# chi-squared test

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## chi-squared test

a statistical routine which is a test of SIGNIFICANCE, comparing the observed results of an experiment or sample against the numbers expected from a theory or prediction. The test produces a value called chi-squared (χ2) which is:

The χ2 number is then converted to a probability value (P) using an χ2 table. If the P value is larger than 5% we can conclude that there is ‘no significant difference’ between the observed results and those expected, any deviation being due to chance. If, however, the probability is less than 5%, it must be concluded that there is a ‘significant difference’ between the observed results and those expected from theory. Note that the χ2test can only be used with data that fall into discrete categories, e.g. heads or tails, long or short, yellow or orange. Take, for example, a sample of 100 plants arising from a cross between two hybrid red parents. Three quarters of the offspring are expected to be red-flowered, one quarter white. The χ2analysis is shown in the table below.

In this example, there are two classes of data (n = 2) so there is one ‘degree of freedom’ (n - 1). Using the Table of χ2 shows that, with one degree of freedom, a χ2 value of 2.61 indicates a greater than 5% chance that the deviation between observed and expected numbers was due to chance alone, i.e. there is no significant difference between the numbers observed and those expected.

## chi-squared test

one of the statistical techniques for determining (1) if there are significant differences between two or more series of frequencies or proportions and (2) whether one series of proportions is significantly different from a control series. Pearson's chi-square is used for unmatched data and McNemar's chi-square for matched data.
References in periodicals archive ?
From the P - values in Chi-squared test, it can be interpreted that the factors associated with the occurrence of gastrointestinal haemorrhage are total leucocyte count more than 10,000/[mm.
From Tables 22 - 27, after performing Chi-squared test, none of the tested factors show any statistically significant association with the occurrence of intra-abdominal abscess.
Factors Affecting Infection and Sepsis, Results of Chi-Squared Test
From Tables 28-32, according to Pearson Chi-squared test, the factors significantly affecting infective and septic complications are total leucocyte count more than 10000, amount of bilirubin more than 10 mg/dL, body mass index less than 17.
The chi-squared test employed by Boncek and Harden is usually encountered when dealing with a multinomial random variable.
If there are only two possible outcomes for each trial, a chi-squared test with only one degree of freedom is still technically valid, but is unnecessarily complex.
Employing a hypothesis test with the binomial random variable--or by employing the Central Limit Theorem to approximate it by a normal random variable--might bring the example within the range of understanding of more students than does use of the chi-squared test.
As a rule of thumb, if you find yourself using a chi-squared test with only one degree of freedom, consider whether there is a simpler way to view the problem.
These important ideas include measures of central tendency, measures of dispersion and the logic behind chi-squared tests, analysis of variance tests and correlation coefficients.
Their topics are chi-squared tests, goodness-of-fit tests based on empirical processes, rank tests, and other non-parametric tests.
Chi-squared tests of the association between mathematics proficiency and the covariates as well as correlation analyses among the covariates suggest that the absence of some variables from the prediction equations may be a results of multicolinearity among the explanatory variables.

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