Statistical conclusions in psychological research are fundamentally probabilistic, meaning that empirical findings are always subject to chance and the possibility of statistical errors, such as Type I or Type II errors. Because researchers cannot completely eliminate these potential errors, the results of any single empirical study can never provide absolute certainty or definitively prove that a scientific theory is true.

Probabilistic Nature of Statistics

In null hypothesis testing, sample size and relationship strength trade off against each other to determine statistical significance. A weak statistical relationship can still reach statistical significance if the sample size is sufficiently large, and conversely, a very strong relationship can be statistically significant even if it is based on a small sample.

Trade-off Between Sample Size and Relationship Strength

Consider two hypothetical studies comparing men and women. In the first, a large sample of $$500$$ women and $$500$$ men yields a strong relationship of Cohen's $$d = 0.50$$. Such a strong result in a large sample is highly unlikely if the null hypothesis were true, meaning the null hypothesis would be rejected. In the second, a small sample of $$3$$ women and $$3$$ men yields a weak relationship of Cohen's $$d = 0.10$$. This weak result in a small sample is quite likely to occur by chance, so the null hypothesis would be retained.

Example of Sample Size and Relationship Strength

Practical significance refers to the real-world importance, usefulness, or meaningfulness of a research finding. Even if a result is statistically significant, it may lack practical significance if the observed effect is trivial or too weak to have any meaningful impact in everyday life or practice.

Practical Significance

In the context of inferential statistics, what does it mean when a research finding is described as statistically significant?

A finding is considered statistically significant when it is highly unlikely to have occurred due to random chance alone. In the context of inferential statistics, achieving statistical significance suggests that the results represent a genuine, real effect within the broader population.

Google

Syracuse University

It  is important to distinguish between statistical significance and practical significance when interpreting statistical results.

Statistical vs. Practical Significance 

Inferential statistics are a set of mathematical techniques used by researchers to determine whether a statistical result or relationship observed in a study's sample reflects something that is genuinely true of the broader population.

Inferential Statistics

Trull , T. J., &amp; Prinstein , M. J. (2013). Research Methods in Clinical Psychology . In Clinical Psychology (Eighth, pp. 93–124). Textbook, Wadsworth Cengage Learning . 

Clinical Psychology Eighth Edition 

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

KPU Research Methods in Psychology - 4th American Edition

The correlation of .19 may be significant, but the magnitude of the relationship is still quite modest. For example, it might be true that in a study involving 5.000. second-year graduate students in clinical psychology across the nation, there is a correlation of 15 between their GRE scores and faculty ratings of academic competence. Even though the relationship is not a chance one, the actual importance is rather small. Most of the variance in faculty ratings is due to factors other than GRE scores. In some cases, a correlation of 15 may be judged important, but in many instances, it is not. At the same time, we should remember that accepting significance levels of .05 as non-chance represents a kind of scientific tradition, but it is not sacred. Other information may persuade us, in certain cases, that significance levels of .07 or 09, for example, should be taken seriously.

Is it a statistical significance always a practical significance?

Statistically Significant

A statistical range calculated around a sample statistic designed to contain the true population parameter a specified percentage of the time, most commonly $$95\%$$. Some researchers advocate using confidence intervals as an alternative to traditional null hypothesis testing because they are often more intuitive to interpret. Furthermore, a confidence interval inherently provides the data needed to perform a null hypothesis test; if a hypothetical population mean falls completely outside the calculated interval, the sample mean is considered statistically significantly different from that hypothetical value.

Confidence Interval

A Type I error is a false positive in null hypothesis testing. It occurs when a researcher mistakenly concludes that their results are statistically significant—thereby rejecting the null hypothesis—when, in reality, the null hypothesis is true and there is no actual relationship in the population. These errors happen because random sampling error can occasionally produce extreme results even when no true effect exists. The predetermined alpha level dictates the probability of committing this error when the null hypothesis is true.

Type I Error

A Type II error is a false negative in null hypothesis testing. It occurs when a researcher mistakenly concludes that their results are not statistically significant—thereby retaining the null hypothesis—when, in reality, the null hypothesis is false and a true relationship does exist in the population. In practical research, Type II errors typically happen because a study lacks adequate statistical power to detect the underlying relationship, often due to an insufficiently large sample size.

Type II Error

In a study of sex differences in talkativeness, Matthias Mehl and his colleagues observed that the women in their sample spoke a mean of $$16,215$$ words per day while men spoke a mean of $$15,669$$ words per day. Despite finding this difference within their specific sample, they ultimately concluded that there was no evidence of a genuine sex difference in talkativeness within the broader population.

Mehl's Study on Sex Differences in Talkativeness

In a study investigating the connection between daily hassles and stress symptoms, Allen Kanner and his colleagues discovered a positive correlation of $$+.60$$ within their sample. Based on this specific sample result, they concluded that a genuine relationship between daily hassles and symptoms exists in the overall population.

Kanner's Study on Daily Hassles and Symptoms

Null hypothesis testing is the most common approach to inferential statistics in psychological research. It provides researchers with a formal, structured process to evaluate whether an observed sample result likely occurred by random chance or whether it accurately reflects a genuine relationship or difference in the broader population.

Learn Before

Related

Learn After