This statistics calculator is intended for evaluation of the extent of difference between observed and expected frequencies. Enter the observed and expected values in the appropriate fields of this Chi Square Calculator and calculate the values of degrees of freedom, chi-square and corresponding P-value (right tail or left tail). You can paste the input data copied from a spreadsheet or csv-file or enter manually using comma, space or ‘enter’ as separators.
Chi Square Test
In probability theory and statistics, the chi-square distribution (also known as chi-squared or ({ chi }^{ 2 })-distribution) with (k) degrees of freedom is the distribution of a sum of the squares of (k) independent standard normal random variables.
The expression for Pearson’s cumulative test statistic, which asymptotically approaches a ({ chi } ^{2})-distribution, is as follows:
Chi-Square Test Calculator. This is a easy chi-square calculator for a contingency table that has up to five rows and five columns (for alternative chi-square calculators, see the column to your right). The calculation takes three steps, allowing you to see how the chi-square statistic is calculated. The web site has three main sections: statistical calculators, which deals mainly with hypothesis testing; p-value calculators, which allow you to derive p-values from Z, t, chi-square and Pearson (r); and descriptive statistics - averages, variance, a standard deviation calculator, and easy histogram and bar chart makers. Using the Chi Square to p-value calculator. Having obtained a Χ 2 statistic from a given set of data you would often want to convert it to its corresponding p-value. This Chi Square to P-value calculator is easy to use and requires minimum input to get the job done. The p -value is the area under the chi-square probability density function (pdf) curve to the right of the specified χ2 value. In Excel: p = CHIDIST (χ2,ν). See Chi-square formulae for more details of the mathematics. Compute the inverse of the p-value for a chi-square distribution.
$${displaystyle chi ^{2}=sum _{i=1}^{n}{frac {(O_{i}-E_{i})^{2}}{E_{i}}}},$$
where (O_{i}) is the number of observations of type (i), (E_{i}) is the expected (theoretical) frequency of type (i), and (n = k + 1) is the number of types (categories) of observations. It’s evident from this equation that the closer the measured values are to those expected, the lower the chi-square sum will be.
The probability (Q) that a ({ chi } ^{2}) value calculated for an experiment with (k) degrees of freedom is due to chance (or, in other words, is consistent with the so called null hypothesis) is:
$${ Q }_{ { chi }^{ 2 },k }={ left[ { 2 }^{ k/2 }Gamma left( frac { k }{ 2 } right) right] }^{ -1 }int _{ { chi }^{ 2 } }^{ infty }{ { left( t right) }^{ frac { k }{ 2 } -1 }{ e }^{ -frac { t }{ 2 } }dt }, $$
where (Γ) is the gamma function, which is the generalization of the factorial function to real and complex arguments:
$$Gamma left( x right) =int _{ 0 }^{ infty }{ { t }^{ x-1 }{ e }^{ -t }dt }. $$
Easy Chi-square Calculator Online
In null hypothesis significance testing, the P-value is the probability of obtaining test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is correct. A very small P-value means that such an extreme observed outcome would be very unlikely under the null hypothesis.
For a given test statistic ({ chi } ^{2}) the right-tail P-value is defined as:
$${ P }_{ right }left( { chi }^{ 2 },k right) = { Q }_{ { chi }^{ 2 },k },$$
and the left-tail P-value is defined as:
$${ P }_{ left }left( { chi }^{ 2 },k right) = 1 – { Q }_{ { chi }^{ 2 },k }.$$
So, this Chi-Square calculator can be used for Chi-Square goodness of fit test or simply to compare the observed sample distribution with the expected probability distribution. Generally speaking, if the right-tail P-value found for the calculated ({ chi } ^{2}) is higher than conventional criteria for statistical significance (0.001-0.05), we usually do not reject the null hypothesis and assume that all the differences are due to chance.
Review sherlock holmes and the great escape.
Related calculators
How To Do Chi Square Ti 84
Check out our other statistics calculators such as Frequency Distribution Calculator or P-value Calculator.