What is the Friedman Test?

S3-SA3-0416

Grade Level:

Class 9

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

The Friedman Test is a special statistical test used when you want to compare three or more related groups or conditions. Imagine you have the same people or items trying out different things, and you want to see if there's a real difference in their performance or results across these different things. It helps check if the 'treatments' (the different things being tried) have significantly different effects.

Simple Example

Quick Example

Imagine a school wants to test three different teaching methods (A, B, C) for Math. They pick 10 students and have each student try all three methods over three different weeks, then give a test after each method. The Friedman Test would help them see if one teaching method generally leads to significantly better or worse scores for these students compared to the others.

Worked Example

Step-by-Step

Let's say 4 judges (J1, J2, J3, J4) are ranking 3 types of samosas (S1, S2, S3) from 1st to 3rd (1 being best). We want to know if there's a significant difference in how the samosas are ranked.

Judge 1: S1=1, S2=2, S3=3
Judge 2: S1=2, S2=1, S3=3
Judge 3: S1=1, S2=3, S3=2
Judge 4: S1=2, S2=3, S3=1

---Step 1: Assign ranks within each judge's ratings. (Already done in this example, as they are ranks).

---Step 2: Sum the ranks for each samosa type.
Sum of ranks for S1 (R1) = 1 + 2 + 1 + 2 = 6
Sum of ranks for S2 (R2) = 2 + 1 + 3 + 3 = 9
Sum of ranks for S3 (R3) = 3 + 3 + 2 + 1 = 9

---Step 3: Calculate the Friedman Test statistic (often called 'chi-squared Friedman' or 'Fr'). The formula is: Fr = [12 / (N * k * (k + 1))] * Sum(Ri^2) - 3 * N * (k + 1), where N is number of judges (4), k is number of samosa types (3), and Ri is the sum of ranks for each samosa.

---Step 4: Plug in the values.
Fr = [12 / (4 * 3 * (3 + 1))] * (6^2 + 9^2 + 9^2) - 3 * 4 * (3 + 1)
Fr = [12 / (4 * 3 * 4)] * (36 + 81 + 81) - 3 * 4 * 4
Fr = [12 / 48] * (198) - 48
Fr = 0.25 * 198 - 48
Fr = 49.5 - 48
Fr = 1.5

---Step 5: Compare the calculated Fr value to a critical value from a chi-squared table (not covered here, but for 2 degrees of freedom and common significance levels, 1.5 is usually less than the critical value).

---Answer: The calculated Friedman statistic (Fr) is 1.5. This value would typically suggest there is no significant difference in how the samosas are ranked by the judges.

Why It Matters

Understanding tests like Friedman is key in data science and AI/ML, helping to compare different algorithms or models accurately. Engineers use it to evaluate designs, and economists might use it to compare different policies. This skill can open doors to exciting careers in data analysis, research, and product development.

Common Mistakes

MISTAKE: Using the Friedman Test when the groups are independent (not related). | CORRECTION: The Friedman Test is specifically for 'related' groups, meaning the same subjects or items are measured under different conditions. If groups are independent, you'd use a different test like Kruskal-Wallis.

MISTAKE: Not ranking the data correctly within each 'block' or subject. | CORRECTION: For the Friedman Test, you must rank the observations for each subject (e.g., each judge, each student) separately across the different conditions, not rank all data together.

MISTAKE: Applying the test when there are only two conditions to compare. | CORRECTION: The Friedman Test is designed for comparing three or more related conditions. For two related conditions, a different test like the Wilcoxon Signed-Rank Test is more appropriate.

Practice Questions

Try It Yourself

QUESTION: A chef tries 3 different recipes (A, B, C) for a new dessert. 5 tasters rank all 3 desserts from 1 (best) to 3 (worst). If the sums of ranks for A, B, and C are 7, 10, and 8 respectively, what is the number of tasters (N) and the number of recipes (k)? | ANSWER: N = 5, k = 3

QUESTION: Why is the Friedman Test considered a 'non-parametric' test? | ANSWER: It's non-parametric because it doesn't assume the data follows a specific distribution (like a normal distribution) and instead works with ranks of the data, not the raw values.

QUESTION: Three different mobile games (G1, G2, G3) are rated by 6 friends (F1-F6) on a scale of 1 to 10 (10 being best). To use the Friedman Test, how would you convert these ratings into ranks for each friend? For example, if Friend 1 rated G1=8, G2=5, G3=9, what would their ranks be? | ANSWER: For Friend 1: G1=8 (rank 2), G2=5 (rank 3), G3=9 (rank 1). You rank them from best to worst (or worst to best, consistently) for each friend individually.

MCQ

Quick Quiz

Which of the following scenarios is best suited for the Friedman Test?

Comparing the average height of students in three different schools.

Comparing the effectiveness of two different medicines on a group of patients.

Comparing the performance of three different cricket bats when used by the same 10 batsmen.

Comparing the favourite colours of boys and girls in a class.

The Correct Answer Is:

Option C is correct because it involves comparing three (or more) related groups (the three cricket bats) where the same subjects (the 10 batsmen) are used for each comparison. Options A, B, and D involve independent groups or only two related groups.

Real World Connection

In the Real World

Imagine an e-commerce company like Flipkart or Amazon trying to figure out which of three new website layouts works best. They could show each layout to the same group of users at different times and track how long they spend, how many items they add to cart, etc. The Friedman Test can help them statistically determine if one layout is significantly better or worse, helping them improve user experience and sales.

Key Vocabulary

Key Terms

STATISTICAL TEST: A method to make decisions about data | NON-PARAMETRIC: A type of test that doesn't assume data follows a specific distribution | RELATED GROUPS: When the same subjects or items are measured under different conditions | RANKS: The position of a value when data is sorted | NULL HYPOTHESIS: A statement that there is no significant difference between groups (what the test tries to disprove)

What's Next

What to Learn Next

Next, you can explore other non-parametric tests like the Kruskal-Wallis Test, which is similar but used for independent groups. Understanding these tests will strengthen your foundation in statistics and prepare you for advanced concepts in data analysis.