Fischer Exact Test
Fischer Exact Test - Related Videos
01:08
Fisher's Exact Test
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2025
Fisher's exact test is a statistical significance test widely used to analyze 2x2 contingency tables, particularly in situations where sample sizes are small. Unlike the chi-squared test, which approximates P-values and assumes minimum expected frequencies of at least five in each cell, Fisher's exact test calculates the exact probability (P-value) of observing the data or more extreme results under the null hypothesis. This feature makes it especially valuable when the assumptions of the...
00:57
Behrens–Fisher Test
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2025
The Behrens-Fisher test is a statistical method designed to address the Behrens-Fisher problem, which arises when comparing the means of two normally distributed populations with unequal variances. Unlike the Student's t-test, which assumes equal variances, the Behrens-Fisher test allows for mean comparison without this restrictive assumption. This flexibility makes it particularly valuable in scenarios where two independent samples exhibit normality but lack variance homogeneity. This test is...
01:17
The Fisher Effect
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2025
The Fisher Effect, named after economist Irving Fisher, is pivotal in financial theory. It illustrates how inflation impacts the economy's interest rates. The Fisher Effect states that the nominal interest rate is the sum of the real interest rate and expected inflation. Understanding this concept is essential for various financial activities, from setting savings account yields to pricing loans and bonds. It helps investors assess the true value of their investments in terms of future buying...
01:16
The Fisher Effect
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2025
The Fisher Effect helps us understand why interest rates often rise when people expect inflation. It tells us that the nominal interest rate (the one you see at the bank or on a loan) is made up of the real interest rate plus expected inflation. In simple terms, if prices are expected to go up, interest rates usually go up too. This helps savers and lenders keep the value of their money from falling over time.Let’s say someone wants to earn a real return of 2% on their savings. If they expect...
01:27
State Function, Exact and Inexact Differentials
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2026
A state function is a thermodynamic property that depends solely on the current state of a system, irrespective of its history or how it arrived at that state. These functions are represented by capital letters, such as U, H, and S, which stand for internal energy, enthalpy, and entropy, respectively.For instance, the value of internal energy depends on the system's state variables and remains unaffected by the process path. This means that whether the system underwent a linear process or a...
FAQs
The row and column totals remain fixed while the test evaluates how likely a particular arrangement of counts would be under the null hypothesis. This constraint defines the set of tables being compared and allows the probability calculation to use the hypergeometric distribution. Consequently, the assessment focuses on the allocation of observations between categories rather than changing overall group or category totals.
The hypergeometric distribution supplies the probability for the observed 2 × 2 table under the assumption that the categorical variables are unrelated. The calculation then includes the observed arrangement and tables considered more extreme. Because these probabilities are computed directly rather than estimated through a large-sample approximation, the result remains useful for small datasets and low expected cell counts.
The main distinction is how each method obtains its evidence. Fischer Exact Test calculates probabilities directly with fixed marginal totals, whereas the chi-square test relies on a large-sample approximation. When a table contains few observations or low expected cell counts, the exact approach avoids depending on an approximation that may be less suitable for the data structure.
The reported probability is not limited to the exact table observed. It also accounts for arrangements judged more inconsistent with the null hypothesis of no association, while preserving the marginal totals. This broader comparison determines the evidence considered by the test and helps researchers evaluate whether the observed relationship between classifications is statistically supported.
First, organize observations for two categorical variables in a 2 × 2 contingency table. Next, identify the null hypothesis of no association and retain the table’s marginal totals. The exact calculation uses the hypergeometric distribution to evaluate the observed arrangement and more extreme arrangements. Finally, interpret the resulting probability in relation to the proposed association.
The method is useful when researchers compare classifications between groups and the resulting contingency table is small or contains low expected cell counts. In biology, medicine, and social science, it can assess whether two categorical classifications are associated without requiring a large sample. Its outcome helps determine whether the observed difference between groups has statistical support.
It evaluates whether the observed allocation of cases across the categories is compatible with a null hypothesis of no association. A probability based on the observed and more extreme tables provides the statistical evidence for that assessment. The result supports interpretation of relationships between classifications, but it does not replace clear identification of the variables and their category structure.