W2 - Statistics

Question 1

Why do we use statistical test

Answer 1

Know, from a single experiment, how likely the result is by chance or if they represent a real difference.

Find out how unlikely our empirical result was under the chance distribution (aka. the null hypothesis H0)

Question 2

What does the t-statistic take into account

Answer 2

t = (M - rho)/Sm

M: Mean of Sample
rho: Mean of Population
Sm: Measure of S.E of the mean based on sample

Question 3

What happens when sample size/df increases to the t-statistic vs df decrease

Answer 3

Df increase: It becomes narrower and more like a normal distribution

Df decrease: Looks broader

Question 4

One-Sample t-test

Answer 4

Compare one group differing from some other specific value (IQ)

Question 5

Pros and Cons of One-Sample t-test

Answer 5

Pros;
- Compare group data to known values

Cons:

• Not sure about population values
• Can’t compare 2 groups / over time

Question 6

Between-group/Independent-Measure t-test

Answer 6

2 Groups; Differing People

Question 7

Pros and Cons of Between-group/Independent-Measure t-test

Answer 7

Pros;

• Measures are independent
• Don’t have to worry about learning effects due to repeated exposure

Cons:

• People in diff. groups may be different
• Can’t study over time

Question 8

Repeated-Measure t-Test

Answer 8

Single Group; Differing Conditions

Question 9

Pros and cons of repeated-measure t-test

Answer 9

Pros:

• Baseline factors consistent
• Can study over time
• Can usually test less people

Cons:

• Measurements are not independent (need to calculate variance differently)
• People know treatment after first condition
• Counterbalance conditions to avoid unwanted order effects (.e.g first half and other half)

Question 10

In a directional t-test, which values do we want to look at

Answer 10

0.10.

Want to capture 5% where Any value > (t-critical) is less likely than 5% to occur by chance. Ignore one tail

Question 11

What does the t-statistic consider (conceptually) and what is it not

Answer 11

• Consider how variable the data is (i.e. how well our sample mean can estimate the population mean)
• Not an effect size measure

Question 12

What is the different between one-sample and independent-measures t-test. What must we additionally consider

Answer 12

General structure of the t-test remains the same: Test whether DIFFERENCE between TWO MEANS significantly differs from chance

• Additional consider two variances when calculating standard error of mean (S.E of mean difference)

Question 13

How do we calculate S.E of mean difference. When can we use this/when can we not

Answer 13

Pooled Variance: SS (a) + SS (b) / df (a) + df (b)

Average of two sample variance

Only can use this if both groups have same sample size

Question 14

What is the different between one-sample and repeated-samples t-test. What must we additionally consider

Answer 14

General structure of the t-test remains the same: Test whether AVERAGE DIFFERENCE SCORE significantly differs from chance

Question 15

What are effect size measures in t-test

Answer 15

Cohen’s d & r^2

Question 16

Difference between Cohen’s d and R^2

Answer 16

Cohen’s d: (Mean difference/SD)
Independent of Sample Size.

R^2: (t-statistic and df)
Percentage of variation explained by experimental manipulation

Question 17

What are some assumptions before running t-test

Answer 17

1. ) Independence of Observations
2. ) Normal distribution
3. ) If comparing between 2 populations (independent/between/paired t-test), samples must have equal variance (Homogeneity)