8, 9, 14, 6, 3, 13, 5, 4 Calculate the variance of these numbers using one of the following formulas: (x)2 s2 = (x2) - n s2 = x – x)2 n -1 n -1 X X2 (X-X`)2 8 64 0 9 81 1 14 196 36 6 36 4 3 9 25 13 169 25 5 25 9 6 36 4 SUM 64 616 104 X-bar =1/n ∑▒xi=64/8=8 s2 = (616-〖64〗^2/8)/(8-1) = 14.8571 Or using the second formula s2 = 1/(8-1)*104=14.8571 * highlighted portions are the equations for sum of squares Suppose we have two distinct groups. Group A includes the numbers 8, 9, 14, 6 and group B includes 3, 13, 5, 4. perform a t-test on these two groups and find a t-score using the space below. (8 points) H0:µ1=µ2 Ha:µ1≠µ2 X1 X2 (X1-X~1) 2 (X2-X~2) 2 8 3 1.5625 10.5625 9 13 0.0625 45.5625 14 5 22.5625 1.5625 6 4 10.5625 5.0625 SUM 37 25 SS1=34.75 SS2=62.75 ^^^Can you explain the last two sections of this graph how did you do this step by step.Highligheted in blue Where SS is equal to the sum of squares (calculated using the equation above). X`1=37/4=9.25 X`2=25/4=6.25 t=(9.25-6.25)/√((34.75+62.75)/(4+4-2)*(1/4+1/4))=1.05247 Degrees of freedom=n1+n2-2=6 Critical value at 5% significant level=2.45 Since tests statistics is less than critical value (1.05247<2.447) the test is not significant and Ho is not rejected We conclude that there is no significant difference between the mean of the two groups It just so happens that this t-test is not significant; however you are still curious as to the amount of unique variance that this t-test explains. Calculate eta2 for your t-score (NOTE: even if you got the above question wrong, you can still get this one right by demonstrating the way that eta2 is calculated (7 points) Eta squared = t^2/(t^2+ (n1+n2-2) ) =〖1.05247〗^2/(〖1.05247〗^2+(4+4-2)) =0.155844 According to Cohen (1988) this is large effect

8, 9, 14, 6, 3, 13, 5, 4

Calculate the variance of these numbers using one of the following formulas:

(Sx)²

s² = S(x²) – n s² = S(x – x)²

n -1 n -1

X-bar =

s² = = 14.8571

Or using the second formula

s² = 14.8571

* highlighted portions are the equations for sum of squares

Suppose we have two distinct groups. Group A includes the numbers 8, 9, 14, 6 and group B includes 3, 13, 5, 4. perform a t-test on these two groups and find a t-score using the space below. (8 points)

H0:µ1=µ2

Ha:µ1≠µ2

^^^Can you explain the last two sections of this graph how did you do this step by step.Highligheted in blue

Where SS is equal to the sum of squares (calculated using the equation above).

X`₁=37/4=9.25

X`₂=25/4=6.25

t==1.05247

Degrees of freedom=n1+n2-2=6

Critical value at 5% significant level=2.45

Since tests statistics is less than critical value (1.05247<2.447) the test is not significant and Ho is not rejected

We conclude that there is no significant difference between the mean of the two groups

It just so happens that this t-test is not significant; however you are still curious as to the amount of unique variance that this t-test explains. Calculate eta² for your t-score (NOTE: even if you got the above question wrong, you can still get this one right by demonstrating the way that eta² is calculated (7 points)

Eta squared =

= =0.155844

According to Cohen (1988) this is large effect