Interrater Reliability
The reliability between measurements made by two different persons (or raters).
Intervention
The maneuver used in an experimental study. It may be a drug or a procedure.
Intrarater Reliability
The reliability between measurements made by the same person (or rater) at two different points in time.
J [top]
K [top]
Kaplan-Meier Product-Limit Method
Statistical method used to analyze survival for censored observations.
Kappa (K)
A statistic used to measure interrater or intrarater agreement for nominal measures.
L [top]
Level of Significance
The probability of incorrectly rejecting the null hypothesis in a test of hypothesis.
(Also see alpha value and P-value.)
Likelihood Ratio
In diagnostic testing, the ratio of true-positives to false-positives.
Linear Regression (of Y on X)
The process of determining a regression or prediction equation to predict Y from X.
Linear Relationship (between X and Y)
A relationship indicating that X and Y vary together according to constant increments.
Log - Rank test
Statistical method used to compare two survival curves with censored observations.
Logistic Regression
The regression technique used when the outcome is a binary, or dichotomous variable.
Longitudinal Study
A study that takes place over an extended period of time.
M [top]
Matching (or matched groups)
The process of making two groups homogeneous on possible confounding factors. It is sometimes done prior to randomization in clinical trials.
Mean
The most common measure of central tendency; a measure of the "typical"individual obtained by
averaging (totaling the various individual results and dividing by the number of results involved) a data set.
Measurement Error
The amount by which a measurement is incorrect because of problems inherent in the measuring process; also called bias.
Measures of Central Tendency
Index or summary numbers that describe the middle of a distribution.
(See mean; median; mode)
Measures of Dispersion
Index or summary numbers that describe the spread of observations about the mean.
(See range; standard deviation)
Median
A measure of central tendency. It is the middle observation; i.e., the one that divides the distribution of values into halves. It is also equal to the 50th percentile.
Medical Decision Making or Analysis
The application of probabilities to the decision process in medicine. It is the basis for cost-benefit analysis.
Meta-Analysis
A method for combining the results from several independent studies of the same outcome so that an overall P-value may be determined.
Mode
The value of a numerical variable that occurs the most frequently.
Morbidity Rate
The number of patients in a defined population who develop a morbid condition over a specified period of time.
Mortality Rate
The number of deaths in a defined population over a specified period of time. It is the number of people who die during a given period of time divided by the number of people at risk during the period.
Multiple Comparisons
Comparisons resulting from many statistical tests performed for the same observations.
Multiple Regression
A multivariate method for determining a regression or prediction equation to predict an outcome from a set of independent variables.
Multivariate
A term that refers to a study or analysis involving multiple independent or dependent variables.
N [top]
Negative Predictive Variable (NPV)
Posterior probability that a patient does not have a disease given a negative diagnostic test.
Nominal Scale
The simplest scale of measurement. It is used for characteristics that have no numerical values (examples are race and gender). It is also called a categorical or qualitative scale.
Nonparametric Method
A statistical test that makes no assumptions regarding the distribution of the observations.
Nonprobability Sample
A sample selected in such a way that the probability that a subject is selected is unknown.
Nonrandomized Trial
A clinical trial in which subjects are assigned to treatments on other than a randomized basis. It is subject to several biases.
Normal Distribution
A symmetric, bell-shaped probability distribution with mean and standard deviation. If observations follow a normal distribution, the interval (mean + 2SDs) contains 95% of the observations. It is also called the Gaussian Distribution.
Null Hypothesis
The hypothesis being tested about a population. Null generally means "no difference" and thus refers a situation in which there is no difference (e.g., between the means in a treatment group and a control group).
Numerical Scale
The highest level of measurement. It is used for characteristics that can be given numerical values; the differences between numbers have meaning; (examples are height, weight, blood pressure level). It is also called an interval or ratio scale.
O [top]
Observational Study
A study that does not involve an intervention or manipulation. It is called case-control, cross-sectional, or cohort, depending on the design of the study.
Observed Frequencies
The frequencies that occur in a study. They are generally arranged in a contingency table.
Odds
The probability that an event will occur divided by the probability that the event will not occur.
Odds Ratio (OR)
An estimate of the relative risk calculated in case-control studies. It is the odds that a patient was exposed to a given risk factor divided by the odds that a control was exposed to the risk factor.
Disease No Disease
Risk factor present a b
Risk factor absent c d
Odds ratio = a x d/b x c
One-Tailed Test
A test in which the alternative hypothesis specifies a deviation from the null hypothesis in one direction only. The critical region is located in one end of the distribution of the test statistic. It is also called a directional test.
Ordinal Scale
Used for characteristics that have an underlying order to their values; the numbers used are arbitrary
(an example is Apgar scores).
Outcome Variable
The dependent or criterion variable in a study; that endpoint variable identified by the investigator as the measurement of interest used to assess study results.
P [top]
Paired t Test
The statistical method for comparing the difference (or change) in a numerical variable observed for two paired (or matched) groups. It also applies to before and after measurements made on the same group of subjects.
Parameter
The population value of a characteristic of a distribution.
Percentile
A number that indicates the percentage of a distribution that is less than or equal to that number.
Placebo
A sham treatment or procedure. It is used to reduce bias in clinical studies.
Point Estimate
A general term for any statistic (e.g., mean, standard deviation, proportion).
Poisson Distribution
A probability distribution used to model the number of times a rare event occurs.
Population
The entire collection of observations or subjects that have something in common and to which conclusions are inferred.
Positive Predictive Variable (PPV)
Posterior probability that a patient has the disease given a positive diagnostic test.
Posttest Odds
In diagnostic testing, the odds that a patient has a given disease or condition after a diagnostic procedure is performed and interpreted. They are similar to the predictive value of a diagnostic test.
Power
The ability of a test statistic to detect a specified alternative hypothesis or difference of a specified
size when the alternative hypothesis is true (i.e., 1-B where B is the probability of a type II error).
More loosely, it is the ability of a study to detect an actual effect or difference.
Predictive Value of a Negative Test
The proportion of time that a patient with a negative diagnostic test result does not have the disease being investigated.
Predictive Value of a Positive Test
The proportion of time that a patient with a positive diagnostic test result has the disease being investigated.
Pretest Odds
In diagnostic testing, the odds that a patient has a given disease or condition before a diagnostic procedure is performed and interpreted. They are similar to prior probabilities.
Prevalence
The proportion of people who have a given disease or condition at a specified point in time.
It is not truly a rate, although it is often incorrectly called prevalence rate.
Probability
The number of times an outcome occurs in the total number of trials. If A is the outcome, the probability of A is denoted P (A).
Proportion
The number of observations with the characteristic of interest divided by the total number of observations. It is used to summarize counts.
Prospective Study
A study designed before data are collected.
P-Value
The probability of observing a result as extreme as or more extreme than the one actually observed from chance alone (i.e., if the null hypothesis is true).
Q [top]
Qualitative Observations
Characteristics measured on a nominal scale.
Quantitative Observations
Characteristics measured on a numerical scale; the resulting numbers have inherent meaning.
Quartile
The 25th percentile or the 75th percentile, called the first and third quartiles, respectively.
R [top]
Random Assignment
The use of random methods to assign different treatments to patients or vice versa.
Random Error or Variation
The variation in a sample that can be expected to occur by chance.
Randomization
The process of assigning subjects to different treatments (or vice versa) by using random numbers.
Randomized Clinical Trial
An experimental study in which subjects are randomly assigned to treatment groups.
Random Sample
A sample of n subjects (or objects) selected from a population so that each has known chance of being
in the sample.
Range
The difference between the largest and the smallest observation.
Rank-Order Scale
A scale for observations arranged according to their size, from lowest to highest or vice versa.
Rate
A proportion associated with a multiplier, called the base, (e.g., 1000, 10,000, 100,000) and computed over a specific period of time.
Ratio
A part divided by another part. It is the number of observations with the characteristic of interest divided by the number without the characteristic.
Regression (of Y on X)
The process of determining a prediction equation for predicting Y from X.
Regression Coefficient
The b in the simple regression equation Y = a + bX It is sometimes interpreted as the slope of the regression line.
Relative Risk (RR)
The ratio of the incidence of a given disease in exposed or at risk persons to the incidence of the disease in unexposed persons. It is calculated in cohort or prospective studies. Relative Risk Reduction (RRR)
proportional reduction in adverse-event rates between experimental and control groups in a trial.
Reliability
A measure of the reproducibility of a measurement. It is measured by kappa for nominal measures and by correlation for numerical measures.
Repeated-Measures Design
A study design in which subjects are measured at more than one point in time. It is also called a split-plot design in ANOVA.
Representative Population (or sample)
A population or sample that is similar in important ways to the population to which the findings of a study are generalized.
Response Variable
(see dependent variable)
Retrospective Cohort Study
(see historical cohort study)
Retrospective Study
A study undertaken in a post hoc manner, i.e., after the observations have been made.
Risk Factor
A term used to designate a characteristic that is more prevalent among subjects who develop a given disease or outcome than among subjects who do not. It is generally considered to be causal.
Risk Ratio
(See relative risk)
Robust
A statistical method in which the value is not affected by violation of test assumptions.
ROC (Receiver Operating Characteristic) Curve
In diagnostic testing, a plot of the true-positives on
the Y axis versus the false-positives on the X axis; used to evaluate
the properties of a diagnostic test.
S [top]
Sample
A subset of the population.
Sampling distribution (of a statistic)
The frequency distribution of the statistic for many samples. It is used to make inferences about the statistic from a single sample.
Scale of Measurement
The degree of precision with which a characteristic is measured. It is generally categorized into nominal (or categorical), ordinal, and numerical (or interval and ratio) scales.
Scatterplot
A two-dimensional graph displaying the relationship between two numerical characteristics or variables.
Selection Bias
Systematic error in sampling the population.
Self-Controlled Study
A study in which the subjects serve as their own controls, achieved by measuring the characteristic of interest before and after an intervention.
Sensitivity
The proportion of time a diagnostic test is positive in patients who have the disease or condition. A sensitive test has a low false-negative rate.
Sensitivity Analysis
In decision analysis, a method for determining the way the decision changes as a function of probabilities and utilities used in the analysis.
Simple Random Sample
A random sample in which each of the n subjects (or objects) in the sample has an equal chance of being selected.
Skewed Distribution
A distribution in which there are a few outlying observations in one direction only. If the outlying observations are small, the distribution is skewed to the left, or negatively skewed; if large, the distribution is skewed to the right, or positively skewed.
Specificity
The proportion of time that a diagnostic test is negative in patients who do not have the disease or condition. A specific test has a low false-positive rate.
Standard Deviation
The most common measure of dispersion or spread It can be used with the mean to describe the distribution of observations. It is the square root of the average of the squared deviations of the observations from their mean.
Standard Error (SE)
The standard deviation of the sampling distribution of a statistic.
Statistic
A summary number for a sample (e.g., the mean). Often used as an estimate of a parameter in the population.
Statistical Significance
Generally interpreted as a result that would occur by chance; e.g., I time in 20, with a P-value less than or equal .05. It occurs when the null hypothesis is rejected.
Statistical Test
The procedure used to test a null hypothesis (e.g., t test, chi-square test).
Stepwise Regression
In multiple regression, a sequential method of selecting the variables to be included in the prediction equation.
Stratified Random Sample
A sample consisting of random samples from each subpopulation (or stratum) in a population. It is used so that the investigator can be sure that each subpopulation is appropriately represented in the sample.
Subjective Probability
An estimate of probability that reflects a person's opinion or best guess from previous experience.
Survey
An observational study that generally has a cross-sectional design; a commonly used design to collect opinions.
Symmetric Distribution
A distribution that has the same shape on both sides of the mean. The mean, median, and mode are all equal. It is the opposite of a skewed distribution.
Systematic Error
A measurement error that is the same (or constant) over all observations. (See also bias)
Systematic Random Sample
A random sample obtained by selecting each kth subject or object.
Systematic Review
An evidence-based summary of the medical literature in which explicit methods are used to perform a thorough literature search and a critical appraisal of studies.
T [top]
Target Population
The population to which the investigator wishes to generalize.
Test-Retest (Reliability)
A measure of the degree to which an instrument or test provides a consistent measure of a characteristic on different occasions.
Test Statistic
The specific statistic used to test the null hypothesis (e.g., the t statistic or chi-square statistic).
Testing Threshold
In diagnostic testing, the point at which the optimal decision is to perform a diagnostic test.
Third Quartile
The 75th percentile.
Threshold Model
A model for deciding when a diagnostic test should be ordered, as opposed to doing nothing or treating the patient without performing the test.
Treatment Threshold
In diagnostic testing, the point at which the optimal decision is to treat the patient without first performing a diagnostic test.
Trial
An experiment involving humans, commonly called a clinical trial. It is also a replication (repetition)
of an experiment.
True-Negative
A test result that is negative in a person who does not have the disease.
True-Positive
A test result that is positive in a person who has the disease.
t Test
The statistical test for comparing a mean with a norm or for comparing two means with small
sample sizes (n < 30). It is also used for testing whether a correlation coefficient or a regression coefficient is zero.
Two-Sample t Test
The statistical test used to test the null hypothesis that two independent (or unrelated) groups have the
same mean.
Two-Tailed Test
A test in which the alternative hypothesis specifies a deviation from the null hypothesis in either direction. The critical region is located in both ends of the distribution of the test statistic. It is also called a directional test.
Type I Error
The error that results if a true null hypothesis is rejected or if a difference is concluded when there is no difference.
Type II Error
The error that results if a false null hypothesis is not rejected or if a difference is not detected when there is a difference.
U [top]
Unbiasedness (of a statistic)
A term used to describe a statistic whose mean based on a large number of samples is equal to the population parameter.
Uncontrolled Study
An experimental study that has no control subjects.
Univariate Analysis
Analysis of the relationship of a single independent and single dependent variable (bivariate analysis).
Utility
Measure of patient desirability or preference for various states of health and illness.
V [top]
Validity
The degree to which a variable actually represents what it is supposed
to be representing. External validity is the degree to which a finding
in a study represents the population as a whole. Internal validity is
the degree to which a finding from a single experimental study
represents the study population within that clinical environment.
Variable
A characteristic of interest in a study that has different values for different subjects or objects.
Variance
The square of the standard deviation.
W X [top]
Y [top]
Yates' Correction
The process of subtracting 0.5 from the numerator at each term in the chi-square statistic for 2 x 2 tables prior to squaring the term.
Z [top]
Z Distribution
The normal distribution with mean zero and standard deviation 1. It is also called the standard normal distribution.
Z Test
The statistical test for comparing a mean with a norm or comparing two means for large samples (n > 30).