PAS 2 Flashcards
When is there strong confidence in a result?
if effect size is large enough to be biologically significant
if effect size is large compared to variation
therefore very unlikely that random variation could account for the difference between the treated and the control
When is there weak confidence in a result?
if effect size is not large compared to variation
therefore random variation in reading might account for the difference between the treated and control means
Examples of a statistical test
What do statistical tests do?
t-test, ANOVA
compare variation with effect size
Uncertainty
How do we decrease uncertainty?
an estimate of how much a measured value differs from a true value
if we take the mean of many observations, we decrease uncertainty in our results and we have more confidence, even when the individual data points overlap
standard error of the mean
Advantage of sem error bars
As the number of observations increases, the sem…
measure of confidence in the experimental result
help to indicate the uncertainty in the results by providing a simple, visual, intuitive way of evaluating statistical confidence
decreases
What is the best estimate for the real mean?
experimental mean
If sem error bars are moderate compared to effect size…
If sem error bars are substantial compared to effect size…
If sem error bars are large compared to effect size…
real answer may be quite a bit larger or smaller than our estimate- but unlikely to be zero - moderate statistical confidence
real answer may be quite a lot large or smaller than our estimate- could even be zero or negative - weak statistical confidence
real answer may be a lot large or smaller than our estimate- could even be zero or negative - weak to very weak statistical confidence
What is biological significance best shown by?
EFFECT SIZE, not statistical significance
More precise ways to evaluate how big or small any effect could be other than sem error bars…
t-test
we get the best estimate, even when we have a small number of observations
What does the t-test calculate?
advantage of the t-test?
What is a 95% confidence interval?
what affects confidence interval?
It is used to compare the means of two groups
It is often used in hypothesis testing to determine whether a process or treatment actually has an effect on the population, or whether two groups are different from each other.
It helps to remove bias by checking if the means are reliably different
Range of values that is 95% likely to contain the true mean
Sample size = smaller sample size will have less accuracy and will be less representative
Variation in population = if the variation in the actual real population is high then the variation in the sample will also be high
what is the effect size used for?
quantify the difference between 2 groups e.g. the difference between the mean for the treated and the mean for the control
It goes beyond – “does it work?” to “how well does it work?”
IF the 95% confidence interval overlaps zero…
IF the 95% confidence interval doesn’t overlap zero…
you know that p>0.05 = no significance
you know that p<0.05 = significant
Which is better, confidence interval or p-value?
confidence interval gives you much more information than a p-value
Advantages of confidence intervals
Disadvantages of confidence intervals
combine numerical information on effect size, statistical confidence and possible variation in the real effect size
ideal for simple comparisons such as treated vs control
harder to apply to more complex experiments e.g. more than one control, more than one treatment
What are the characteristics of a normal distribution graph?
• The x axis is the continuous scale of measurements
• The peak of the curve represents the mean
• The y axis shows the probability density (the relationship between observations and their probability.)
○ The probability of finding the variable x close to the mean is very high.
○ The probability of finding the variable away from the mean is lower
68% of all the data lies within 1 SD -/+.
2 standard deviations away this would cover a total area of 95%.
3 standard deviations away from the mean then this would be 99.7%.
