I am to conduct an independent samples t-test by hand for two groups of data points:
group 1: 15, 15, 19, 21, 25, 25, 28, 19, 19
group 2: 13, 20, 13, 12, 16, 14, 3, 18
I have the correct answer, which is around t= 3.018
I feel like I have tried everything and still am not getting this answer when I do it by hand.
To perform an independent samples t-test by hand, follow these steps:
Step 1: Calculate the mean for each group.
For group 1:
mean1 = (15 + 15 + 19 + 21 + 25 + 25 + 28 + 19 + 19) / 9 = 21.11
For group 2:
mean2 = (13 + 20 + 13 + 12 + 16 + 14 + 3 + 18) / 8 = 14.625
Step 2: Calculate the variance for each group.
For group 1:
variance1 = Σ((x1 - mean1)^2) / (n1 - 1)
= ( (15 - 21.11)^2 + (15 - 21.11)^2 + (19 - 21.11)^2 + (21 - 21.11)^2 + (25 - 21.11)^2 + (25 - 21.11)^2 + (28 - 21.11)^2 + (19 - 21.11)^2 + (19 - 21.11)^2) / (9 - 1)
= 49.67
For group 2:
variance2 = Σ((x2 - mean2)^2) / (n2 - 1)
= ((13 - 14.625)^2 + (20 - 14.625)^2 + (13 - 14.625)^2 + (12 - 14.625)^2 + (16 - 14.625)^2 + (14 - 14.625)^2 + (3 - 14.625)^2 + (18 - 14.625)^2) / (8 - 1)
= 24.82
Step 3: Calculate the pooled variance.
pooled variance = ((n1 - 1) * variance1 + (n2 - 1) * variance2) / (n1 + n2 - 2)
= ((9 - 1) * 49.67 + (8 - 1) * 24.82) / (9 + 8 - 2)
= 38.53
Step 4: Calculate the t-value.
t = (mean1 - mean2) / sqrt(pooled variance * (1/n1 + 1/n2))
= (21.11 - 14.625) / sqrt(38.53 * (1/9 + 1/8))
= 6.485 / sqrt(38.53 * (0.111 + 0.125))
= 6.485 / sqrt(38.53 * 0.236)
= 6.485 / sqrt(9.09)
= 6.485 / 3.018 (approximately)
The calculated t-value is 2.151 (approximately), not 3.018 as you mentioned. Please double-check your answer or calculations to ensure accuracy.