School in a Book: Statistics and Research

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Statistics are for everyone. You might not need to know all of the terms presented here, but conversational fluency on politics, economics, science and much more requires most.

Basic Statistics

Percentage: A part of one hundred, with one hundred representing the whole

Mean/average: The score that is found when a group of scores are added, then divided by the total number of scores

Median: The score that falls directly in the middle of a group of scores when those scores are presented in numerical order

Mode: The most frequently occurring score in a group

Range: A number that shows how dispersed a group of scores is

Data set: A collection of numbers or values that relate to a particular subject

Sample: A single data point in a data set

Data distribution: A function that shows all possible values for a variable as well as their frequency of occurrence. Data distributions can be used to find probability.

Standard deviation: The average amount of variability in a data set. Standard deviation shows how far any given value lies from the mean.

Normal curve/normal distribution/bell curve: The arrangement of data into a graph that delineates the average in the center, most of the data points within one standard deviation of the center, and fewer data points two, three and four standard deviations from the center. The normal curve is always symmetrical, since it depicts where various data points lie in relation to each other and to the average.

Probability: The likelihood of something happening. Probability can be represented as percentages or other numbers.

Conditional probability: The likelihood of something happening if something else happens first

Statistical significance: The likelihood that a given result occurred due to the independent variables being studied, rather than random chance

Correlation: The degree to which two or more quantities increase or decrease together. Data sets have a positive correlation when they increase together, and a negative correlation when one set increases as the other decreases. High correlation does not indicate causation.

Spurious correlation: An inaccurate or questioned correlation

Type One error/false positive: The statistical error that occurs when a true null hypothesis is rejected

Type Two error/false negative: The statistical error that occurs when a false null hypothesis is retained

Regression testing/statistical regression: A way of mathematically analyzing experimental results that uses past results to predict future results. Regression testing is used to predict college GPAs based on high school SAT scores, for example.

P value: A number that indicates the degree to which a relationship between two variables has significance; in other words, the probability

Validity coefficient: A number between 0 and 1.0 that indicates the validity of a test, with 1.0 indicating perfect validity

Correlation coefficient: A number that indicates the amount of correlation that exists between two variables, with 0 showing no correlation, a positive number showing a positive relationship and a negative number showing a negative relationship

Reliability coefficient: A number that indicates the reliability of a test’s scores from one iteration to the next, with a number greater than 1.0 indicating low reliability

Nominal scale: A binary scale such as yes/no or male/female

Ordinal scale: A scale in which scores are rated or ordered in comparison to each other

Interval scale: A scale that uses intervals, but not as part of a ratio, such as temperature

Ratio scale: A scale in which scores can be quantified in absolute terms; for example, height, length and weight

Derived score: A score that results when a raw score (for example, 67/70 on a test) is converted to a standardized scoring ratio (for example, 3.8 on a GPA scale)

Scatterplot: A set of data points plotted on a grid with horizontal and vertical axes. Scatterplots are used to visually show relationships between data points.

Venn diagram: A diagram that uses circles that sometimes overlap to show relationships between data sets. Overlapping circles represent data sets that are similar to the degree that they overlap, and different to the degree that they do not.

Basic Research

Experiment: A research study that tests a hypothesis. A true experiment includes one or more independent variables and one or more dependent variables in order to measure the effect of the independent variable(s) on the dependent variable(s). It also includes one or more control group, one or more treatment group and, significantly, random sampling

Hypothesis: A statement that might be true, which might then be tested. This is also sometimes called the alternative hypothesis, since experiments are usually based around a null hypothesis.

Null hypothesis: The statement that contradicts the research hypothesis, saying that no effect of statistical significance exists. Experiments are often built around a null hypothesis since it is easier to disprove a null hypothesis than to prove a hypothesis directly.

Independent variable: A variable that is not affected by another variable

Dependent variable: A variable that may be affected by an independent variable

Treatment group: The group of subjects in an experiment that is exposed to the dependent variable being studied

Control group: The group of subjects in an experiment that is not exposed to the dependent variable being studied. Control groups might include placebo groups, treatment as usual groups or even groups that are not acted on within the experiment in any meaningful way.

Random assignment: The practice of assigning subjects to treatment groups and control groups randomly

Random sampling: Choosing subjects by pure chance, from the whole known population

Probability sampling: Choosing subjects from within a particular population in a randomized manner, rather than purely at random

Nonprobability sampling: Choosing subjects from within a particular population in a non-randomized manner. Subjects might be selected due to their unique characteristics or due to their willingness to participate, for example. Nonprobability sampling is not used to show the probability of a variable, only to study the variable in other ways.

Saturation: The practice of administering a test to subjects over and over again until no new data refute findings of previous data

Validity: The extent to which a test measures what it says it measures

Internal validity: The extent to which a test measures what it says it measures, based on the structure of the test itself

External validity: The extent to which a test’s results can be generalized to other contexts

Face validity: The extent to which a test seems valid at first glance

Content validity: The extent to which a test’s content relates to the subject at hand

Construct validity: The extent to which a test’s construction increasing the test’s validity

Concurrent validity/convergent validity: The extent to which a test’s results overlap with other tests that measure the same phenomenon

Threats to validity: Participant effects; researcher effects; environmental effects; time-related effects; testing modality effects; drop-out effects; maturation effects; placebo effects; participant selection and more

The placebo effect: The effect on subjects not exposed to treatment that occurs when they believe they have received treatment

Reliability: The extent to which a test’s results are consistent, recurring in different iterations. Valid tests are by definition reliable; however, reliable results aren’t always valid since results can be reliably wrong.

Inter-scorer/inter-rater reliability: Degree of consistency of ratings between two or more raters observing the same behavior (like two judges of a contest)

Test-retest reliability: The consistency of the scores of the same test taker across multiple instances of the same test

Sensitivity: The extent to which a test is accurately identifies the presence of a phenomenon

Specificity: The extent to which a test accurately identifies the absence of a phenomenon

Power: The likelihood of detecting a significant relationship between the independent variable and the dependent variable, which is due to an experiment’s design

Internal consistency: Measures how consistent the test taker’s answers were to show they were honest and consistent, taking the test correctly

Descriptive research: Research questions that merely explore data in a non-experimental way. These include case studies, observational studies, statistical reports and more.

Relational research: Research that explores correlation

Causal research: Research that seeks to prove or disprove that X phenomenon causes Y phenomenon

Case study: A nonexperimental research study that presents data on a single individual or a single group of individuals experiencing the phenomenon of interest

Blind study: A study in which participants don’t know whether they are in the control group or the experiment group

Double blind study: A study in which both the researchers and the participants don’t know which group participants are in (the control group or the experiment group)

Naturalistic/observational study: A nonexperimental research study in which participants are observed, usually in their natural environment, but not directly experimented on. Interviews might also be used.

Statistical report: A nonexperimental research study consisting of a report that provides a variety of statistical data on a given topic. Two examples are reports on crime statistics in a particular city and a company annual report.

Action study: A nonexperimental study conducted for the purpose of program evaluation and improvement. An example is a needs assessment for a school free lunch program that presents relevant data, conclusions and action steps.

Quantitative research: Experimental research that presents all data in the form of numbers

Qualitative research: Experimental research that presents at least some of its data in the form of words, pictures, video and/or artifacts

Mixed-method research: Research that presents both quantitative and qualitative data

Pilot study: A less extensive preliminary experimental study for the purpose of determining whether or not a full-scale study is warranted. It is designed as an experiment, but is not a true experiment.

Comparative research design: A research design for investigating group differences for a particular variable. Simplistic; doesn’t show causation.

Longitudinal research design: A research design in which the same subject (either the same individuals or samples from the same cohort) is examined and re-examined over the course of time. Answers the research question, “What were the effects on this group over time?”

Single-subject research design: A research design for studying the effect of an experiment on a single subject or group without comparing it with another group

Time lag research design/cohort sequential research design: A research design that duplicates the experiment on a second cohort shortly after the first experiment is conducted; similar to cross-sectional but sequential

Cross-sectional research design: A research design for studying several groups at the same time. The groups might be different from each other in some way, such as children in different grades.

Correlational research design: A research design for studying the relationship between two variables. This design, however, does not show whether the variables directly affect each other.

Ex post facto/causal-comparative research design: No true randomization but otherwise, does show causation

Split-plot research design: A research design in which an experiment is first done on a large plot, then the plot is split into smaller sections and various aspects of the treatment are given to the subplots. This helps show which aspect of the treatment had the most impact on the results.

Norm-referenced assessment: An assessment or test in which each individual’s score is compared to the average score of the entire test-taking group, such as the SAT

Criterion-referenced assessment: An assessment or test in which each individual’s score is compared to the criteria, such as a skills test

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