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# The set of contrasts

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a. Before the experiment findings are processed, the set of contrasts that completely account for all of the variation between grades can be constructed as a planned set of comparisons. Otherwise, it can be produced as an unplanned series of comparisons based on pre-existing experiment data.

The following set of contrasts is a planned one because there are four groups in the experiment. Furthermore, the crucial question for researchers is if the mean of group eight differs from the mean of any other grade. As a result, the hypothesis permitting testing of the key expectation is complex:

H01: (m2+m4+m6)/3 - m8 = 0.

In addition there are hypothesis investigating the difference between classes within "before 12-13 age".H02: m2 – m4 = 0; H03: m2 – m6 = 0; H04: m4 – m6 = 0.

b. The sample value of the complex contrast assessing the main expectation of the researcher in this design is 20, as all grades are included in comparison.

c. The error rate basis for analysis performing could be 0.05; however, it could be adjusted in the case of non-orthogonal set of contrasts to avoid undervaluation of statistical difference and inadequate results. For adjustment could be used Bonferroni procedure.

d. An alternative way to analyze the data may be post-hoc set of hypothesis that takes in account means the researcher got in the experiment. Next, I provide an orthogonal set of contrasts allowing comparing all four grades’ means, where contrast three (colored) tests the main expectation. It will provide the most reliable difference as mean for grade 2 is the lowest, therefore the difference is the most clear.

M2

M4

M6

M8

1

-1

0

0

0

0

1

-1

1

0

0

-1

0

1

-1

0

e. LMATRIX for the (a) variant of hypothesis set:

/LMATRIX = “first and second and third vs. forth” additive 1/3 1/3 1/3 -1

/LMATRIX = “first vs. second” additive 1 -1 0 0

/LMATRIX = ‘first vs. third” additive 1 0 -1 0

/LMATRIX = “second vs. third” additive 0 1 -1 0

April 06, 2023
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Expertise Hypothesis
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