T Tests Flashcards
What is the purpose of an unpaired t test for 2 indep means and e.g?
- Compares means from 2 indep samples/people e.g. comparing mean heights of boys and girls
What is unpaired t test based on?
sampling dis of 2 sample means (normal)
What does unpaired t test allow?
Calc of diff and CI for diff
What is null and alt hypothesis for unpaired t test?
- null: 2 samples come from pops with same mean
- alt: there is mean diff between 2 samples
What are 3 assumptions of unpaired t test?
- Quant data (continuous/discrete) normally dis. Data checked for symmetry using dot plot, histogram/normal plot
- SD are the same for both samples. Checked by inspecting them - if diff, Satterthwaite approx may be used
- Sig tests are available to check for normality + sim of SD but not helpful guides as are often non-sig for small samples even if appears to be non-normality/diff in SD. Also tend to be sig for large samples even if skewness/diff in variance appear to be minor (so visual test may be better)
Why might assumptions not hold for unpaired t tests?
- stat test is doubtful and p value is wrong
- t test quite robust to slight skewness if 2 samples are same size but less robust if variances clearly diff
How would you try to correct assumptions that don’t hold for unpaired t test?
- try transformation of data (use log transformation)
- skewness + non-similar SD often go together + correcting 1 by transforming data may correct the other as well
What parameter has t dis got?
degrees of freedom
What is DOF related to?
sample size (which is n1+n1-2)
Describe t dis
- no single t dis - each n1+n2-2 (Sample) gives diff shape
- for large sample (>100), t dis close to normal dis
What is the unpaired t test also known as?
2 sample t test
What happens to SD + SE when calc for unpaired t test?
- SD combined/pooled from SDs of the 2 diff samples
- SE are also combined SE based on 2 SD from both samples
What does the paired (matched) t test do?
- analyses mean diff in paired sample
- each person matched to a sim/same person at diff occasions
How do you check assumptions using a histogram to see if data are normal for unpaired data?
- histogram shows data close to symmetry
- 2 SDs are similar
- can conclude t est assumptions hold for these data
What is paired t test based on?
- sampling dis of mean diff (normal)
What does paired t test allow?
- calc of mean diff + CI for diff
What is null hypothesis for paired t test?
mean change/diff is 0 in pop
What are assumptions for paired t test?
- quant data follow normal dis - data can be checked visually using dot plot, histogram/normal plot
- variances (SD) don’t vary with values of data
Why might assumptions for the paired t test not hold?
- stat test is doubtful and P value may be wrong
- try transformation of data - transform raw data not diff
- paired t test only requires diff to be normal. Sometimes original data can be skewed but when diff/change is calc, diff may be normally dis
What is paired t test aka?
- one-sample t test
How do you 95% CI calc for paired t test for small samples?
- calc t value and use this to read theological t value an n-1 DOF
- use this t value as multiplier
How do you calc 95% CI for unpaired t test for large samples?
- use 1.96 instead of t value as multiplier
How do you check assumptions to see if diff are normal for paired t test?
- check histogram to see if data diff fit normal dis
- can conclude t test assumptions hold for these data
What are requirements for large sample size in unpaired and paired t test?
- unpaired: >50 per group
- paired: >100
- requirements for data to be normal less critical for mathematical reasons
How do you find p value for paired t test?
- look for value corresponding to theoretical t value at n-1 DOF
What is a p value?
- probab (value must be from 0-1) of getting sample mean diff as far/large as that obtained by current trial (exp/sample data)
- or further away from what was specified if null hypothesis is true
What does it mean if probab (p-value) is small?
ev against null hypothesis
How small should the p value be?
common criteria p = 0.05
What can you say about null hypothesis for p value = 0.0016?
- if null hypothesis were true, there would be 0.16% chance of seeing such a sample mean diff
- conclude sig diff + reject null hypothesis
How do you conduct hypothesis testing for a paired t-test?
- formulate specific hypothesis
- evaluate strength of ev: use estimates from sample
- decide whether/not data supports hypothesis
- start with null hypothesis
- look at p value to determine stat sig
What is the strict wording of the null hypothesis and give e.g?
- must state the word: pop
- must state size of diff being looked at
- e.g. in pop of S London stroke patients, mean change
- in SBP between 24hrs + 1 week following treatment is 0
What do you expect when null hypothesis is true for paired t test? What is the reason it might not be?
- expect sample mean diff in SBP close to 0
- if not, diff further away from 0 in either -ve/+ve direction - cast doubt on null hypothesis
How close/far from O can null hypothesis be?
- use t-test to assess that
How can 95% CI + P-value be used to accept/reject null hypothesis?
- if 95% CI doesn’t include null hypothesis (0 is not included within the range) - ev to reject null hypothesis
