To effectively rule out threats to internal validity—such as history, maturation, testing, instrumentation, regression to the mean, and spontaneous remission—researchers can add a control group to a pretest-posttest design. A control group does not receive the experimental treatment but is subjected to the same external events, passage of time, and repeated measurements as the treatment group. By comparing the posttest changes between the two groups, researchers can isolate the actual effect of the treatment from these alternative explanations, although doing so means the study is no longer a one-group design.

Control Group in Pretest-Posttest Designs

An everyday example of regression to the mean involves an amateur bowler who typically averages a score of $$150$$. If she suddenly bowls an exceptionally high game of $$220$$, statistical probability suggests her next game will be significantly lower, regressing back toward her long-term average of $$150$$. This natural fluctuation demonstrates how extreme performances or scores are usually followed by more typical, average results, rather than indicating a permanent improvement or decline.

Example of Regression to the Mean

In a research study, what condition primarily makes regression to the mean a severe threat to internal validity?

Regression to the mean acts as a severe threat to internal validity when participants are selected for a research study specifically because of their extreme initial scores. Statistically, individuals who achieve exceptionally high or low scores on a pretest are highly likely to score closer to the population average on a subsequent posttest simply due to natural, random variability. This makes it incredibly difficult to determine whether a shift in scores was genuinely caused by the experimental treatment or was merely the result of statistical regression.

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Regression towards the mean is a phenomenon that occurs when resampling a single random variable. 

The phenomenon arises when the first sample of the random variable appears extreme, while the second sample appears much closer to the mean. This result occurs when the first sample is extremely above and below the mean.

Regression to the Mean

A one-group pretest-posttest design is a quasi-experimental research method where a single group of participants is measured on a dependent variable both before and after a treatment is administered. Unlike a within-subjects experiment, this design does not counterbalance the order of conditions because the treatment must inherently occur between the initial baseline measurement (pretest) and the subsequent measurement (posttest). While an improvement in posttest scores compared to pretest scores might intuitively suggest that the treatment was effective, such conclusions are difficult to make with certainty because the absence of a control group leaves the study highly vulnerable to alternative explanations and threats to internal validity.

One-Group Pretest-Posttest Design

https://kpu.pressbooks.pub/psychmethods4e/

KPU Research Methods in Psychology - 4th American Edition

Father and son heights are an example of regression to the mean in this book. Above average height father will tend to have a son who is shorter, while still above average. 

Conversely, an above average height son will tend to have a father who is also above average, but shorter. 

While this seems like a contradiction, these are tendencies across an entire population that will always trend toward the mean height.

This reversability of prediction in regression to the mean is why there is no difference between cause and effect in this situaton.


The Book of Why: Regression to the Mean

Regression to the mean can be explained by a correlation coefficient with the absolute value smaller than 1.

Regression to the mean explained by correlation

While using a Galton board to present to inheritance, on the board on the left, Francis Galton noticed that the balls piled up in a normal distribution or a bell-shaped curve. In the board, in the middle, the A and B were first thought as different generations with the distribution widened each time through them. The board on the right had chutes to move the distribution closer together with his explanation for regression to the mean.

Francis Galton ended discovering a statistics law instead of a hereditary. Galton thought that regression to the mean was a casual process but eventually realized that statistics and causation were separate.

Origins of Regression to the Mean  

Regression to the Mean as a Threat to Internal Validity

Which of the following best describes the statistical phenomenon of regression to the mean?

An interrupted time-series design is a quasi-experimental approach and a variant of the pretest-posttest design. In this methodology, a researcher takes a time series—multiple measurements of a dependent variable at regular intervals—both before and after a treatment is introduced. The treatment effectively 'interrupts' the ongoing measurements. Unlike the simpler pretest-posttest design, which relies on a single before-and-after measurement, the inclusion of multiple measurements allows researchers to better distinguish the actual effect of the intervention from normal variation.

Interrupted Time-Series Design

In research design, history serves as an alternative explanation for changes in a dependent variable, representing a significant threat to internal validity. This threat occurs when extraneous external events happen between the pretest and posttest measurements, unintentionally causing a shift in the participants' scores. For instance, if an anti-drug education program is being evaluated, an unexpected and highly publicized celebrity drug overdose occurring during the study period could independently influence participants' attitudes, confounding the results and making it impossible to determine if the education program was the true cause of the change.

History as a Threat to Internal Validity

Maturation is a threat to internal validity that occurs when participants undergo natural developmental or physiological changes—such as growing older, learning, or becoming fatigued—between the pretest and posttest measurements of a study. These natural, ongoing changes, rather than the experimental treatment itself, may be the actual cause of any observed differences in the dependent variable over time. For example, over the course of a year-long intervention, children naturally become better reasoners, which could be misconstrued as an effect of the intervention.

Maturation as a Threat to Internal Validity

The testing threat to internal validity occurs when the mere act of taking a pretest inadvertently influences a participant's responses on the subsequent posttest. Completing the initial measurement might inspire further thought, conversation, or practice regarding the topic being studied. This increased awareness or familiarity can independently cause a change in the posttest scores, regardless of whether the actual experimental treatment was effective.

Testing as a Threat to Internal Validity

Instrumentation threatens a study's internal validity when the fundamental characteristics of the measuring instrument or process change between the pretest and posttest. This issue frequently arises in observational studies where human observers are used to measure behavior, as they may gradually gain skill, become fatigued, or unconsciously alter their evaluation standards over time. Additionally, instrumentation effects can manifest when the participants themselves change their approach to the measurement tool, such as taking a survey very seriously during the novel pretest but becoming bored and less careful with their responses during the posttest.

Instrumentation as a Threat to Internal Validity

Spontaneous remission is the natural tendency for many medical conditions and psychological problems to gradually improve over time without any formal treatment or intervention. This phenomenon acts as a significant confounding variable in studies that lack a control group; researchers evaluating a treatment using a simple pretest-posttest design may falsely attribute a patient's recovery to their specific intervention, when in reality, the condition would have naturally improved on its own.

Spontaneous Remission

A practical example of a one-group pretest-posttest design involves evaluating an anti-drug education program for elementary school students. Researchers first measure the students' baseline attitudes toward illegal drugs (the pretest). Next, they implement the anti-drug curriculum over a specified period. Finally, they measure the students' attitudes again (the posttest). By comparing the pretest and posttest scores, researchers can see if attitudes changed, though the lack of a control group makes it difficult to definitively attribute any change solely to the educational program.

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