Inferential Statistics Flashcards
What form can inferential statistics take?
Estimation
Hypothesis Testing
Types for estimation
Point estimation
Interval estimation
What is estimation?
Using sample data we estimate the distribution of a parameter in the population from which the sample was drawn
What is point estimation?
Estimate a singe value for a parameter that will be close t true value of the parameter - effect size
What is interval estimation
Find an interval that has a given probability of including the true value of the parameter within its specified range
What is the interval in interval estimation?
Confidence interval
What is the probability in interval estimation?
Confidence coefficient
What is hypothesis testing?
We test the null hypothesis that a specified parameter of the population has a specified value by looking at the samples value
What are hypotheses?
Conjectural statements that provisionally link two variables
What are theories?
Sets of definite propositions or facts that are more or less verified already
How does one examine the relationship between two variables?
Probability theory
What is Poppers logic re hypothesis testing?
To prove something is very difficult.
To disprove something is relatively easy.
Hence science does not use the method of verification but methods of falsifiability.
What is the null hypothesis also known as?
H0
What do statistical methods try to do with respect to H0?
Try to refute this statement using statistical inference
What is another name for the alternate hypothesis?
H1
How can one state a hypothesis?
One-tailed
Two-tailed
What is a one tailed hypothesis?
Refers to the statement that differences between groups occurs in one direction only e.g. A->B
What would the alternative hypothesis be in a one-tailed hypothesis?
A is not -> B
What is a two-tailed hypothesis?
Refers to the statement that differences exist between two groups but the direction of the difference is not specified i.e. may be A->B or B->A
What would alternative hypothesis be in a two-tailed hypothesis?
A=B
What happens to significance levels in a two tailed hypothesis?
They are halved
Which type of hypothesis needs a larger difference to reject the null hypothesis?
Two tailed
Why do two tailed hypothesis need a larger difference to reject the null hypothesis?
Significance levels are halved
Which type of hypothesis are considered more rigorous?
Two-tailed
Why are two-tailed hypotheses considered more rigorous?
Significance level is halved so larger differences are needed to reject the null hypothesis
How is the null hypothesis tested?
By gathering data relevant to the hypothesis and determining how well it fits H0
What is used when we test how our data fits with H0?
Significant level, p
What is the significance level, p?
The probability of rejecting H0 when H0 is true
What does a higher significance level, p mean?
The higher the p, the better the fit between the data and H0
What does a low p value suggest?
Casts doubt upon the validity of H0
What can we assume if the value of p is very low?
We can reject H0
What are random errors?
Fluctuations in direction in measured data due to precision limitations of measurement devide
What are random errors often a result of?
Researchers inability to take measurement in the same way to get the same result
What are systematic errors?
Reproducible errors that are consistently in the same direction
What errors can occur during hypothesis testing?
Type 1
Type 2
What happens in Type 1 errors?
Incorrect rejection of the null hypothesis - false positive claim in favour of research hypothesis
What is the likelihood os a Type 1 error?
alpha
At what alpha level can we mainly avoid Type 1 errors?
<0.05
What is another name for alpha?
Level of statistical significance i.e. p
What can lead to Type 1 errors?
Repeated testing of hypothesis using same data
Multiple subset analysis
Secondary analysis
Why does multiple testing of same data lead to type 1 error?
At least one test will be positive in 20 if p is set at 0.05
What is a Type 2 error?
Incorrect acceptance of the null hypothesis - false negative rejection of research hypothesis
What is the name of the likelihood of a type 2 error?
Beta
What can lead to Type 2 error?
Small sample size
Large variance
What refers to the power of the study?
1 - beta
What is the traditional level of beta?
20%
What is the traditional level of power?
80%
What happens as we try to lower Type 1 error?
Risk of Type 2 error increases
Define power
Ability of a study to detect a difference between two groups if such a difference truly exists
What does power depend on
Sample size
Mean effect difference (effect size)
Variability of observations
Acceptable level of p
What variability increases power?
Lower variability
What should be run to find the variance?
Small pilots
Or from previously published works in similar clinical examples
What is the formula for standardised difference?
Target difference in means / SD of observations
What is standardised difference an expression of?
Effect size
Who created the nomogram used to calculate sample size?
Altman
What is used in a nomogram to calculate sample size?
Standardised difference and power values
Which error is increased as p increased?
Type 1
Methods to increase power
Larger p value Larger sample size Larger effect size Reduce variability One-sided test Most powerful test that appropriate assumptions will allow
What does it mean to use a larger effect size?
Consider only larger deviations from null hypothesis to be significant
When might larger effect size not be desirable? e
If a small difference can have a huge clinical impact
How can one reduce variability?
Making more precise measurements
Matching subjects
What must one check before choosing to use a one sided test?
Check if it is possible to make strong (supported) assumptions
Which tests are more powerful?
Parametric
Which type of hypothesis is more powerful?
One tailed
Purpose of CI
To see how close the approximation of a measure in a sample is to the population
What does a smaller CI mean?
The better the representativeness of the sample to the population
What does one need to look out for when interpreting the CI?
Degree of confidence
Width of the interval
Upper and lower limit
Capturing the value of no difference
What is the common degree of confidence used?
95%
How does one derive the degree of confidence?
From the complement of conventional p value which is 5%
What will happen to CI if there is a higher degree of confidence?
Wider interval will be seen
What does a wide interval at a fixed degree of confidence indicate?
That the estimate is not precise
What does a narrow interval of CI suggest?
Very precise estimate
What does width of the CI depend on?
Size of the standard error i.e. variability, which will depend on sample size
Which type of studies give wide CI?
Small studies
What does capturing the value of no difference suggest?
If the 95% CI crosses the 0 point for the difference between means then the result is not statistically significant.
Similar if it crosses 1 for ratio measures or infinity for inverse ratios (NNT)
What is the value of no difference referring to?
The value at which the results are not statistically significant
Value of no difference for means?
0
Value of no difference for ratios?
1
Value of no difference for NNTs?
Infinity
How can one reduce the width of the CI?
Smaller degree of confidence level e.g. 90% instead of 95%
Reduce standard deviation
Take larger sample sizes
Value or no difference for absolute risk reduction
0
Value of no difference for relative risk reduction
0
Value of no difference for relative risk
1
What do CI inform us about?
Degree of confidence in the sample
Precision of a result
Clinical significance
Statistical significance
Formula of effect size
Difference in outcomes between intervention and controls divided by SD
What is effect size a measure of?
Difference in point estimates
What does effect size refer to?
Group of indices (independent of sample size) differing in the mode of measurement of magnitude of treatment effect
Importance of ES in meta-analyses
ES measures are the common currency of meta-analyses that summarise the findings from a specific area of research
Why are ES helpful in meta-analyses?
As individual studies often report outcome using different scales so using ES helps consolidate findings
What can be used to measure ES?
Cohens d
What is Cohens D?
Standardised difference between two means
Calculation of Cohens d
Difference mean mean M1 and M2 divided by SD of either group
Grading of ES based on Cohens d
- 2 = small
- 5 = medium
- 8 = large
How can ES be interpreted?
assuming control and experiment group values are normally distributed with equal SDs, effect size can be interpretted just like Z scores of standard normal distribution
What does ES of 1 mean?
That the score of the average person in the experimental group is 1 standard deviation above average person in control
What does ES 0 mean
50% of controls would be below average person in experimental group
What does ES 0.1 mean
54% of controls would be below average person in experimental group
What does ES 0.5 mean?
69% of controls would be below average person in experimental group
What does ES 1 mean?
85% of controls would be below average person in experimental group
What does ES 2 mean?
98% of controls would be below average person in experimental group
What does ES of 3 mean?
99.9% of controls would be below average person in experimental group
Who suggested the common language effect size (CLES)
McGraw and Wong (1992)
What is CLES?
Probability that a score sampled at random from experimental group will be greater than score sampled from controls
If p value is 0.05, how many times does one need to calculate data to get a positive result by chance
20
What is Bonferroni correction?
To correct for multiple testing leading to false positive
Disadvantage of Bonferroni correction?
Can lead to false negatives
Formula for Bonferroni correction?
Significance level for multiple tested data is altered as (normal significance level / number of statistical analyses carried out)
What does Bonferroni correction do to the outcome?
Treats each outcome as an individual event
What is a family wise error?
Probability that any one of a set of comparisons or significance tests is a Type 1 error
What is a false discovery rate?
Instead of controlling chance of any false positives (like Bonferroni), this controls expected proportion of false positives
What tests can be used to avoid false positives when using multiple tests?
Bonferronis correction False discovery rate Scheffe test Tukeys honestly significant difference test Dunnet test
