Independent Trials
Independent Trials - Related Videos
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)...
05:08
Manipulating an Independent Variable through Embodiment
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2023
Source: Laboratories of Gary Lewandowski, Dave Strohmetz, and Natalie Ciarocco—Monmouth University In any experiment, the researcher attempts to manipulate participants in one group to have different thoughts, experiences, or feelings than the other groups in the study. Some manipulations are overt, while others can be quite subtle. Embodiment is a growing research area focused on the theory that subtle physical experiences can unconsciously influence a person’s thoughts. For example if a...
02:36
Law of Independent Assortment
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2026
While Mendel’s Law of Segregation states that the two alleles for one gene are separated into different gametes, a different question of how different genes are inherited remains. For example, is the gene for tall plants inherited with the gene for green peas? Mendel asked this question by experimenting with a dihybrid cross; a cross in which both parents are homozygous for two distinct traits resulting in an F1 generation that are heterozygous for both traits.Let’s think of two homozygous...
01:18
Independent and Dependent Sources
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2024
In electrical circuits, sources play a crucial role in providing power for the operation of the circuit. These sources can be broadly categorized into two types: independent and dependent. Independent voltage or current sources supply a fixed amount of voltage or current, respectively, which is unaffected by other elements within the circuit. These are represented using specific symbols. Independent voltage sources are symbolized with polarities (+ and -), indicating the direction of the...
FAQs
For a specified sequence, calculate the probability of each required outcome and multiply those probabilities together. This approach accounts for every ordered result in the sequence, rather than treating the trials as one combined event without structure. In statistics, the resulting value estimates how likely that exact sequence is under the assumed trial probabilities.
Independence alone does not establish a binomial model. The repeated trials must also classify outcomes as success or failure and maintain a constant probability for the relevant outcome. When those conditions hold, the model provides a consistent framework for evaluating repeated results and estimating the likelihood of observing a specified number or pattern of successes.
Independent-trial calculations provide a probability benchmark for observed results. Researchers can compare the likelihood of a sequence or outcome pattern with what the assumed probabilities predict. An outcome that appears unusual may still occur through chance variation, so the calculated likelihood helps distinguish an unexpected but plausible result from a pattern that warrants closer statistical attention.
First, identify the repeated experiments or events and specify the possible outcomes. Next, determine the probability associated with each required result, then multiply the relevant probabilities for a particular sequence. If outcomes are reduced to success or failure with a constant probability, a binomial model can organize the analysis and support interpretation of the observed data.
A binomial model is appropriate when repeated trials are independent, each outcome is classified as success or failure, and the probability remains constant from trial to trial. These conditions allow researchers to analyze repeated results using one consistent probability structure. The model can then estimate the likelihood of outcomes such as a particular number of successes.
The framework supports analysis whenever researchers examine repeated experimental data or events whose outcomes can be evaluated probabilistically. In sampling, it helps assess observed selections; in quality control, it supports evaluation of repeated results; and in clinical studies, it helps estimate how likely observed patterns are under specified trial probabilities.