### Three steps to reproducible results

This exercise is a part of Educator Guide: Replication Crisis Spurs Reforms / View Guide

Directions: Define key science terms relating to topics in social science, experimental design and math/statistics using contextual clues from “Replication crisis spurs reforms.” Consult an outside resource if necessary.

#### Social science

What is social science?

Social science is the scientific study of humans, human behavior and human relationships. The social sciences are fields such as psychology, economics and political science.

What is psychology?

Psychology is the study of the human mind, especially in relation to actions and behavior.

What is economics?

Economics is the study of the production, distribution and consumption of goods and services as well as the financial system that is used for those processes.

#### Experimental design

What is experimental design?

Experimental design is how an experiment is set up to make relevant and accurate measurements subject to the constraints of available resources and time.

What is a hypothesis?

A hypothesis is a proposed explanation for a phenomenon. In science, a hypothesis is an idea that must be rigorously tested before it is accepted or rejected.

What is a control?
A part of an experiment where there is no change from normal conditions. The control is essential to scientific experiments. It shows that any new effect is probably due to only the part of the test that a researcher has altered. It gives scientists something against which they can compare their experimental data.

What is data analysis?

Data analysis is the process of interpreting information collected during experiments in order to identify and minimize errors and look for meaningful trends in the results.

What is reproducibility or replication?

Reproducibility or replication is the ability of a researcher to independently recreate an experiment or study, under the same conditions, and yield the same results.

#### Math and statistics

What is statistics?

In science, statistics is the practice of collecting and analyzing numerical data in large quantities and interpreting the data’s meaning. Much of this work involves reducing errors that might be attributed to random variation.

What is a null hypothesis?

In research and statistics, a null hypothesis is a statement acknowledging that there might be no difference or relationship between two or more things being tested. Conducting an experiment is often an effort to reject the null hypothesis, or prove that there is a difference between two or more conditions.

What is statistical significance?

In research, a result is significant (from a statistical point of view) if the likelihood that the observed difference between two or more conditions could be due to chance is very small. Obtaining a result that is statistically significant means there is a very high likelihood that any difference that is measured was not the result of random events.

What is the p value?

The p value is the probability of seeing a difference as big as or bigger than the one observed if there is no effect of the variable being tested. Scientists generally conclude that a p value of less than 5 percent (written 0.05) is statistically significant, or unlikely to occur due to some factor other than the one tested. It’s important to note that statistical significance does not indicate the presence of a causational relationship between groups. And, not all scientists agree about how to effectively use p values when analyzing results. Read more about the topic: “Statistics: Make conclusions cautiously.”

What is the mean?

One of the several measurements of the “average size” of a data set. The most commonly used is the arithmetic mean, obtained by adding the data and dividing by the number of data points.

What is standard deviation?

The standard deviation is the amount that each set of data varies from the mean. A smaller standard deviation means the values or data points are closer together. In other words, there is less variation among the results. Smaller standard deviations are preferable in scientific measurements.

What are error bars?

An error bar is a line (vertical or horizontal) drawn through a point or a bar on a graph. The distance from one end of the line to the other represents how precise a measurement is, or how far the true value of something might fall from the data point reported in an experiment. Generally error bars indicate the standard deviation in both directions away from the mean.

What is curve fitting?

Curve fitting is taking a mathematical function that best describes a hypothesis (which may be a simple line, a polynomial, a bell curve or some other shape depending on the circumstances) and adjusting its main parameters (where it intersects the axes, its size, its slope, or other parameters) to make it best fit the data points plotted on a graph. Curve fitting can give a sense of how well a hypothesis (represented by the curve) explains experimental results (represented by the data points). Curve fitting is also a way to use measured data to determine the appropriate values for physical constants in the formula for the curve’s shape.

#### Discussion beyond the article:

Dig deeper into the methodology of experimental design. Can you create your own study and reproduce the results after you answer these questions?

How many samples are needed to test a hypothesis?

You need at least one test sample and two control samples — one positive and one negative.

What is the sample size of an experiment?

The sample size is the number of individuals from a population tested in an experiment. The sample size should be large enough to adequately represent a population in the study.  A mathematical test called a power analysis will help to determine the sample size needed.

What are the consequences of not having a large enough sample size?

If your sample size doesn’t represent the population, you will not get meaningful results.

What are potential consequences of having too big a sample size?

Trivial differences might appear to be statistically significant even though they aren’t meaningful. Also, a larger sample size requires more time and resources.

Note: Students can become familiar with how to use a sample size calculator, such as this one offered by SurveyMonkey: https://www.surveymonkey.com/mp/sample-size-calculator. Students can discuss levels of confidence.

Once a sample size is determined, how does a scientist choose which individuals to include in a study or experiment?

Randomization is often a technique used to select a number of individuals within a population to participate in or be observed as part of an experiment.

What is the number of trials in an experiment?

The number of trials is how many times the experiment is run. Generally, conducting more trials reduces the likelihood for error in the results.