研究法簡介

何明洲中山醫學大學心理系

Single Factor – Two Levels

Single Factor – Two Levels

• Independent groups design: use random assignment– IV, manipulated– Between-subject

• Matched groups design: use matching procedure– IV, manipulated– Between-subject

Single Factor – Two Levels

• Nonequivalent groups design– IV, subject– Still need to match participants– Between-subject

• Repeated-measures design– IV, manipulated– Within-subject

Analyzing single factor and two-level design

• t test for independent groups and dependent groups

EXAMPLE: THE t AND F TESTS

t value is a ratio of two aspects of the data, the difference between the group means and the variability within groups

t = group difference within group variability

Multilevel designs

如果只有 2 levels (e.g., no reward and $4) ，資訊量太少，可能誤判為 linear

Add more levels forreplication and extension

LINEAR VERSUS POSITIVE MONOTONIC FUNCTIONS

Analyzing Single-Factor, >2 levels

F Test (analysis of variance, ANOVA 變異數分析 ) ≥ 2 conditions (or groups)When 2 conditions, F = t2

When more than 2 conditions, why not use t test?

EXAMPLE: F TEST

用 t test 作多重比較 , 至少出現一個 type I error 機率1 – (1 – alpha)c (C: # of paired comparisons)

• 噪音程度 ( 無 , 低 , 中 , 高 ) 對記憶的影響– C = 4!/(2!2!) = 6– 1-(1-.05)6 = .26 (=26%!!!)

• F test 同時比較多組 , alpha 控制在 .05H0: μ1 = μ2 = μ3 = μ4 …

EXAMPLE: F TEST

Total variance = systematic variance + error variance

Systematic variance: deviation of group means from the grand mean between-group varianceGrand mean: 全部皆平均 , 假設無任何因 IV 所引發的差異

Error variance: deviation of individual scores in each group from their respective group means within-group variance

EXAMPLE: F TEST

Total variance = systematic variance + error variance

變異的程度反應整個實驗情境和總人數所帶有的變異程度

實驗情境越多 , 總人數越多 , 則變異程度大不能只考慮變異程度 , 須考慮平均每個實驗情境和人數 , 所帶有的變異程度

F = (systematic variance/dfsystematic) / (error variance/dferror)

Factorial Designs

> 1 IVs

INCREASING THE NUMBER OF INDEPENDENT VARIABLES:

FACTORIAL DESIGNS> 1 IVs Factorial Designs 多因子設計 : Designs wi

th more than one independent variable (or factor)噪音（高 vs. 低）影響雙字詞記憶噪音（高 vs. 低） x 詞頻（高 vs. 低）

Presentation rate

2-sec 4-sec

Type of training

Imagery

Rote

Factorial matrix

Factor B

B1 B2

Factor A A1 A1B1 A1B2

A2 A2B1 A2B2

Factorial matrix

INCREASING THE NUMBER OF INDEPENDENT VARIABLES:

FACTORIAL DESIGNSSimplest Factorial Design

2 x 3x 4 (two-by-two) factorial designHas two independent variables, each IV has 2 levels4 conditions

Number of levels of first IV x

Number of levels of second IV x

Number of levels of third IV…

INCREASING THE NUMBER OF INDEPENDENT VARIABLES:

FACTORIAL DESIGNSInterpretation of Factorial Designs (A x B)

Main effects of an independent variable ： effect of A factor ONLY (regardless of B factor, average out B factor)

Interaction between the independent variables (how does effect of A factor vary with B factor?) ，條件機率A (A1, A2) x B (B1, B2)

使用圖表讓讀者瞭解

詞頻

高 低

噪音程度

高 A1B1 A1B2 A1

低 A2B1 A2B2 A2

B1 B2

詞頻

高 低

噪音程度高 A B

低 C D

A - B = C – D 詞頻的效果是否隨者噪音程度改變

A – C = B – D 噪音效果是否隨者詞頻程度改變

INCREASING THE NUMBER OF INDEPENDENT VARIABLES:

FACTORIAL DESIGNS詞頻

高 低

噪音程度高 10 5

低 10 5

7.5

7.5

10 5

Interaction NSMain effect of 噪音 NSMain effect of 難度 *

INCREASING THE NUMBER OF INDEPENDENT VARIABLES:

FACTORIAL DESIGNS詞頻

高 低

噪音程度高 5 10

低 10 5

7.5

7.5

7.5 7.5

Interaction *Two main effects NS

INCREASING THE NUMBER OF INDEPENDENT VARIABLES:

FACTORIAL DESIGNSType of question

misleading unbiased

Knowledge

naive 18 13

knowledgeable 41 13

15.5

27

29.5 13

Interaction *Two main effects *

INCREASING THE NUMBER OF INDEPENDENT VARIABLES:

FACTORIAL DESIGNS

INCREASING THE NUMBER OF INDEPENDENT VARIABLES:

FACTORIAL DESIGNS

• 2 x 3 x 4 factorial design– How many IVs?– How many levels of each IV– How many total conditions– How many DVs?

Varieties of Factorial Design

• Mixed factorial design: 有 between and within subject variables, 沒有 subject variable

• P x E factorial designs: 有 subject variable和 manipulated variable （均為 between)

• Mixed P x E factorial : 有 subject variable和 manipulated variable （有 between 和 within)

INCREASING THE NUMBER OF INDEPENDENT VARIABLES:

FACTORIAL DESIGNS

• Interactions and Simple Main Effects( 單純主要效果 )

• 當有 interaction 時，必作的統計分析• Simple main effect: examine mean differences at e

ach level of the independent variable• 依研究目的決定要作哪些 simple main effect

INCREASING THE NUMBER OF INDEPENDENT VARIABLES:

FACTORIAL DESIGNS Interactions and Simple Main Effects

Simple main effect of B1: A1|B1 vs. A2|B1Simple main effect of A1: B1|A1 vs. B2|A1

Anxiety level

Low Moderate High

Task

Difficulty

Easy 4 7 10

Hard 7 4 1

(Easy vs. Hard)|Low

(L vs.M vs.H)|Easy

INCREASING THE NUMBER OF VARIABLES: FACTORIAL

DESIGNS

INCREASING THE NUMBER OF INDEPENDENT VARIABLES:

FACTORIAL DESIGNSIncreasing the Number of Independent Vari

ables in a Factorial Design2 x 2 x 2 噪音高低 x 作業難易 x 性別

男 女

作業難易 作業難易

噪音高低

噪音高低

噪音高低 x 作業難易 x 性別

3-way interaction 2-way interaction ( 男生中，噪音高低 x 作業難易 ) simple simple main effect

Presenting data

Text

Table

Figure

Discrete and continuous variable

Continuous variable

圖表• 運用之法，存乎一心，沒有絕對對錯，重要的是「好理解」且「點出重點」

點出文章重點

48

48.5

49

49.5

50

50.5

51

51.5

Cola A Cola B

0

50

100

Cola A Cola B

圖表尺度的影響

1.注意尺度2.加上信賴區間

48

48.5

49

49.5

50

50.5

51

51.5

Cola A Cola B

0

50

100

Cola A Cola B