Statistics Flashcards
When do we use z instead of t?
If we know population SD
What is the basic idea of t-statistic?
(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
What are the pros and cons of the One-Sample Design?
Pros:
- Used if we know population values
Cons:
- Won’t known population values
- Cannot compare 2 groups/ change over time
What are the pros and cons of the Between-groups/ independent-measures design?
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
What are the pros and cons of the 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
What are the t-tests quick formulas for:
(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)
For tcrit and tempirical, Given alpha is 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
