W2 - Stats (Short) Flashcards
When do we use z instead of t
If we know population SD
t-statistic: Basic idea
(M - μ) / SM
SM : (Estimated) Standard Error from our sample
How does the t-distribution vary as a function of df
Lower df
- Broader
- More extreme values are more probable
Higher df
- More normal
- More extreme values are less probable
One-Sample Design. Pros and Cons
Pros:
- Used if we know population values
Cons:
- Won’t known population values
- Cannot compare 2 groups/ change over time
Between-groups/ independent-measures design. Pros and Cons
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
Within-group design/ repeated-measures design
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
t-tests quick formulas:
(a) One-Sample
(b) Independent Samples
(c) Paired Samples
(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)
tcrit and tempirical. Given alpha at .05, what does it mean
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
What is pooled variance
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
When do we calculate effect sizes
Calculating the effect size only makes sense when the t-test revealed a significant result
What is cohen’s d
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
What is r2
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
t-test assumptions: why must normality and homogenity be met
Normality:
- t-tests are robust to large samples
Homogenity (in independent):
- Mess up pooled variance
