Counternull
Encyclopedia
In statistics
, and especially in the statistical analysis of psychological
data, the counternull is a statistic used to aid the understanding and presentation of research results. It revolves around the effect size
, which is the mean magnitude of some effect divided by the standard deviation
.
The counternull value is the effect size that is just as well supported by the data as the null hypothesis
. In particular, when results are drawn from a distribution that is symmetrical about its mean, the counternull value is exactly twice the observed effect size.
The null hypothesis is a hypothesis
set up to be tested against an alternative. Thus the counternull is an alternative hypothesis that, when used to replace the null hypothesis, generates the same p-value
as had the original null hypothesis of “no difference.”
Some researchers contend that reporting the counternull, in addition to the p-value, serves to counter two common errors of judgment:
These arbitrary statistical thresholds create a discontinuity, causing unnecessary confusion and artificial controversy
.
Other researchers prefer confidence interval
s as a means of countering these common errors.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, and especially in the statistical analysis of psychological
Psychology
Psychology is the study of the mind and behavior. Its immediate goal is to understand individuals and groups by both establishing general principles and researching specific cases. For many, the ultimate goal of psychology is to benefit society...
data, the counternull is a statistic used to aid the understanding and presentation of research results. It revolves around the effect size
Effect size
In statistics, an effect size is a measure of the strength of the relationship between two variables in a statistical population, or a sample-based estimate of that quantity...
, which is the mean magnitude of some effect divided by the standard deviation
Standard deviation
Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...
.
The counternull value is the effect size that is just as well supported by the data as the null hypothesis
Null hypothesis
The practice of science involves formulating and testing hypotheses, assertions that are capable of being proven false using a test of observed data. The null hypothesis typically corresponds to a general or default position...
. In particular, when results are drawn from a distribution that is symmetrical about its mean, the counternull value is exactly twice the observed effect size.
The null hypothesis is a hypothesis
Statistical hypothesis testing
A statistical hypothesis test is a method of making decisions using data, whether from a controlled experiment or an observational study . In statistics, a result is called statistically significant if it is unlikely to have occurred by chance alone, according to a pre-determined threshold...
set up to be tested against an alternative. Thus the counternull is an alternative hypothesis that, when used to replace the null hypothesis, generates the same p-value
P-value
In statistical significance testing, the p-value is the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true. One often "rejects the null hypothesis" when the p-value is less than the significance level α ,...
as had the original null hypothesis of “no difference.”
Some researchers contend that reporting the counternull, in addition to the p-value, serves to counter two common errors of judgment:
- assuming that failure to reject the null hypothesis at the chosen level of statistical significance means that the observed size of the "effect" is zero; and
- assuming that rejection of the null hypothesis at a particular p-value means that the measured "effect" is not only statistically significant, but also scientifically important.
These arbitrary statistical thresholds create a discontinuity, causing unnecessary confusion and artificial controversy
Controversy
Controversy is a state of prolonged public dispute or debate, usually concerning a matter of opinion. The word was coined from the Latin controversia, as a composite of controversus – "turned in an opposite direction," from contra – "against" – and vertere – to turn, or versus , hence, "to turn...
.
Other researchers prefer confidence interval
Confidence interval
In statistics, a confidence interval is a particular kind of interval estimate of a population parameter and is used to indicate the reliability of an estimate. It is an observed interval , in principle different from sample to sample, that frequently includes the parameter of interest, if the...
s as a means of countering these common errors.
Further reading
- Rosnow, R. L., & Rosenthal, R. (1996). Computing contrasts, effect sizes, and counternulls on other people's published data: General procedures for research consumers. Psychological Methods, 1, 331-340