Statistics

Question 1

When do we use z instead of t?

Answer 1

If we know population SD

Question 2

What is the basic idea of t-statistic?

Answer 2

(M - μ) / S_M

S_M : (Estimated) Standard Error from our sample

Question 3

How does the t-distribution vary as a function of df?

Answer 3

Lower df

• Broader
• More extreme values are more probable

Higher df

• More normal
• More extreme values are less probable

Question 4

What are the pros and cons of the One-Sample Design?

Answer 4

Pros:

• Used if we know population values

Cons:

• Won’t known population values
• Cannot compare 2 groups/ change over time

Question 5

What are the pros and cons of the Between-groups/ independent-measures design?

Answer 5

2 groups, 2 different set of people.

Pros:

• Independent measurement
• No learning effects (due to repeated exposure)

Cons;

• Need large sample size to counter individual variability
• Cannot study over time

Question 6

What are the pros and cons of the Within-group design/ repeated-measures design?

Answer 6

2 groups, 1 same set of people.

Pros:

• Change over time
• No need to consider differences because they will affect both conditions equally
• Smaller sample size

Cons:

• Measures are not independent. Variance is different
• Learning Effects
  
  • Just be careful

Question 7

What are the t-tests quick formulas for:

(a) One-Sample
(b) Independent Samples
(c) Paired Samples

Answer 7

(a) One Sample

• t = Mean Diff / Estimated SE of Mean
  
  • Estimated SE of Mean: sample SD/root (n)

(b) Independent Samples

• t = Diff between group mean / Estimated SE of Mean
  
  • Have to consider variances of both groups (Pooled Variance = Average Variance)
  • Only applicable for equal sample size for the formula to be applied

(c) Paired-Samples

• t = Mean Difference / Estimated SE of Mean
  
  • Estimated SE of Mean: sample SD/root (n)

Question 8

For t_crit and t_empirical, Given alpha is at .05, what does it mean?

Answer 8

Empirical > Crit

• Reject H₀
• Unlike to occur due to chance, but there’s a 5% chance that we are wrong
  
  • i.e. Null is true and a rare event has happened, or the null is false

Crit > Empirical

• Fail to reject H₀

Question 9

What is pooled variance?

Answer 9

Consdering two variances (each group) when calculating the standard error of the mean (called SE of mean difference)

TLDR pooled variance is average of 2 sample variance

Question 10

When do we calculate effect sizes?

Answer 10

Calculating the effect size only makes sense when the t-test revealed a significant result

Question 11

What is cohen’s d?

Answer 11

Effect Size

• Independent of the sample size
• Mean difference divided by standard deviation
  
  • d = 0.2 small
  • d = 0.5 medium
  • d= 0.8 large

Question 12

What is r²?

Answer 12

Percentage of variation explained by the experimental manipulation/treatment

• Use t-statistic and df
• Not independent of sample size
  
  • r² ~ 0.01 small
  • r² ~ 0.09 medium
  • r² ~ 0.25 large

Question 13

t-test assumptions: why must normality and homogenity be met?

Answer 13

Normality:

• t-tests are robust to large samples

Homogenity (in independent):

• Mess up pooled variance