## What does a chi square test tell you?

The **Chi**–**square test** is intended to **test** how likely it is that an observed distribution is due to chance. It is also called a “goodness of fit” statistic, because it measures how well the observed distribution of data fits with the distribution that is expected **if** the variables are independent.

## What is chi square test with examples?

**Chi**–**Square** Independence **Test** – What Is It? if two categorical variables are related in some population. **Example**: a scientist wants to know if education level and marital status are related for all people in some country. He collects data on a simple random **sample** of n = 300 people, part of which are shown below.

## How do you do a chi square test?

Divide the squares obtained for each cell in the table by the expected number for that cell [ (O – E)^{2} / E ]. Sum all the values for (O – E)^{2} / E. This is the **chi square** statistic.

## What does P 0.05 mean in Chi Square?

A **p**-value higher than **0.05** (> **0.05**) is not statistically significant and indicates strong evidence for the null hypothesis. This **means** we retain the null hypothesis and reject the alternative hypothesis. You should note that you cannot accept the null hypothesis, we **can** only reject the null or fail to reject it.

## How do you interpret chi square value?

For a **Chi**–**square** test, a p-**value** that is less than or equal to your significance level indicates there is sufficient evidence to conclude that the observed distribution is not the same as the expected distribution. You can conclude that a relationship exists between the categorical variables.

## Where do we use chi square test?

The **Chi Square** statistic is commonly **used** for **testing** relationships between categorical variables. The null hypothesis of the **Chi**–**Square test** is that no relationship exists on the categorical variables in the population; they are independent.

## What are the null and alternative hypothesis in chi square test?

**Hypotheses**. **Null hypothesis**: Assumes that there is no association between the two variables. **Alternative hypothesis**: Assumes that there is an association between the two variables. If the observed **chi**–**square test** statistic is greater than the critical value, the **null hypothesis** can be rejected.

## What is the symbol for Chi Square?

The term ‘chi square’ (pro- nounced with a hard ‘ch’) is used because the **Greek letter χ** is used to define this distribution. It will be seen that the elements on which this dis- Page 4 Chi-Square Tests 705 tribution is based are squared, so that the symbol χ2 is used to denote the distribution.

## What is critical value chi square?

So for a test with 1 df (degree of **freedom**), the “critical” value of the chi-square statistic is 3.84. What does critical value mean? Basically, if the chi-square you calculated was bigger than the critical value in the table, then the data did not fit the model, which means you have to reject the **null** hypothesis.

## What is the p value for chi square test?

The **P**–**value** is the probability that a **chi**–**square** statistic having 2 degrees of freedom is more extreme than 19.58. We use the **Chi**–**Square** Distribution Calculator to find **P**(Χ^{2} > 19.58) = 0.0001. Interpret results. Since the **P**–**value** (0.0001) is less than the significance level (0.05), we cannot accept the null hypothesis.

## What does P.05 mean?

A statistically significant test result (**P** ≤ 0.05) **means** that the test hypothesis is false or should be rejected. A P value greater than 0.05 **means** that no effect was observed.

## Why do we use 0.05 level of significance?

The **significance level**, also denoted as alpha or α, is the probability of rejecting the null hypothesis when it is true. For example, a **significance level** of **0.05** indicates a 5% risk of concluding that a difference exists when there is no actual difference.

## How do you accept or reject the null hypothesis in Chi-Square?

If your **chi**–**square** calculated value is greater than the **chi**–**square** critical value, then you **reject** your **null hypothesis**. If your **chi**–**square** calculated value is less than the **chi**–**square** critical value, then you “**fail to reject**” your **null hypothesis**.