Question

The following data were obtained from a two-factor independent-measures experiment with n = 5 participants in each treatment condition

                        AROUSAL

                                              LOW             MEDIUM           HIGH

DRUG

Control	M = 3	M = 6	M = 9
Cannibis	M = 3	M = 4	M = 3

DV = Number of errors

State the hypotheses for each of the three separate tests included in the two-factor ANOVA. 2) Draw a graph representing what means would be being compared for each hypothesis test 3) indicate what decision you would expect to be making for each null hypothesis 4) state what conclusion you would make for the IV and DV given that decision 5) Give an OVERALL conclusion about the IVs and DVs and finally 6) Indicate what you would do next.

Answer 1

1) The hypotheses are:

H₀ : levels of arousal does not have any significant effect on the treatment condition.

H₀ : drug levels does not have any significant effect on the treatment condition.

H₀ : Interaction of arousal and drug does not have any significant effect on the treatment condition.

2) Table of means: M_ij denotes mean of observations from (i,j)th cell.

DRUG	AROUSAL-L	AROUSAL-M	AROUSAL-H	Mean of observations from each Drug level
Control	M11=3	M12 =6	M13 =9	M10 =6
Cannibis	M21 =3	M22 =4	M23 =3	M20 = 3.33
Mean of observations from each AROUSAL state	M01 = 3	M02 = 5	M03 = 6	M= mean of all observations = 4.67

H₀ : levels of arousal does not have any significant effect on the treatment condition.

which is equivalent to H₀ : M₀₁ = M₀₂ = M

H₀ : drug levels does not have any significant effect on the treatment condition.

which is equivalent to H₀ : M₁₀ = M₂₀ = M

H₀ : Interaction of arousal and drug does not have any significant effect on the treatment condition.

which is equivalent to H₀ : M_ij = M where i and j both not equal to 0.

3) For H₀ : Interaction of arousal and drug does not have any significant effect on the treatment condition. we can expect that we will be failed to reject null hypothesis as in the problem it is mentioned that it's an independent measure experiment. In this test it null hypothesis is rejected, then it is not reasonable to check for the independent effect of factors.

We cannot say anything without testing for the independent factors.

As we don't know that value of the actual observations, we cannot find the total sum of squares or error sum of squares.

4) Here independent variables are AROUSAL and DRUG and dependent variable is error. So if both the independent variables are found to be significant in testing, then it can be said that each of them have separate significant effect on treatment conditions.

5) we can go for testing of independent effects of factors only when their interaction effect is found to be insignificant. Then testing of independent factor can conclude whether the factor has significant effect on treatment conditions or not.

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