Related Experiment Video
Updated: Jul 10, 2026

07:11
CorrelationCalculator and Filigree: Tools for Data-Driven Network Analysis of Metabolomics Data
Published on: November 10, 2023
Can scientifically useful hypotheses be tested with correlations?
1Department of Psychology, University of California, Los Angeles 90095-1563, USA. bentler@ucla.edu
The American Psychologist
|November 21, 2007
Summary
Psychological theories can be tested directly on correlation structures, bypassing complex covariance transformations. This simplifies hypothesis testing in psychological research.
Area of Science:
- Psychology
- Statistics
Background:
- Psychological theories have historically used correlation coefficients (standardized covariances).
- Recent methodological shifts necessitated transforming theories into hypotheses on covariances.
- This transformation presents an unnecessary complication in hypothesis testing.
Discussion:
- New methodologies allow direct testing of hypotheses on latent structures of correlations.
- This approach simplifies the process of validating psychological theories.
- The study provides two examples illustrating this direct testing methodology.
Key Insights:
- Directly testing correlation structures is now methodologically feasible.
- Complex covariance transformations are often unnecessary for hypothesis testing.
- This advances the statistical analysis of psychological theories.
Outlook:
- Future research can leverage these direct methods for more efficient theory validation.
- Potential for broader application across different psychological domains.
- Further exploration of the limitations of correlation structures is warranted.
Related Concept Videos
Statistical Hypothesis Testing
Hypothesis testing is a critical statistical procedure facilitating informed, evidence-based decisions. It begins with a hypothesis, which is a tentative explanation, or a prediction about a population parameter. This hypothesis can be either a null hypothesis (H0), indicating no effect or difference, or an alternative hypothesis (Ha), suggesting an effect or difference.
Statistical significance measures the probability that an observed result occurred by chance. If this probability, known as...
Statistical significance measures the probability that an observed result occurred by chance. If this probability, known as...
Correlations
Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between...
What is a Hypothesis?
A hypothesis can be a simple sentence or statement about a property or any phenomenon observed or predicted for a population. It is usually a claim about a property of the population. It can be stated for any field observations or experiments. A hypothesis statement cannot be said to be right or wrong as it is merely a statement. It needs to be tested through an elaborate data collection process and an appropriate statistical test. A hypothesis should be a general but not a vague statement. It...
Accuracy and Errors in Hypothesis Testing
Hypothesis testing is a fundamental statistical tool that begins with the assumption that the null hypothesis H0 is true. During this process, two types of errors can occur: Type I and Type II. A Type I error refers to the incorrect rejection of a true null hypothesis, while a Type II error involves the failure to reject a false null hypothesis.
In hypothesis testing, the probability of making a Type I error, denoted as α, is commonly set at 0.05. This significance level indicates a 5% chance...
In hypothesis testing, the probability of making a Type I error, denoted as α, is commonly set at 0.05. This significance level indicates a 5% chance...
Types of Hypothesis Testing
There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed.
When the null and alternative hypotheses are stated, it is observed that the null hypothesis is a neutral statement against which the alternative hypothesis is tested. The alternative hypothesis is a claim that instead has a certain direction. If the null hypothesis claims that p = 0.5, the alternative hypothesis would be an opposing statement to this and can be put either p > 0.5, p < 0.5, or p ≠ 0.5.
When the null and alternative hypotheses are stated, it is observed that the null hypothesis is a neutral statement against which the alternative hypothesis is tested. The alternative hypothesis is a claim that instead has a certain direction. If the null hypothesis claims that p = 0.5, the alternative hypothesis would be an opposing statement to this and can be put either p > 0.5, p < 0.5, or p ≠ 0.5.
Correlation and Causation
Correlation and CausationStatistical tests can calculate whether there is a relationship, or correlation, between independent and dependent variables. A relationship between variables shows correlation, but it does not show cause-and-effect. A direct cause-and-effect relationship requires additional controlled experiments. If no consistent relationship exists between the variables, then there is no correlation.Correlation versus CausationIf the dependent variable increases or decreases when the...

