Question

Research Scenario: You have been raising Bombina orientalis, or Oriental fire-bellied toads, and measured the frogs’ jumps in centimeters. Your latest study looks at males and females’ reactions to being raised in a room with another animal. You set up three terrariums, each with six male and six female frogs. Each terrarium is in a separate room. Let A1 = male frogs, A2 =female frogs, B1 = frogs raised in a room with a dog, B2 = frogs raised in a room with a cat, and B3 = frogs raised in a room with a parrot.

Data

	B1	B2	B3
A1	45	23	39
	42	30	27
	41	31	31
	48	23	27
	42	33	37
	43	36	24
A2	32	36	49
	29	43	48
	31	37	44
	33	25	43
	25	32	36
	34	40	44

1. Restate the research and null hypothesis for each variable (and don’t forget the interaction).

2. What are the degrees of freedom of the F distribution for each variable and the interaction?

3. What is the value of F for the two main effects?

4. Is there a significant main effect of roommate? Explain and support your position.

5. Is there a significant main effect of gender? Explain and support your position.

6. Is there a significant interaction between the sex of the frogs and the species of roommate? Explain and support your position.

Answer 1

1. Null hypotheses-

There would be no difference in frog's jump between male and female frogs.

There would be no difference in frog's jump among frogs raised in a room with a dog, frogs raised in a room with a cat, and frogs raised in a room with a parrot.

There would be no interactive effect of two variables on frog's jump.

• Research hypotheses-

There would be a significant difference in frog's jump between male and female frogs.

There would be a significant difference in frog's jump among frogs raised in a room with a dog, frogs raised in a room with a cat, and frogs raised in a room with a parrot.

There would be interactive effect of two variables on frog's jump

2.

df_A (B/W rows)= 1

df_B (B/W Column)= 2

df (Interaction)= 2

df (within group)= 30

3.

F- Value for-

Variable A- 1.77

Variable B- 10.4

4. There is a significant main effect of roommate at 0.01 level.

5. There is no significant main effect of gender.

6. There is no significant interaction between the sex of the frogs and the species of roommate.

Explanation-

X1	X2	X3	X4	X5	X6	X12	X22	X32	X42	X52	X62
45	23	39	32	36	49	2025	529	1521	1024	1296	2401
42	30	27	29	43	48	1764	900	729	841	1849	2304
41	31	31	31	37	44	1681	961	961	961	1369	1936
48	23	27	33	25	43	2304	529	729	1089	625	1849
42	33	37	25	32	36	1764	1089	1369	625	1024	1296
43	36	24	34	40	44	1849	1296	576	1156	1600	1936
∑ X1= 261	∑ X2=176	∑ X3= 185	∑ X4= 184	∑ X5=213	∑ X6= 264	∑ X12= 11387	∑ X22= 5304	∑ X32= 5885	∑ X42= 5696	∑ X52=7763	∑ X62= 11722

Here-

Grand sum of X or ∑ X= 1283

Grand sum of squares= 47757

n₁= 6, n₂=6, n₃=6, n₄=6, n₅=6, n₆=6

       N= 36

SS between amounts of first IV (Task difficulty)

SS between amounts of second IV (Arousal level)

df_A (B/W rows)= r-1

df_A (B/W rows)= 2-1

df_A (B/W rows)= 1

df_B (B/W Column)= k-1

df_B (B/W Column)= 3-1

df_B (B/W Column)= 2

df (Interaction)= (r-1) (k-1)

df (Interaction)= (2-1) (3-1)

df (Interaction)= 2

df (within group)= N-rk

df (within group)= 36-(2*3)

df (within group)= 36-6

df (within group)= 30

Source of variance	Sum of square	Df	Mean square = SS/df	f-ratio = Mean square A or B or A*B/ Mean square of within group	Level of significance
B/W A		1		1.77	NS
B/W B		2		10.4	0.01
Interaction A*B		2	88.6	3.71	NS
Within group	716.5	30	23.9