Week 10 Kuracloud: Statistical Inference

Question 1

Inferential statistics

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Answer 1

= the methods we use to infer the results from a study sample to the wider population.

Question 2

Population/Target population

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Answer 2

= group from which sample is drawn

Question 3

Sample

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Answer 3

= people who take part in study (participants)

Question 4

For the sample to be representative of the population:

Answer 4

each person in the population of interest should have an equal chance of being selected in the sample

Question 5

Sampling Frame

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Answer 5

= list of all people/objects in target population

Question 6

Sampling distribution

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Answer 6

= frequency distribution of all means of samples of a population
- approximately normal distribution
- mean of sampling distribution is same as mean of population
- SD of sampling distribution = standard error of the mean

Question 7

Standard error

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Answer 7

= variations in means from multiple sets of measurements, SD of sampling distribution
- can be estimated from single set of measurements:
SE = (standard deviation)/sqrt(n)
(standard deviation divided by square root of sample size)

Question 8

Confidence Interval

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Answer 8

= range in which we are pretty sure the population parameter (e.g. means, medians, difference of means and differences of medians) lies
Depends on:
- variation within population (proprtional to confidence interval)
- size of sample (inversely proportional to confidence interval)

Question 9

Methods for calculating confidence intervals

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Answer 9

• informal
• traditional normal-based formulas: stated level of confidence affects confidence interval length
• bootstrapping

Question 10

95% confidence interval (95%CI)

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Answer 10

= 1.96 SE above and below sample mean
because normal distribution of sample means –> 95% of sample means are within 1.96 SE of distribution

Question 11

95% confidence interval for sample proportions

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Answer 11

= sample proportion +/- 1.96 x SE
calculated from SE of a sample proportion

Question 12

Comparing population means or proportions

2

e.g. means cancer in smoke vs nonsmoke in population

Answer 12

• estimate differences in population means or proportions using sample means or proportions
• calculate 95% confidence interval of measure of difference using standard error of differences in means or proportions
  95% confidence interval = mean difference +/- (1.96 x SE)

Question 13

Methods of comparing 2 proportions

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Answer 13

• absolute difference in 2 proportions
• risk ratio
• odds ratio
• prevalence ratio
  if SE known, 95% confidence interval can be calculated for each

Question 14

null hypothesis (H0)

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Answer 14

= no relationship between exposure and outcome

Question 15

Alternative hypothesis (HA)

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Answer 15

= not null hypothesis

Question 16

p-value

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Answer 16

= probability of getting observed result if null hypothesis is true (chance that observed estimate is result of sample variation)
p > 0.05: not significant: no/weak evidence against H0
p < 0.05: significant: evidence against H0 (justify rejection)
P < 0.01: highly significant: strong evidence against H0
P < 0.001: very highly significant: very strong evidence

Question 17

Statistical test for numerical outcome variables

4

Answer 17

• 2 groups, paired observations: paired t-test (Wilcoxob signed rank test)
• 2 independant groups: two-sample t-test, linear regression (Mann Whitney test)
• > 2 groups: ANOVA, linear regression (Kruskall Wallis test)
• numerical exposure variable: Pearson correlation, linear regression (Kendall’s rank correlation, Spearmans correlation)

Question 18

Statistical tests for binary outcome variables

3

Answer 18

• 2 exposure groups: chi-squared test, logistic regression
• > 2 exposure groups: chi-squared test, logistic regression
• > 2 ordered exposure groups: chi-squared test, logistic regression

Question 19

If the 95% CI does not contain the null value:

Answer 19

p<0.05

Question 20

Value of no difference

Answer 20

• comparing means: 0
• comparing proportions using ratio: 1

Question 21

Sample estimate/effect size

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Answer 21

= difference between 2 groups
- difference of means
- difference of proportions
- ratio of proportions or odds