PSYC 515 - Research Methods and Statistics in Psychology II

PSYC 515 WORKSHEET: Factorial designs (Week 3)

Review of Material: How to conduct and present factorial designs using SPSS (Week 3)

Information from: Week 3 presentations and assigned readings in the e-book

Additional practice: Jackson ebook ch. 12 –Chapter 12 Exercise Q#11 and Chapter 12 Study Guide – scroll down to “Self-test problems” Q#1

Note: this is an OPTIONAL worksheet to practice applying some of this week’s key concepts. Please make sure you complete all assigned readings and watch this week’s presentations before attempting the worksheet! Try to complete it on your own, then check your answers with the answer key details (at the end of the document).

**NOTE** because these are rather lengthy problems, the answers are provided below but are demonstrated step-by-step in Watch items for the corresponding module: week. Please attempt these problems on your own before watching the videos, or at least read the scenario before watching the videos!

Practice 1 – 3 x 3 (Two-way) ANOVA

A researcher is attempting to determine the effects of instructional method on learning the letters of the alphabet in young children. She found 15 children in each age group (2, 3, and 4-year-olds) and randomly assigned them to a teaching strategy – learning the alphabet by recitation, identification, or by tracing. The number of letters correctly identified for each child is recorded below.

	Recite	Identify	Trace
2-year-olds	5	2	1
	7	5	2
	6	6	0
	7	5	1
	2	4	2
3-year-olds	20	5	11
	23	8	7
	22	10	6
	18	9	7
	21	6	10
4-year-olds	25	26	17
	26	18	16
	26	25	15
	19	24	19
	20	17	14

Practice 2 – 2 x 2 (or Two-way) Repeated Measures ANOVA

A researcher is attempting to determine the effects of practice and environment on a timed task. Participants in an experiment are given a computerized search task. They search a computer screen of various characters and attempt to find a particular character on each trial. When they find the designated character, they press a button to stop a timer. Their reaction time (in seconds) on each trial is recorded. Subjects each participate in 4 sessions – they practice for 2 or 4 hours in both quiet and noisy environments. The reaction time data for the 10 subjects who underwent all conditions appear below.

Quiet		Noisy
2 hours	4 hours		2 hours	4 hours
12	11		10	8
13	12		10	8
12	13		10	10
11	12		8	10
11	11		7	5
10	8		5	6
10	8		7	8
10	10		6	6
12	13		6	6
12	13		7	8

Practice 3 – 2 x 3 Mixed Design ANOVA

A researcher is attempting to determine the effects of practice and gender on a timed task. Participants in an experiment are given a computerized search task. They search a computer screen of various characters and attempt to find a particular character on each trial. When they find the designated character, they press a button to stop a timer. Their reaction time (in milliseconds) on each trial is recorded. Subjects practice for 2, 4, or 6 hours across all three sessions (all participants complete all three sessions). The reaction time data for the 10 subjects (5 women / 5 men) appear here.

	Women	Men
2 Hours	120	115
	135	123
	122	134
	113	128
	114	117
4 Hours	109	82
	107	86
	105	107
	89	108
	73	95
6 Hours	75	53
	57	65
	78	87
	62	69
	74	85

ANSWER KEY for Factorial designs (Week 3)

Because these are rather lengthy, videos were created to walk you step-by-step through the process. Please watch the relevant videos to check your work (you can skip to the end to see if your results match mine if you think you solved them correctly!) Or, just watch the videos over the types you most struggle with! Please note you need to include the effect size for each main effect and interaction – although it is in the output in the videos, I did not include it in the video write-ups. They are shown here, demonstrated in this week’s SPSS presentation, and are included in the Helpful Hints document.

Practice 1 – 3 x 3 (Two-way) ANOVA shows how to run a factorial design when both factors are BS, and when you need to interpret post hoc analyses, including a significant interaction that requires you to “split” your data file to run additional post hoc analyses. How to create a line graph for a significant interaction is shown.

Independent variables and levels for each:

· BS factor: AGE (three levels – 2, 3, and 4 y/o)

· BS factor: STRATEGY (recite, identify, trace)

Dependent variable: number of correctly identified letters of the alphabet (SCALE scale of measurement)

Final write-up including the effect sizes:

Using a 3 x 3 ANOVA with the between subjects factor of age (2, 3, 4 y/o) and strategy (recite, identify, trace), on the number of correctly identified letters in the alphabet revealed a significant main effect of age F(2, 36) = 180.083, p<.001, Ƞp2 = 0.909, a significant main effect of strategy F(2, 36) = 41.312, p<.001, Ƞp2 = 0.697, and a significant Age x Strategy interaction F(4, 36) = 10.983, p<.001, Ƞp2 = 0.550. Post hoc analyses were conducted using one-way ANOVAs for each age group. For the 2 y/o group, both recite and identify strategies were more effective than trace (p = .003 and p = .018, respectively), although there was no difference between recite and identify strategies (p = .583). For the 3 y/o group, the recite strategy was more effective than both identify and trace strategies (p < .001) although there was no difference between the identify and trace strategies (p = .890). In the 4 y/o group, both recite (p = .015) and identify (p = .042) were more effective strategies compared to tracing, although there was no difference between recite and identify strategies (p = .837).

** if you do not see where/ how to get these results, please view “Watch: 3 x 3 BS ANOVA” in which I show you how (must have internet access): Caveat to the video: Please note you need to include the effect size for each main effect and interaction – although it is in the output in the videos I did not include it in the write-ups while I was making them. They are shown here AND are demonstrated in this week’s SPSS presentation.

Practice 2 – 2 x 2 (or Two-way) Repeated Measures ANOVA shows how to run a factorial design when both factors are WS, and you need to combine two columns within SPSS to be able to interpret a significant ME that is WS. The appropriate graph for a WS significant ME when you have two WS factors is also shown.

Independent variables and levels for each:

· WS factor: HOURS (two levels – 2 and 4 hours)

· WS factor: ENVIRONMENT (two levels – quiet and noisy)

Dependent variable: reaction time (in seconds) (SCALE scale of measurement)

Final write-up including the effect sizes:

A 2 x 2 Repeated Measures ANOVA was conducted for number of hours practiced (2 and 4 hours) and environment (quiet and noisy) on reaction time in a computerized search task. There was no main effect of hours F(1, 9) = 0.213, p = .656, Ƞp2 =.023 or Hour x Environment interaction F(1, 9) = 0.033, p = .859, Ƞp2 =.004. The main effect of environment was significant F(1, 9) = 58.418, p < .001, Ƞp2 =.867. As shown in Figure 1, participants responded slower in quiet environments.

(note no post hoc needed since df = 1)

** if you do not see where/ how to get these results, please view “Watch: 2 x 2 WS ANOVA” in which I show you how (must have internet access): Caveat to the video: Please note you need to include the effect size for each main effect and interaction – although it is in the output in the videos I did not include it in the write-ups while I was making them. They are shown here AND are demonstrated in this week’s SPSS presentation.

Practice 3 – 2 x 3 Mixed Design ANOVA shows how to run a factorial design analysis when one factor is BS and the other is WS. The appropriate graph for a significant main effect of a WS factor (when there is only one WS factor) is shown.

Independent variables and levels for each:

· BS factor: GENDER (two levels – male and female)

· WS factor: TIME (three levels – 2, 4, or 6 hours of practice)

Dependent variable: reaction time (in ms) (SCALE scale of measurement)

Final write-up including the effect sizes:

A 2 x 3 Mixed Design ANOVA was conducted to determine if gender (male or female) and number of hours practiced (2, 4, or 6 hours) affect reaction time in a computerized search task. There was no main effect of gender F(1, 8) = 0.064, p = .807, Ƞp2 =.008 or Gender x Hour interaction F(2, 16) = 0.126, p = .882, Ƞp2 =.016. The main effect of hours practiced was F(2, 16) = 77.854, p < .001, Ƞp2 =.907. As shown in Figure 1, participants reacted faster with more practice (pairwise comparisons were all significant, p < .001).

** if you do not see where/ how to get these results please view “Watch: 2 x 3 Mixed Design ANOVA” in which I show you how (must have internet access): Caveat to the video: Please note you need to include the effect size for each main effect and interaction – although it is in the output in the videos I did not include it in the write-ups while I was making them. They are shown here AND are demonstrated in this week’s SPSS presentation.

NOTE: There are still opportunities for extra practice! Try completing Jackson ebook ch. 12 –Chapter 12 Exercise Q#11 and Chapter 12 Study Guide – scroll down to “Self-test problems” Q#1