Question

A researcher is studying memory for different types of words under low, and high memory load. She uses concrete words (e.g., dog, boat) and abstract words (e.g. love, height) in a factorial design, with five participants in each cell. With part of the information in the summary table, please finish the table and conduct the analysis.

Source	SS	df	MS	F
Between	2000
Word Type	750
Memory Load			125
Load*Type
Within Treatment				------------
Total	3500		------------	------------

a. Test and draw conclusions about the main effect of memory load.

b. Test and draw conclusions about the main effect of word type.                                 

c. Test and draw conclusions about the memory load x word type interaction

Answer 1

Source	SS	df	MS	F
Between	2000	3	666.67	7.11
Word Type	750	1	750	8
Memory Load	125	1	125	1.33
Load*Type	1125	1	1125	12
Within Treatment	1500	16	93.75	------------
Total	3500	19	------------	------------

Number of levels for word type = a = 2

Number of levels for Memory Load = b = 2

Replications in each cell = r = 5

df word type = a - 1 = 2 - 1 = 1

df Memory Load = b - 1 = 2 - 1 = 1

df Load*Type = (a - 1) * (b - 1) = 1 * 1 = 1

df Between = df word type + df Memory Load + df Load*Type = 1 + 1 + 1 = 3

df Within Treatment = ab(r-1) = 2 * 2 * (5 - 1) = 16

df Total = abr - 1 = 2 * 2 * 5 - 1 = 19

MS found with below formula ,

MS = SS / df

SS Load*Type = SS Between - (SS word type + SS Memory Load) = 2000 - (750 + 125) = 1125

SS Within Treatment = SS Total - SS Between = 3500 - 2000 = 1500

F Between = MS Between / MS Within Treatment = 666.67 / 93.75 = 7.11

F word type = MS word type / MS Within Treatment = 750 / 93.75 = 8

F Memory Load = MS Memory Load / MS Within Treatment = 125 / 93.75 = 1.33

F Load*Type = MS Load*Type / MS Within Treatment = 1125 / 93.75 = 12

Critical value of F at 0.05 significance level and df = 1, 16 is 4.49

a.

Since the observed F (1,33) is less than the critical value, we fail to reject the null hypothesis H0 and conclude that there is no significant main effect of memory load.

b.

Since the observed F (8) is greater than the critical value, we reject the null hypothesis H0 and conclude that there is significant main effect of word type.

c.

Since the observed F (12) is greater than the critical value, we reject the null hypothesis H0 and conclude that there is significant interaction effect of memory load and word type.