Imagine you are doing a Related-Samples t-test, and you are on Step Three of the hypothesis test

Imagine you are doing a Related-Samples t-test, and you are on Step Three of the hypothesis test. The sample of difference scores that you calculated is -2, -4, -3, +1. What is the correct t-obtained? NOTE: The answer options also show many numbers that you calculate as part of the WORK for getting the t-obtained. VERY IMPORTANT HINT: The SS of these difference scores is 14.00. Group of answer choices
Imagine you are doing a Related-Samples t-test, and you are on Step Three of the hypothesis test. The sample of difference scores that you calculated is -2, -4, -3, +1. What is the correct t-obtained?ÂÂ

NOTE: The answer options also show many numbers that you calculate as part of the WORK for getting the t-obtained.ÂÂ

VERY IMPORTANT HINT: The SS of these difference scores is 14.00.

Group of answer choices

1. MD (mean of D’s) = -1.17

SD (standard deviation of D’s) = 2.14

SMD (standard error) = 0.87

t-obt = -1.34

2. MD (mean of D’s) = -2.20

SD (standard deviation of D’s) = 3.35

SMD (standard error) = 1.50

t-obt = -1.47

3. MD (mean of D’s) = -1.67

SD (standard deviation of D’s) = 3.21

SMD (standard error) = 1.86

t-obt = -0.90

4. MD (mean of D’s) = -2.00

SD (standard deviation of D’s) = 2.16

SMD (standard error) = 1.08

t-obt = -1.85

The Correct Answer and Explanation is :

The correct answer is option 4.

Here’s how the calculations work:

1. Mean of the Difference Scores (MD):
   [
   MD = \frac{-2 + (-4) + (-3) + 1}{4} = \frac{-8}{4} = -2.00
   ]
   So, MD is -2.00.
2. Standard Deviation (SD):
   We are given the sum of squares (SS) for the difference scores, which is 14.00. To calculate the SD, we divide the SS by the degrees of freedom (which is (N-1) where (N) is the sample size) and then take the square root:
   [
   SD = \sqrt{\frac{SS}{N-1}} = \sqrt{\frac{14.00}{4-1}} = \sqrt{\frac{14.00}{3}} = 2.16
   ]
3. Standard Error of the Mean Difference (SMD):
   The standard error (SMD) is calculated by dividing the SD by the square root of the sample size:
   [
   SMD = \frac{SD}{\sqrt{N}} = \frac{2.16}{\sqrt{4}} = \frac{2.16}{2} = 1.08
   ]
4. t-obtained (t-obt):
   Finally, the t-statistic is calculated as:
   [
   t_{obt} = \frac{MD}{SMD} = \frac{-2.00}{1.08} \approx -1.85
   ]

Thus, the t-obtained is approximately -1.85, which corresponds to option 4.

Let me generate a visualization of this calculation process for clarity.

Here is the step-by-step visualization of the Related-Samples t-test calculation. It shows how we arrived at the mean of the differences, standard deviation, standard error, and the t-obtained value. Let me know if you need any further explanation!