Independent Values
Independent Values - Related Videos
01:24
Biodiversity and Human Values
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2019
Human civilization relies on biodiversity in many ways. Sudden changes in species biodiversity result in environmental changes that can modify weather patterns and therefore human civilizations. Humans are dependent on agriculture, which developed when ancestral humans found species that made suitable foods. At least 11,000 years ago, humans started to select plant and animal species to be cultivated on farms. Going back for thousands of years, humans have been artificially selecting species...
01:29
Professional Values
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2023
Nurses are responsible for caring for patients during birth, death, illness, and healing. Professional values guide the decisions and actions that nurses make in their careers. If nurses know the decisions and actions to take, providing patients with exceptional care is possible. The values that are the foundation of the nursing profession are altruism, autonomy, human dignity, and social justice. First, altruism refers to the concern for the welfare and well-being of others without personal...
01:31
Critical Values
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2025
A critical value is a definite value obtained from a particular probability distribution at a predecided confidence level (or a predecided significance level) for a given population parameter. The critical value provides demarcation that separates the sample statistics that are likely to occur from the ones that are unlikely to occur based on the given probability distribution and the population parameter to be estimated. The critical value for normal distribution is obtained from the z...
01:21
Introduction to Test of Independence
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2025
In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their individual probabilities. Tests of independence are chi-square tests involving the use of a contingency table of observed (data) values. The test statistic for a test of independence is similar to that of a goodness-of-fit test: where: O = observed values E = expected values (which should be at least 5) A test of independence determines whether...
01:16
Hypothesis Test for Test of Independence
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2023
The test of independence is a chi-square-based test used to determine whether two variables or factors are independent or dependent. This hypothesis test is used to examine the independence of the variables. One can construct two qualitative survey questions or experiments based on the variables in a contingency table. The goal is to see if the two variables are unrelated (independent) or related (dependent). The null and alternative hypotheses for this test are: H0: The two variables (factors)...
FAQs
The key mathematical check compares a joint probability with the product of the corresponding marginal probabilities. If P(A and B) equals P(A)P(B), the events satisfy the required factorization for independence; a mismatch indicates that knowing one event changes the probability of the other. This distinction determines whether standard probability calculations can be applied.
For random variables, independence concerns the entire joint distribution rather than only one selected pair of outcomes. The joint distribution must factor into the distributions of the separate variables. This broader requirement matters because limited agreement between a few observations does not establish independence across all values or support the same statistical conclusions.
Dependence changes how much information observations collectively provide. When values are related, treating them as independent can distort the calculated standard error, which then affects confidence intervals and p-values. As a result, an analysis may report evidence or precision that does not accurately reflect the structure of the observations.
In sampling and experiments, independence supports treating observations as separate contributions to probability and inference calculations. Analysts therefore consider whether one sampled or measured value could provide information about another before applying standard methods. When the assumption is reasonable, the resulting calculations can use the intended relationship among observations without accounting for additional dependence.
Regression and hypothesis testing commonly rely on independence when estimating uncertainty and evaluating evidence. If observations are dependent, the reported standard errors, confidence intervals, or p-values may be affected, even when the measured values themselves appear plausible. Checking this condition helps analysts interpret model results and test conclusions with appropriate caution.
Repeated measurements and clustered observations are important signals that values may not be independent because observations share a measurement history or group context. Rather than applying an independence-based calculation automatically, analysts should recognize the dependence and choose an appropriate model. This step helps prevent overstating the strength of evidence in statistical results.