PAS 3 Flashcards
What does taking the mean of multiple observations do to uncertainty?
Decreases but does not eliminate uncertainty.
What is the percentage CI of around 1 sem around the mean
68%, meaning there is a 68% chance that the real answer is within that interval.
What does a region of +2 sem around the mean mean?
It is a 95% CI
What is an issue of sem with small numbers of observations?
Underestimates MOE
What do you need to do for triplicate observations sem?
what needs to be done to sem for triplicate observations
You need to double the sem error bars to get a 68% CI
What are the 2 types of experiments and what do they mean?
What is paired data
Have independent measures
Have repeated measures: where you have paired data, multiple repeated measures. Paired data typically arises when you make measurements on the same subject (before and after treatment)
What is effect size
Difference between means of two groups
How can uncertainty be estimated?
Uncertainty can be estimated roughly by looking at sem error bars. Or more exactly by calculating a 95% CI for the difference in the means
What is wrong with the old statistics?
a. Based on a wrong conceptual model
i. There is an effect (alternative hypothesis is true) or no effect (alternative hypothesis is true). Ignores effect size and biological significance.
b. Encourages definite decisions (accept or reject null hypothesis) based on inadequate data.
i. P ≤ 0.05 is only weak evidence for a real effect. P > 0.05 is little or no evidence against a real effect
c. Uses the semantically misleading term “statistically significant”
i. It really means the data is statistically indicative
ii. It does not tell you about the biological significance of the real effect
10. For paired data, why measure each subject twice, before and after?
This eliminates the uncertainty due to variation between individual subjects
How do you estimate effect size for paired data?
- calculate the effect size for each individual
- take the mean
How do you estimate uncertainty for effect size
Calculate the 95% CI for the effect using a paired t-test
Do not try comparing sem error bars
What is bonferroni correction?
Multiply the p-value by the number of independent tests. if it is still less than 0.05, then it may be significant.
Why perform conservative test
helps to avoid Type 1 errors (false positives) but may cause a lot of Type 2 errors (false negatives)
What does Post hoc mean
Afterwards tests
Example of a post hoc test
Tukeys post hoc test. This compares 2 groups at a time. Gives an individual confidence interval and p value for the comparison. It includes a multiple testing correction.
What is ANOVA
It is a one way analysis of variance.
• Looks at all of the data in all of the groups together
• Looks at the overall variation (variance) within the groups
• This measures the overall variability of the data
• Then looks at the overall variation (variance) between the groups
• Is the variability within the groups sufficient to explain the variation between groups?
• Technically, what is the probability of getting that large a variance between groups, if there is no real effect, so assuming only random variation (null hypothesis is true)?
• Looks at all of the data in all of the groups together
• Looks at the overall variation (variance) within the groups
• This measures the overall variability of the data
• Then looks at the overall variation (variance) between the groups
• Is the variability within the groups sufficient to explain the variation between groups?
• Technically, what is the probability of getting that large a variance between groups, if there is no real effect, so assuming only random variation (null hypothesis is true)?
Why are send not used for small number of observations
Underestimated the uncertainty
What are the types of experiments and give examples
Independent measures eg patients vs control or transgenic animals vs control animals
Repeated measures, paired data or multiple repeated measures
Why should you not compare sem error bars for compared data
Idk
What is p hacking
Crossing out or not involving certain data.
Eg is p=0.052, close to 0.05, so they change experiment condtions to get p<0.05
Changing the measurement to get p as smaller than or equal to 0.05
or to make all sorts of different comparisons and tests, and if one of them comes out significant, you publish that one and do not publish the others.
Publishing significant data and leaving out unsignificant ones. This is scientific fraud
Structure of spliced rna called ?
Lariat
In an independent groups experiment
the effect size is the best estimate of the true answer. The uncertainty (MOE) can be estimated from the sem error bars. This gives a roughly 80% CI, (assuming at least 10 observations in each group and a rough approximate distribution). A better approach is to use a t-test to calculate the exact 95% CI, and to use half the 95% CI instead of sem on the error bars on the graph
For paired data
The sem error bars for each group are not a good indicator. Calculate the difference for each pair of data points. Then plot the mean and 95% CI for these results.
Multiple groups and multiple tests
Increased likelihood of type 1 errors.
Important to show all tests and comparisons
if there are a large number of comparisons.
a) use a multiple ttesting correction or
b) use anova followed by a post hoc test.
Quantitative experiments
We want to measure the size of an effect
Random error/ random variation causes uncertainty in the result
Taking the mean of multiple observations decreases, but does not eliminate, uncertainty
How large is the uncertainty (margin of error-MOE)?
Assuming a normal distribution:
S.e.m. is one measure of uncertainty (MOE)
A region ± 1 s.e.m. around the mean is a 68% confidence interval (CI)
There is a 68% chance that the real answer is within that interval
A region ± 2 s.e.m. around the mean is a 95% confidence interval (CI)
what does independent measures mean?
The 2 groups have no relation whatsoever.
What things do you need to assume in order to be able to compare error bars?
Comparing error bars will work, assuming
The groups are independent measures, not paired data
There are at least 10 observations
The data is roughly similar to a normal distribution
Comparing error bars gives a rough estimate of the 80% CI
What do the upper and lower ends of CI tell you?
The upper end of the CI tells you how big the real effect might perhaps be
Possibly bigger and more biologically significant than the difference in the means
The lower end of the CI tells you how small the real effect might perhaps be
Possibly too small to be biologically significant. Possibly zero or even negative.
Describe paired data
Typical example is when you measure each subject twice, once before and once after treatment
This eliminates uncertainty due to variation between individual subjects
To estimate effect size
Calculate effect size (before to after) for each individual
Then take the mean
what does a paired t test tell you?
95% confidence interval
when is it possible to just use a t test to get 95% CI
small groups are of positive and negative controls , known hypothesis
Given the assumptions
There are a fairly small number of different groups, and
It is clear in advance what the experimental question is- what is the key comparison
Then it is reasonable to calculate the 95% CI (and a p-value) using a t-test
Not to use in large groups because p value will show higher chance of getting significant data when it could be false-type 2 error.
how to estimate uncertaininty for paired data values
To estimate uncertainty (1)
Take the list of effect sizes for each individual
Calculate the s.e.m. for this data
Plot error bars of ± 2 s.e.m. to estimate the 95% CI
Works reasonably for >10 observations
Or better (2)
Use a paired t-test to calculate the 95% CI for the effect using a paired t-tes
DO NOT try comparing s.e.m. error bars
what does p<0.05 mean
P < 0.05 tells us the chance of getting data that looks like a real effect, when there is no real effect, and only random variation, is α = 0.05
Which is 5% or 1 in 20
p value tells you something that looks real from random data, and if you do to many experiments, the values start to look signifiant, even though they arent. A lot of type 1 errors.
what is the correct way to deal with multiple testing
Report all comparisons and statistical tests
Then those reading the paper know whether to be sceptical
Performing multiple tests, and only reporting the ones that are
statistically significant, is an example of “p-hacking”
Use a multiple testing correction
Bonferroni correction- multiply the p-value by the number of independent tests. Is it still less than 0.05?
Conservative test: helps to avoid Type 1 errors (false positives) but may cause a lot of Type 2 errors (false negatives)
Use 1-way analysis of variance (ANOVA)
Describe 1 way Analysis testing ANOVA
Looks at all of the data in all of the groups together
Looks at the overall variation (variance) within the groups
This measures the overall variability of the data
Then looks at the overall variation (variance) between the groups
Is the variability within the groups sufficient to explain the variation between groups?
could variation in groups, explain variation between groups?
Technically, what is the probability of getting that large a variance between groups, if there is no real effect, so assuming only random variation (null hypothesis is true)?
ANOVA does the same thing as T test but uses multiple groups and looks at the data overall, not the individual comparisons.
If the p-value is large, it is quite possible that the differences between groups are just random variation
If the p-value is small, it is less likely that these are random differences
If p ≤ 0.05 (old criterion) or p ≤ 0.005 (new criterion) then the data is “statistically significant”
Meaning that the data is statistically indicative, not necessarily that the effects are biologically significant.
What is a problem of ANOVA
iF YOU GET A SIGNIFICANT result, you want to know which treatment, which groups show significance, and ANOVA doesnt tell you that. Therefore we move onto POST hoc tests.
What are post hoc tests for?
If first completed ANOVA, and ANOVA gives you a small p value, then it is reasonable to ask which comparisons are responsible for the difference. First graph data, look at error bars, any thing that looks scientifically significant? then do post hoc test. But first look atdata, then do anova followed by post hoc test.
A post hoc test is like a t-test, where you take 2 different conditions and then compare them. It takes account ANOVA.
Which post hoc test depends on which statistical package is available in the lab. Eg, Tukeys post hoc test.
As researchers, we don’t want to know that something is going on, we want to know what is going on
Which groups show an effect/ are different from the others?
FIRST- look at the data. Hopefully it should be obvious.
THEN- confirm with a post hoc test, e.g. Tukey’s post hoc test
This compares two groups at a time (like a t-test)
Gives an individual confidence interval and p-value for the comparison
But includes a multiple testing correction