Stats p-values Flashcards
What is the critical threshold?
This is the threshold that there is enough evidence to support something is not by chance.
Threshold is usually set to 5%.
So for the probability of something is 1.43%, this is less than 5%, and the null hypothesis is rejected (not due to chance.
If the probability is above 5%, then the null hypothesis is not rejected, as it can not be assumed that it is due to chance.
What is the null hypothesis?
It assumes no effect in the population - e.g. there is no difference, or association between 2 things.
It is easy to test - either it is accepted or rejected.
What is the alternative hypothesis?
This is assumed to hold if the null hypothesis is not true, suggests there is a difference, in an unspecified direction.
It related more directly to the research question.
It cannot be proven however.
What are confidence intervals?
Confidence intervals extend either side of the estimate (mean) by some multiple of the standard error.
Standard error of the mean = standard deviation / square root of total number of observations.
The larger the standard error, the less precise the estimate is.
What is the value for confidence intervals?
CI are usually set at 95%.
To indicate 95% CI for the mean, use:
Population mean –> sample mean +/- u x SEM.
U is a multiple of SEM.
What is the interpretation of CI?
If we repeat our study 100 times, and calculate a 95% CI for each repetition, on average 95 of the 100 Cis would contain the true value.
This is not saying there is a 95% chance that the true value is in our CI range.
What is the use of confidence intervals?
Indication of how reliable our estimate is, given the data we have.
What is the use of P-values?
Devised to indicate how unlikely our result would be if there is actually no real effect.
What are the types of alternative hypothesis?
It is a statement of inequality.
Non-directional, difference between groups but direction is not specified.
Direction, reflects a difference and a direction (smaller/greater) between groups.
What are one-tailed tests?
Tests the hypothesis.
Mutually exclusive - the effect is either smaller or larger.
What are two-tailed tests?
Tests the hypothesis.
Tests for difference, direction is unspecified.
What is a significance level?
The level, chosen at the beginning of the study, which will lead us to reject the null hypothesis if the p-value lies below it.
It must be chosen before data collection begins, to avoid bias.
Most used level is 5% (=0.05).
What is a type 1 error?
Reject the null hypothesis when it is true.
What is a type II error?
We do not reject the null hypothesis when it is false
Conclude there is not enough evidence of an effect when one truly exists.
What is a p-value?
The probability of obtaining the observed result or something more extreme if the null hypothesis were true.
This is not the probability that the null hypothesis is true.
The smaller the p-value, the greater the evidence against the null hypothesis.
How are p-values interpreted?
If 0.05 is the thresholds, then p<0.05 is statistically significant, and the null hypothesis is rejected.
p>0.05 is not statistically significant, and the null hypothesis cannot be rejected.
What does a not significant p-value mean?
Not significant does not mean there is no effect or difference.
It means there is insufficient evidence to support the existence of a difference or effect, given pre-determined criteria.
What is the relationship between confidence intervals and p-values?
Calculate the mean
The difference of the mean
If the confidence interval line overlaps then it is not significant at 95%
If the line overlaps then it is significant
How do you test for normality?
This is continuous data.
Examine with a histogram - should look like a symmetric bell-shaped curve.
If the curve has a long drawn out tail, on either side, the data is skewed.
What are data transformations?
Transform data to become close enough to normality for tests to be valid.
Perform the same mathematical transformation on every observation in your data set.
If the data becomes normal after transformation, perform your statistical test on the transformed data.
Back-transform any summary measures e.g. mean, confidence interval.
What are useful data transformations?
Right skewed data - use logs, square roots or reciprocals.
Left skewed data - use squares, cube etc.
