written 2.8 years ago by
binitamayekar
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Paired T-Test
- A paired t-test is also called a Correlated Paired t-test, a Paired-Samples t-test, or Dependent Samples t-test.
- Paired T-Test is used when two samples are somehow connected or dependent or perform tests on the same things.
- In the given scenario, two classification algorithms called A and B test the accuracy on the same 10-fold cross-validation samples.
- Therefore, here paired t-test is applicable to determine the performance differences of the two classification algorithms A and B are statistically similar or not.
Step 1 –
The null hypothesis in the paired t-test assumes the means are equal.
Therefore,
Null Hypothesis:
H0 - There is no difference between classification algorithms A and B. The expected accuracies of classification algorithms A and B are the same.
$$H_0: µ_d = 0$$
Step 2 –
Find out Differences by subtracting the accuracies of algorithm B from the accuracies of algorithm A.
A |
B |
Difference (A - B) |
73 |
93 |
-20 |
81 |
83 |
-2 |
82 |
83 |
-1 |
72 |
90 |
-18 |
85 |
89 |
-4 |
86 |
78 |
8 |
87 |
93 |
-6 |
89 |
90 |
-1 |
93 |
95 |
-2 |
81 |
90 |
-9 |
Step 3 –
Find out the square of all the differences generated in step 1.
A |
B |
Difference (A - B) |
Square of the Difference |
73 |
93 |
-20 |
400 |
81 |
83 |
-2 |
4 |
82 |
83 |
-1 |
1 |
72 |
90 |
-18 |
324 |
85 |
89 |
-4 |
16 |
86 |
78 |
8 |
64 |
87 |
93 |
-6 |
36 |
89 |
90 |
-1 |
1 |
93 |
95 |
-2 |
4 |
81 |
90 |
-9 |
81 |
Step 4 –
Find out the sum of differences and the sum of the square of differences.
Therefore,
Sum of Differences = ∑ D = - 55
Sum of Square of Differences = ∑ D2 = 931
Step 5 –
Calculate the value of t using the formula of t-test.
Where,
Sample Size = N = 10
Sum of Differences ∑ D = - 55
Sum of Square of the Differences ∑ D2 = 931
Therefore,
Now, we get the value of t = - 2.081
Step 6 –
Find out the Degree of Freedom (DF) = Sample Size (N) - 1
Therefore,
Degree of Freedom (DF) = Sample Size (N) - 1 = 10 - 1 = 9
Step 7 –
Find out the p-value in the t-table, using the Degrees of Freedom (DF) calculated in step 6.
Also the value of the Alpha Level is given as 0.05 (5%).
Therefore,
p-value = 2.262 .....(for DF = 9 and Alpha level = 0.05 using t-table)
Step 8 –
Compare the p-value = 2.262 with calculated t-value = - 2.081
The calculated t-value is less than the t-table value at an Alpha Level of 0.05 (5%)
The p-value is greater than the Alpha Level: p > 0.05.
Hence, We can ACCEPT the Null Hypothesis (H0) that there is no difference between the classification Algorithm A and B.
That means Classification Algorithms A and B are Extremely Similar.