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TESTING THE TEST 2
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X Scores out of 28 |
x = individual deviation from MEAN |
X squared |
x squared |
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3 |
x =10.667 - 3 |
x = 7.67 |
9 |
58.78 |
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5 |
x =10.667 - 5 |
x = 5.67 |
25 |
32.11 |
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5 |
x =10.667 - 5 |
x = 5.67 |
25 |
32.11 |
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5 |
x =10.667 - 5 |
x = 5.67 |
25 |
32.11 |
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6 |
x =10.667 - 6 |
x = 4.67 |
36 |
21.78 |
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6 |
x =10.667 - 6 |
x = 4.67 |
36 |
21.78 |
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6 |
x =10.667 - 6 |
x = 4.67 |
36 |
21.78 |
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7 |
x =10.667 - 7 |
x = 3.67 |
49 |
13.45 |
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7 |
x =10.667 - 7 |
x = 3.67 |
49 |
13.45 |
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8 |
x =10.667 - 8 |
x = 2.67 |
64 |
7.11 |
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9 |
x =10.667 - 9 |
x = 1.67 |
81 |
2.78 |
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10 |
x =10.667 - 10 |
x = 0.67 |
100 |
0.44 |
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11 |
x =10.667 - 11 |
x = - 0.33 |
121 |
0.11 |
|
11 |
x =10.667 - 11 |
x = - 0.33 |
121 |
0.11 |
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12 |
x =10.667 - 12 |
x = - 1.33 |
144 |
1.78 |
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12 |
x =10.667 - 12 |
x = -1.33 |
144 |
1.78 |
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13 |
x =10.667 - 13 |
x = -2.33 |
169 |
5.44 |
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14 |
x =10.667 - 14 |
x = -3.33 |
196 |
11.11 |
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15 |
x =10.667 - 15 |
x = -4.33 |
225 |
18.77 |
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16 |
x =10.667 - 16 |
x = -5 .33 |
256 |
28.44 |
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16 |
x =10.667 - 16 |
x = -5.33 |
256 |
28.44 |
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17 |
x =10.667 - 17 |
x = -6.33 |
289 |
40.11 |
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20 |
x =10.667 - 20 |
x = -9.33 |
400 |
87.10 |
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22 |
x =10.667 - 22 |
x = -11.33 |
484 |
128.44 |
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S X = 256 |
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609.31 |
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The Mean is the sum total of the students' scores divides by N (the number of students or scripts) S X / 24 = 10.667 |
Standard Deviation: (s) = the square root of [ S x ² the sum of the individual deviation from the Mean squared divided by (Number of scripts - 1)] |
S x squared = 609.31 / 23 = 26.49. The square Root of 26.49 is 5.147 |
S x ² = 609.31 s = 5.147 |
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Data needed to check the MEAN, RELIABILITY & STANDARD DEVIATION
N = 24 Swedish Pensioners tested together or the number of scripts sampled.
n = the number of items in the test = 28
X = raw scores 3,5,5,5,6,6,6,7,7,8,9,10,11, 11, 12, 12, 13, 14, 15, 16, 16, 17, 20, 22.
X² is the student's raw score multiplied by itself e.g. 3 x 3 = 9
S X the sum of all the raw scores = 256
M = the MEAN (a measure of central tendency): M = S X / N i.e. 256/24=10.667.
x = the individual deviation from the MEAN = (Mean minus each student's raw score)
x² =individual differentiation from the mean multiplied by itself in each case
S x² = the sum of the above (individual differentiations from the mean²) = 609.31
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S (standard deviation) |
= |
The square root of [ S x² divided by (N-1)] |
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|
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The square root of [ 609. 31 / 24-1] = The square root of 26.49 = 5.147 |
s (standard deviation) = 5.147
To calculate the reliability of a test, use the Kuder-Richardson formula:
r (reliability) =1 minus [M the Mean multiplied by (n the number of items minus the Mean) divided by (n the number of items multiplied by s² the standard deviation squared) ].
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R (reliability) |
= |
1 minus [10.667 multiplied by (28 - 10.667) divided by (28 x 26.49)] = |
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|
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1 minus 0.249 = 0.751 |
r (reliability) = 0.751
I administered the same test on a younger sample of 52 students of mixed nationality with the following results:
N = 52 (number of students or scripts)
n = 28 (number of items in the test)
M = S X / N (606/52) = 11.654 ( sum all the scores and divide by the no. of scripts)
s (standard deviation) = 5.5338
r (reliability) = 0.778
Note: the reliability based on my larger sample of younger students of mixed nationality was somewhat higher than the reliability based on my smaller sample of elderly Swedish learners.
A scientific pocket calculator or computer statistics software will allow you to calculate standard deviations and reliability a lot more quickly.
Before celebrating the fact that the reliability of the test is 78 % (i.e. greater than 75 %), the test's validity also needs to be investigated.
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