# CHI SQUARE TEST by Katha Sanyal

Student at St. Thomas College
Apr. 4, 2022
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### CHI SQUARE TEST by Katha Sanyal

• 1. X2-Test PA P E R 5 : B I O S TAT I S T I C S & C O M P U T E R A P P L I C AT I O N I N B I O T E C H N O L O G Y SUBMITTED BY: Katha Sanyal G U I D E D B Y: Ms. Sulagna Ghosh M S c . B I O T E C H N O L O G Y S E M E S T E R I I S E S S I O N 2 1 - 2 2
• 2. S Y N O P S I S IMPORTANT TERMS INTRODUCTION CHARACTERISTICS OF CHI-SQUARE TEST CHI-SQUARE DISTRIBUTION CALCULATIONS OF X 2 APPLICATIONS CONDITIONS REFERENCES
• 3. PARAMETRIC TEST NON PARAMETRIC TEST HYPOTHESIS I M P O R TA N T T E R M S Test in which population follows a fixed set of parameters. Test in which population does not follow a constant parameter. A definite statement about population parameters.
• 4. I M P O R TA N T T E R M S • No statistical relationship and significance exists in a set of given single observed variable. • All the observed variables are equal. NULL HYPOTHESIS (H0) • In contrast to Null Hypothesis, Alternative Hypothesis considers 1 variable to be dominating over the other. ALTERNATIVE HYPOTHESIS (H1)
• 5. DEGREE OF FREEDOM (n-1) or (r-1)(c-1) Degrees of freedom refers to: The maximum number of logically independent values r = rows c = columns
• 7. CONTINGENCY TABLE A contingency table is A tabular representation of categorical data.
• 8. INTRODUCTION • Developed by Karl Pearson (1900) • Non-parametric test • Follows Chi-square distribution • Measures difference between observed and expected values
• 9. X2 = (𝒇𝒐 − 𝒇𝒆)2/ 𝒇𝒆
• 10. CHARACTERISTICS OF CHI-SQUARE TEST • Based on frequencies only • Non-parametric TEST • Testing difference between entire set of the expected and observed frequencies SIGNIFICANCE • Testing hypothesis and not for estimation APPLIED FOR
• 11. CHI-SQUARE DISTRIBUTION k=d.f.= 1,2,3,4,6,9 If null hypothesis is true, X2 can be closely approximated by a continuous curve known as chi-square distribution. For small no. of d.f., X2 skewed to right. As no. of d.f. increases, curve becomes more symmetrical. RELATIVE FREQUENCY CHI-SQUARE VALUE Source: https://www.statisticshowto.com/probability-and- statistics/chi-square/
• 12. C A L C U L AT I O N S O F X 2 STEP I Expected Frequencies fe STEP II Put in formula χ2 = ∑(fo – fe)2/fe STEP III Compare the values with the table value for given degree of freedom at either 5% or 1%.
• 13. E X A M P L E Examples to demonstrate application of χ2 test 1. Apply χ2 test to find the efficacy of drug from the data given in Table 11.1 reproduced in Table 11.4. The table is reproduced with expected (E) values noted below the observed (O).
• 14. E X A M P L E STEP I Expected Frequencies fe STEP II STEP III Put in formula χ2 = ∑(fo – fe)2/fe Check degree of freedom at either 5% or 1%. Source: Khanal A. B. (2016). MAHAJAN’S METHODS IN BIOSTATISTICS FOR MEDICAL STUDENTS AND RESEARCH WORKERS (Eight Edition ed.). The Health Sciences Publisher. (222-224)
• 15. DEGREE OF FREEDOM (n-1) or (r-1)(c-1) r = rows c = columns Source: https://www.mun.ca/biology/scarr/4250_Chi- square_critical_values.html DRUG IS EFFICACIOUS
• 17. TEST OF GOODNESS OF FIT OF DISTRIBUTION To determine whether there is a significant difference between observed frequency and theoretical frequency distribution such as binomial, poisson and normal. If X2 (calculated) > X2 (tabulated), with (n-1) d.f, then null hypothesis is rejected otherwise accepted. And if null hypothesis is accepted, then it can be concluded that the given distribution follows theoretical distribution.
• 18. TEST OF INDEPENDENCE OF ATTRIBUTES To determine whether or not 2 attributes are associated. Ex: To check whether a new medicine is effective in controlling fever or not, X2 test is useful.
• 19. T E S T O F H O M O G E N I T Y To test whether two or more independent random samples are drawn from the same population or from different populations. X2(calculated)< X2 (tabulated), then null hypothesis is accepted and it can be concluded that there is a uniformity in the occurrence of the events.
• 20. Data must be in the form of frequencies Precise numerical value should be given Random observations should be recorded Items must be independent. No group should contain very few items. Overall number of items must be reasonably large C O N D I T I O N S
• 21. R E F E R E N C E S Khanum, Khan (2008). FUNDAMENTALS of BIOSTATISTICS (3rd Revised Edition ed.). Hyderabad: UkaaZ Publications. (218-235) Khanal A. B. (2016). MAHAJAN’S METHODS IN BIOSTATISTICS FOR MEDICAL STUDENTS AND RESEARCH WORKERS (8th Edition ed.). The Health Sciences Publisher. (218-234)

### Editor's Notes

1. Most frequently employed statistical technique in health sectors
2. Parameters – mean, std deviation