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Chi Square Test | Chi-Square Test Explained | Probability & Statistics Tutorial

This presentation on probability and statistics gives a basic overview of the chi-square distribution. It explains how to use the chi-square distribution to conduct goodness of fit test to determine whether the null hypothesis should be accepted or rejected.<br><br>In this presentation, we will discuss - <br>1. Research and Null Hypothesis<br>2. Expected and Observed Frequency<br>3. Chi-Square Test<br>4. Example

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Chi Square Test | Chi-Square Test Explained | Probability & Statistics Tutorial

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  1. What’s in it for you? Research and Null Hypothesis Expected and Observed Frequency Calculating Expected Frequency Chi-Square Test Example

  2. Research and Null Hypothesis

  3. Click here to watch the video

  4. Research and Null Hypothesis The null hypothesis (H0) states that no association exists between the two variables in the population, and therefore the variables are statistically independent The research hypothesis (H1) proposes that the two variables are related in the population

  5. Expected and Observed Frequencies

  6. Expected and Observed Frequency Observed frequencies (fo)is the cell frequencies actually observed in a table Expected frequencies (fe)is the cell frequencies that would be expected in a table if the two tables were statistically independent

  7. Calculating Expected Frequency To obtain the expected frequencies for any cell in which the two variables are assumed independent, multiply the row and column totals for that cell and divide the product by the total number of cases in the table Expected Value =

  8. Chi-Square Test

  9. Chi-Square Test However, like all inferential techniques it assumes random sampling Chi-square test is an inferential statistics technique designed to test for significant relationships between two variables Chi-square requires no assumptions about the shape of the population distribution from which a sample is drawn

  10. Limitations Of The Chi-Square Test The chi-square test is sensitive to sample size. The size of the calculated chi-square is directly proportional to the size of the sample, independent of the strength of the relationship between the variables The chi-square test does not give us much information about the strength of the relationship or its substantive significance in the population

  11. Calculating The Chi-Square fe= expected frequencies fo = observed frequencies

  12. Hypothesis Testing With Chi-Square Chi-square follows five steps: • Making assumptions (random sampling) • Selecting the sampling distribution and specifying the test statistic • Stating the research and null hypotheses • Computing the test statistics • Deciding and interpreting the result

  13. Degree Of Freedom

  14. Degree Of Freedom Calculating Degrees of Freedom is key when trying to understand the importance of a Chi-Square statistic and the validity of the null hypothesis Degree of Freedom refers to the maximum number of logically independent values that have the freedom to vary in the data sample df = (r – 1)(c – 1) r = Number of rows c = Number of columns

  15. Degree Of Freedom How many degrees of freedom would a table with 3 rows and 2 columns have?

  16. Example

  17. Example The below table gives the relationship between handedness and gender in the U.S.A. This data is also known as HANES data Null Hypothesis: Gender and Handedness are independent

  18. Example Expected Value = =

  19. Example 2

  20. Example 2 2 2 2 2 2 2 = 12

  21. Example Chi-squared = 12 Degrees of freedom= 2 Alpha value = 0.05 The Null hypothesis is rejected: Based on the HANES data, handedness and gender are very likely not independent

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