# Chi-Square (χ2) Statistic.

The chi-square statistic is used to test the null hypothesis that two or more variables are independent. In other words, the chi-square statistic tests whether or not there is a relationship between the variables.

The chi-square statistic is calculated by taking the sum of the squared difference between the observed values and the expected values, divided by the expected values.

The chi-square statistic is used to test hypotheses about categorical data. Categorical data are data that can be divided into groups, such as gender, age group, or eye color.

The chi-square statistic is used to test for independence between two variables. The null hypothesis is that the two variables are independent; the alternative hypothesis is that the two variables are not independent.

The chi-square statistic is used to test for goodness of fit. The null hypothesis is that the data fit the expected values; the alternative hypothesis is that the data do not fit the expected values.

The chi-square statistic can be used to test for trends in data. The null hypothesis is that there is no trend in the data; the alternative hypothesis is that there is a trend in the data.

The chi-square statistic is used to test for differences in proportions. The null hypothesis is that the two proportions are equal; the alternative hypothesis is that the two proportions are not equal.

The chi-square statistic is used to test for differences in means. The null hypothesis is that the two means are equal; the alternative hypothesis is that the two means are not equal. What is chi square distribution in simple words? The chi-square distribution is a statistical distribution that is used to determine how likely it is that a given statistical model is correct. The chi-square distribution is used to test hypotheses about the distribution of a random variable. Who introduced chi-square test? The chi-square test is a statistical test that is used to determine whether two sets of data are statistically significantly different from each other. The chi-square test was introduced by Karl Pearson in 1900.

#### How do I interpret chi-square results in SPSS?

The chi-square statistic is used to test the null hypothesis that there is no difference between two categorical variables. The p-value is the probability of observing a chi-square statistic as large or larger than the one that was actually observed, given that the null hypothesis is true.

If the p-value is less than 0.05, then the null hypothesis is rejected and there is evidence that there is a difference between the two variables.

What is chi-square test used for? A chi-square test is used to examine how well a theoretical distribution matches an observed distribution. The chi-square statistic is used to assess the goodness of fit of an observed distribution to a theoretical distribution. The chi-square test can be used to test hypotheses about the distribution of a categorical variable.

##### Where chi-square test is used?

The chi-square test is used in a variety of situations, most commonly in hypothesis testing or in estimation of population parameters.

In hypothesis testing, the chi-square test is used to determine whether there is evidence of a difference between two or more groups, or whether there is evidence of a relationship between two variables. For example, the chi-square test could be used to test whether there is a difference in the proportion of people in different age groups who support a particular political party.

In estimation of population parameters, the chi-square test is used to estimate the value of a population parameter, such as the population mean or population proportion. For example, the chi-square test could be used to estimate the proportion of people in a population who have a particular disease.