Midterm #2

Question 1

T statistic

Answer 1

used to test hypothesis about unknown popn mean (µ) when **value of σ is unknown **

Question 2

Formula of:

• T statistic vs. Z statistic

Answer 2

T statistics formula is identical to z-score formula except estimated standard error is used instead of **standard error (σ/√n) **

Question 3

Estimated Standard Error

Answer 3

S_x-bar = s/√n

• sample standard deviation used instead

Question 4

**Degrees of freedom **

Answer 4

# of scores in sample that are **independant and free to vary **

Question 5

The **larger **the value of df….

Answer 5

the more closely t distribution _approximates _normal distribution

Question 6

t distribution

Answer 6

complete set of values computed for every possible random sample for specific sample size (n) or **specific degrees of freedom (df) **

• approximates shape of normal distribution

Question 7

One-sample T-test

• formula
• degrees of freedom

Answer 7

df = n - 1

Question 8

Two-sample Independant T-test

Answer 8

most popular in psychology until early 1960s

• **2-group design: ***treatment *vs. control
• extension of one-sample t-test

Question 9

Two-sample Independant T-Test

• formula

Answer 9

t = ( x̄₁ - x̄₂) / √ [(SS₁ + SS₂)/(n₁+ n₂ - 2)] (1/n₁ + 1/n₂)

Question 10

**Two-sample independant t-test **

• **(3) **assumptions

Answer 10

1) **normality **
2) **homogeneity of variance **
3) independance

Question 11

Two-sample Independant T-test

• degrees of freedom
• null & alternative hypothesis

Answer 11

df = n₁ + n₂ - 2

H₀ : μ₁= μ₂

H_I : μ₁ ≠ μ₂

Question 12

1) normality

Answer 12

difference between popns are normally distributed

Question 13

2) homogeneity of variance

Answer 13

both samples are drawn from populations whose **variances are the same **

σ₁²=σ₂²

Question 14

3) independance

Answer 14

scores from the 2 populations are independant or **unrelated **

Question 15

**Two-sample Dependant T-test **

• used in what circumstances?

Answer 15

used for Matching or **Repeated Measures **(Within-subjects) Designs

Question 16

Matching

Answer 16

• popular strategy in education & developmental psychology
• random assignment = impossible
• ​address confounds in research

Question 17

Repeated Measures/Within-Subjects Design

Answer 17

popular in cognitive psychology & learning

• creates **carry-over effects **
• reduces error variance or noise
• statistically complicated

Question 18

Two-sample Dependant T-test

• **(1) assumption **

Answer 18

normality

Question 19

Two-sample **Dependant **T-test

• degrees of freedom
• null & alternative hypothesis

Answer 19

df = n_pairs - 1

H_o: μ_D = 0

H₁: μ_D ≠ 0

Question 20

Two-sample **Dependant **T-test

Sample of D scores (difference in scores):

• mean
• sum of squares (SS)
• variance
• standard deviation
• standard error

Answer 20

• **mean: **d-bar = ΣD/n_pairs
• **sum of squares (SS): **SS_d = ΣD² - (ΣD)²/n
• **variance: ** S_d² = SS_d/(n-1)
• **standard deviation: **S_d = √S_d²
• **standard error: **S_d-bar = S_d/√n `

Question 21

If you have 3+ levels of a treatment, multiple t-tests would?

How do we **keep **α = 0.05?

Answer 21

inflate **familywise **Type 1 error beyond 5%

use ANOVA

Question 22

**Analysis of Variance (ANOVA) **

Answer 22

hypothesis-testing procedure used to evaluate mean differences (usually 3+ levels) between 2+ treatments

Question 23

**One-Way ANOVA **

Answer 23

technique used for **3+ **treatment levels/samples

• n must be equal for each
• employs Fisher (F) distribution
  
  • ​negativeF values = impossible
  • **positively **skewed
• considered an **Omnibus test **

Question 24

One-Way ANOVA

• ideal case for rejecting H_o?

Answer 24

**large **variability between treatments but **small **variability within each treatment

Question 25

**One-Way ANOVA **

• what values needed?

Answer 25

SS_total

SS_within

SS_between

MS (mean square)

F_obtained

F_critical

df

Question 26

One-Way ANOVA

• calculating SS
• calculating MS

Answer 26

SS_t = Σx² - (Σx)²/N

SS_w = Σx² - (Σx_A)²/n

SS_b = SS_t = SS_w

MS = SS/df

Question 27

One-Way ANOVA

• degrees of freedom
• F values

Answer 27

(a = # of treatments)

**df_b **= a - 1

df_w = a (n-1) = N - a

df_t = df_w + df_b = N - 1

F_{<strong>obtained</strong>}= MS_b/MS_w

F_critical

• df_numerator= df_b
• df_denominator= df_w

Question 28

If 3+ treatments for one-way ANOVA…

Answer 28

**post-hoc **test **required to determine source of difference

Question 29

**Post-Hoc Test **for ONE-WAY ANOVA

Answer 29

Tukey Honest Significant Difference (HSD)

Question 30

Tukey Honest Significant Difference (HSD)

Answer 30

**Tukey HSD = q √ (MS_w/n) **

q = studentized range statistic (Table B.5)

df for error term = df_w

k = # of treatments