24. Statistical Inference

Question 1

statistical inference

Answer 1

• using a sample to make statements about the population
• needed because we can’t measure effect in entire populations
• process of drawing conclusions about effects in a population
• using data on a sample drawn from that population, PATTERNS revealed through analysis of sample data -> generalized to population

Question 2

why do we use random sampling?

Answer 2

• each member of the population has an equal chance of being chosen
• study sample is representative of population
• provides greatest probability that findings in the sample will closely approximate the overall population
• findings can be “generalized”

Question 3

what are the three main explanations for any observed effect?

Answer 3

1. the effect is due to bias or confounding
2. the effect is due to chance (this is where statistics comes in)
3. the effect is real

Question 4

bias vs confounding

Answer 4

bias is a systematic error in the design or implementation of a study: creates an association which is not true

confounding is an association that is true, but potentially misleading

Question 5

hypothesis testing

Answer 5

involves choosing between 2 propositions:

1. null hypothesis : no real difference b/w groups, observed effect is due to chance
2. alternate hypothesis: real difference exists between groups

we are looking to “reject” the null hypothesis (we want to show that the observed effect is greater than what we would expect based on chance alone)

a null hypothesis may occur when you find an observed effect in the sample population, but there is no effect on the entire population (that you are trying to represent)

Question 6

P value

Answer 6

• the probability that the observed effect could be due to chance alone
• probability of obtaining the results if the null hypothesis were true
• P value of 0.05 means that there is only a 5% probability of obtaining observed result if it wasn’t real (but a 95% probability that the observed result is real and representative of the entire population)
• the lower the P value, the stronger the evidence found

Question 7

P value and significance

Answer 7

• if p-value is less than a certain value (0.05) we conclude that chance alone is unlikely to explain the effect we see
• therefore we REJECT the null hypothesis
• we can call result “statistically significant”
• 0.05 is called the alpha level (so P

Question 8

P > 0.05

Answer 8

• does NOT mean that there is no difference between the two groups or that the two are equivalent
• it just means that we are unable to rule out that chance explains the effect we observed

Question 9

confidence intervals

Answer 9

• estimated range of values likely to include an unknown population effect
• the “level” of confidence is the probability that the interval produced by a statistical method includes the true value of the population effect (usu 95%)
• I.e. there is an X% chance that the range will cover the true mean; accounting for variability from sample to sample

Question 10

null value for difference in means? relative risk? odds ratio?

Answer 10

difference in means = 0
RR = 1
OR = 1

Question 11

confidence intervals around differences between groups?

Answer 11

• if the confidence interval does NOT contain the NULL value, then we can say with X% confidence that the observed effect is not due to chance alone
• –then the result is statistically significant (P

Question 12

confidence interval vs P-value?

Answer 12

confidence interval is more informative than a p-value

in addition to statistical significance (given by P value), CI also gives you an idea of how large or how small the effect is likely to be

Question 13

what are the two types of quantitative variables?

Answer 13

continuous (measurement) and discrete

Question 14

what are the two types of qualitative variables?

Answer 14

nominal and ordinal

Question 15

what type of variable is age?

Answer 15

continuous (quantitative)

Question 16

what type of variable is a score of 1-5?

Answer 16

discrete (quantitative) (it is a number, but not continuous)

Question 17

what type of variable is sex?

Answer 17

nominal (qualitative)

Question 18

what type of variable is age category?

Answer 18

ordinal (qualitative) (some ordering of things)

Question 19

what types of variables are categorical?

Answer 19

discrete, nominal, ordinal

Question 20

what are dichotomous variables?

Answer 20

a type of categorical variable that is binary (eg have outcome or not)

Question 21

what descriptive statistic tests can be used for continuous variables?

Answer 21

• mean/median (for center or average)

- variance, range (for spread or distribution)

Question 22

what inference/hypothesis testing can be used for continuous variables?

Answer 22

• student’s t-test (for difference in mean of 2 groups)
• analysis of variance (for difference between more than 2 groups)
• confidence interval around mean difference

Question 23

variance and standard deviation are what?

Answer 23

statistics that tell you how tightly data are clustered around the mean:

• variance is the average squared distance between the data and the mean
• standard deviation is the square root of the variance
• when the data are pretty tightly bunched together, the standard deviation is small
• when the data are spread apart, you have a relatively large standard deviation

Question 24

standard error

Answer 24

the standard error of the mean tells us how VARIABLE these means are likely to be from one sample to the other (if you were to do repeated sampling)

• SE = SD/sqrt(N)
• if SE is small, we would expect a similar mean if we were to repeat our study (mean is precisely estimated)
• if SE is large, we would expect a different result if we were to repeat our study (mean is not preceisely estimated)

Question 25

______ is the basis of calculating the t-test statistic and confidence intervals.

Answer 25

SE

Question 26

t-test

Answer 26

a ratio between the observed effect (difference in means) and the standard error of the effect (variability in the means from sample to sample)

• so we want mean difference to be high and variability (SE) to be small
• we compare the observed t-statistic to a critical value to determine statistical significance

Question 27

what type of descriptive statistics can be used for categorical variables?

Answer 27

frequencies, proportions, %

Question 28

what type of inference/hypothesis testing can be used for categorical variables?

Answer 28

• Chi-square test and p-value
• fisher’s exact test and p-value (for small sample sizes(
• RR and CIs
• OR and CIs

Question 29

Chi-square test

Answer 29

• chi-square statistic and associated P-value
• used to test significance of categorical data (2X2 data, 2X3 data, 3X3 data, etc)
• asks how much do the data we observe differ from whta would be expected under the null hypothesis?
• similar to t-statistic, compare the observed chi-square statistic to a critical value to determine statistical significance

Question 30

what is the conceptual formula of the t-test? and what does it do?

Answer 30

mean difference/measure of variability in means

tells you difference between two means

Question 31

what is the conceptual formula for analysis of variance (F statistic)? and what does it do?

Answer 31

variance between groups/variance within groups

tells you difference among many means

Question 32

what is the conceptual formula for the chi-square test? and what does it do?

Answer 32

extent to which frequencies are not consistent with the null hypothesis/size of sample

tells you differences in frequencies

Question 33

power

Answer 33

the ability to detect a difference between study groups when one does exsit

depends on:

• sample size
• actual or true difference between groups (usually inversely related to sample size)
• level of statistical significance (usu set at 0.05)

power analysis should be performed a priori (if you read a study where results were “not significant” and power for that outcome was not reported, consider the possibility that the study was underpowered

Question 34

how do you maximize the power of a study?

Answer 34

• ensure adequately sized sample of study subjects

- choose the most precise and accurate measures of exposure and outcome (reduces variance of the measurements)

Question 35

statistical significance vs clinical significance

Answer 35

• statistics tell you whether a result is statistically significant, but not whether the result is clinically important
• small effect with a “significant” p-value might not be clinically significant (because it would require a large population for the intervention to have an effect)
• a large effect with a “non-significant” p-vale might be clinically significant (if sample size was small or if supported by other studies/biological plausibility)