W2 - Statistics
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Why do we use statistical test
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)
What does the t-statistic take into account
t = (M - rho)/Sm M: Mean of Sample rho: Mean of Population Sm: Measure of S.E of the mean based on sample
What happens when sample size/df increases to the t-statistic vs df decrease
Df increase: It becomes narrower and more like a normal distribution Df decrease: Looks broader
One-Sample t-test
Compare one group differing from some other specific value (IQ)
Pros and Cons of One-Sample t-test
Pros; - Compare group data to known values Cons: • Not sure about population values • Can’t compare 2 groups / over time
Between-group/Independent-Measure t-test
2 Groups; Differing People
Pros and Cons of Between-group/Independent-Measure t-test
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
Repeated-Measure t-Test
Single Group; Differing Conditions
Pros and cons of repeated-measure t-test
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)
In a directional t-test, which values do we want to look at
0.10. Want to capture 5% where Any value > (t-critical) is less likely than 5% to occur by chance. Ignore one tail
What does the t-statistic consider (conceptually) and what is it not
• Consider how variable the data is (i.e. how well our sample mean can estimate the population mean) • Not an effect size measure
What is the different between one-sample and independent-measures t-test. What must we additionally consider
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)
How do we calculate S.E of mean difference. When can we use this/when can we not
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
What is the different between one-sample and repeated-samples t-test. What must we additionally consider
General structure of the t-test remains the same: Test whether AVERAGE DIFFERENCE SCORE significantly differs from chance
What are effect size measures in t-test
Cohen’s d & r^2
Difference between Cohen’s d and R^2
Cohen’s d: (Mean difference/SD) Independent of Sample Size. R^2: (t-statistic and df) Percentage of variation explained by experimental manipulation
What are some assumptions before running t-test
• ) Independence of Observations • ) Normal distribution • ) If comparing between 2 populations (independent/between/paired t-test), samples must have equal variance (Homogeneity)