Flashcards
STEPH Review
Cards in this deck (63)
- 1Outcome variableA characteristic which we believe to be affected by the values taken by other variables
- Also called a response or dependent variable - 2Explanatory variableA factor that may influence the outcome
- Also called independent or predictor variable - 3Qualitative variable- characterises a certain quality of a subject
- Also known as categorical data - 4Binary data- Only has 2 categories
- Also known as dichotomous
-Simplest type of categorical variable
e.g.: sex, vaccinated status,etc.. - 5Unordered categorical variable- Categories may be listed in any order, they are distinct from each other
- Also known as nominal variable
e.g.: ethnic group, marital status - 6Ordered categorical variable- Different categories are ordered on some scale (there is a natural ordering)
- Also called ordinal data
E.g.: age groups, severity of disease - 7Quantitative variable- Represents a counted or measured quantity (on scale, with units)
- also known as numerical data
- can be discrete or ccontinuous
e.g.: weight, blood pressure, # of children - 8Frequency distributionshows the frequencies with which the different possible values of a variable occur in a group of subjects
- can show numbers or percentages - 9Relative frequenciesShow the percentage of the total data set for each category
- 12 infections out of 40 patients = 30% of infections - 10Cumulative relative frequenciesThe running total of the relative frequencies (reading from top to bottom)
( can add up relative frequencies %, or calculate cumulative frequency, then look for its percentage) - 11HistogramUsed to display relative frequencies of continuous variables
-Area represents frequency
-Width is the size of the interval - 12Bar chart/Pie chart- used to display qualitative data
- 13Frequency polygonsUsed to display frequency distributions.
- constructed by joining the midpoints of the tops of the vertical bars of a histogram
- Useful if more than one frequency distribution needs to be shown on one graph - 14Standard deviationThis is the measure of spread used in conjunction with the mean
(based on deviations of the observations from the mean)
- quantifies variability of a distribution
square root of the variance - 15Random sampling- chance alone determines who is included in a sample
- Each individual has a known probability of being chosen, regardless of who's been chosen already (can apply statistical theory)
- removes selection bias - 16Sampling unitCan be an individual person, a household, a school, a health clinic etc..
- 17Target populationThe population in which we are actually interested, the one you want to make conclusions about
- Can also be called reference population - 18Study populationThe population of sampling units from which we draw our sample
(usually more limited than target population) - 19Sample designthe scheme for selecting the sampling units from the study population
- 20Sampling framethe list of units from which the sample is to be selected
(The existence of an adequate and up-to-date sampling frame often defines the study population)
e.g.: electoral register, list of households
- can be built by conducting a census - 21Simple random sampling (SRS)Steps:
1. Draw up a sampling frame.
2. Choose a random selection of the required number of units by:
using random number tables
or
using random numbers generated by a computer program - 22Systematic random samplingStarting from a random starting point, sampling units are selected at regular intervals from a predetermined sampling list.
- sampling interval is found by dividing the population by the required sample size
- Random starting point is found within the sampling interval
- We assume there is no underlying pattern to the sampling list - 23Sampling distributionrepresents the frequency of the proportions estimated from each possible sample of a population
(should resemble a normal distribution) - 24Standard errorThis is the measure of the average amount of error in a sample proportion
(how far, on average, we expect our observed proportion (p) to differ from the true population proportion (π) - 25Confidence intervalQuantifies the statistical uncertainty of our estimates
(gives a range of values within which we are reasonably confident the population value lies)
- if 2 confidence intervals don't overlap, there is evidence of a real difference between 2 groups - 26Null hypothesis- What we are trying to disprove
- no true statistical association between 2 factors, 2 treatments are equally effective, etc.. - 27Alternative hypothesisWhat we're trying to prove, what the study is about
- opposite to null hypothesis - 28P-valueUsed in statistical tests to quantify probability
E.g.: p<0.001 - the chances of getting a difference between 2 factors is less than 1 in 1000 - 29Interpretation of p-values- p>0.1 - insufficient evidence
- 0.05 - 30Comparing two proportions (percentages)- We use to Z test
- Null: there is no difference between the two proportions
(the larger the z value, the smaller the probability (p-value))
- once you get z test, use table to find value, then multiply by 2 to find p-value
- Calculate 95% CI interval, using different SE from Z test. - 31Sampling variability of a mean- To get the CI interval, use normal formula X +/- 1.96 (SE)
- If n<20, use T distribution to find the factor (it isn't always 1.96)
- This factor will depend on the degree of freedom - 32Degrees of freedomv= n-1
= sample size minus 1 - 33Comparing two means- Use Z test
- purpose of significance test is to assess whether the difference between the two sample means may be explained entirely by sampling error
- if sample is too small, use T test - 34Analysis of variance (ANOVA)- used to compare means of 2 or more groups
- it assesses how much of the overall variation in the outcome is attributable to differences between the population means in the different groups
- Represented by F statistic in Stata
F = 1 --> chance
F >1 --> real difference between groups
- null: there is a difference between the mean between groups, and the mean within groups??? - 35Assumptions for methods of inference (Statistical tests)- We assume the sampling distribution of each sample and of the difference between them are approximate to the normal distribution
- Z test: The true standard deviations are assumed to be estimated accurately by the sample standard deviations
- T test: assumes that the true SD and sample SD are equal to some common value - 36Association between two categorical variables- Make a 2x2 table
- Use chi squared test
- Null: there is no association between the 2 variables
- large values of chi squared indicate that there is an association
- Chi squared test assumes that sampling distribution of each proportion and difference between them are approx. normal - 37Contuinity correction- used for the 2x2 table for categorical variable
- Adjusts the value of z to allow for the fact that we are modelling a discrete variable with a continuous distribution
- Effect is more substantial with small samples - 38Chi squared test for trend- When there are 2 rows, but more than 2 columns, and an ordered categorical variable is involved
- need to assign numerical scores to different categories in order to calculate means (1,2,3..)
- Then use sig test to see if there is any difference between the 2 means - 39Validity of Chi Squared test- Chi squared test based on assumption that the calculated stats follow the chi-squared distribution - this is reasonable for large sample sizes (>40)
- If N is <20, or between 20 and 40, and the smallest expected value is <5, then use Fisher's Exact Test instead - 40Comparison of proportions from paired data- Rearrange 2x2 table, into discordant and concordant pairs
- Use McNemar's chi squared test to assess whether observed difference in discordant groups is bigger than what we would expect by chance
- Can also apply a continuity correction
OR: r/s - 41Measures of effect (effect estimates) used- Risk difference (for differences in proportions/excess disease burden)
- Risk ratio (more for cohort)
- Odds ratio (OR) (ratios for associations/causality)
- Protective effect: 1/RR or 1/OR
- Rate (if you want to take into account person time) - 42Confounder- Must be a risk factor for the disease
- Must be associated with exposure
- Must not be on causal pathway between exposure and disease
(These should be considered at the study design stage)
THERE IS NO STAT TEST FOR CONFOUNDING - 43Stratified analysis- When exposure is divided into distinct groups (with very similar values of the confounding variable) to see if there are any differences between them
- can be done to adjust for confounders
- Use the Mantel Haenszel chi squared test to do this - 44Test of homogeneity- Test for effect modification
- If after stratifying, the different groups' OR are very different, then the factor is a potential effect modifier
- Test of homogeneity tests the hypothesis that the ORs in the two strata are the same
- Need to check p-value - 45Multi-stage sampling- Reduces costs, and only need a sampling frame for the selected clusters, and not the whole population
- If it involves more than 2 stages, after the 1st stage, the same number of units needs to be selected in all other stages - 46Primary sampling units (PSU)Units at the first stage of multistage sampling
- 47Self-weighting sampleA sample in which, taking each stage of selection into account, every study unit in the population has an equal chance of being included in the sample
(better, as it will give us unbiased estimates of the true population mean or proportion) - 48Probability proportional to size (PPS)- Accounts for the fact that different clusters may not have the same number of individuals
- Would first need a list of all the PSUs, and an approximate number of how many households are in each
- First use PPS to select PSUs, and then can use SRS to select second stage units (should have the same number of SGUs in each cluster) - 49Determinants of precision of estimates in surveysPrecision of estimates will depend on:
- size of sample selected (more precise with large samples)
- amount of clustering in survey design (more precise with more clusters)
- variability between clusters of the item whose value is being measured (more variability, less precision or would need more clusters) - 50Simple linear regression- This shows us the relationship between 2 quantitative variables, by showing the regression line
- Follows: y =a+bx
a is the intercept/constant, where line crosses y axis
b is the slope, average increase/decrease in y per unit increase in x (also called regression coefficient)
- predicted values of increase in y = increase in X x b - 51Correlation Coefficient (r)This measures the closeness with which the points lie along around the regression line
- always lies between -1 and 1
- Positive values of r --> upward slope (b>0)
- Negative values of r --> downward slope (b<0)
- The less the scatter, the closer to 1 r is.
- r = 0 --> no linear relationship - 52R squaredthe proportion of the variation in outcome (y) explained by the regression
- 53Power- The probability of detecting a difference in means of the population
- The probability that the test of significance will reject null hypothesis when it is wrong ( how many type II errors we can avoid) - 54Type I errorWhen the null hypothesis is true, and you reject it
- Level of significance e.g. 95% indicates how much we are willing to accept that we are wrong when we reject the null. In this case, it would be 5% - 55Type II errorWhen the null hypothesis is false and we fail to reject it
- this will depend on the power of the test - 56Precision= 1.96 X standard error of estimate
- Can be used to calculate sample size needed
n= 3.84 X p(100-p/ (precision squared)
- The precision of an estimate is measured by the widths of the confidence intervals (these will depend on the SE of the estimate) - 57Disadvantages of a survey design- Sample is not self-weighting
- If multistage clustered sample was used, then the standard errors must take into account the clustered design or they will be too small - 58Probability weights in a weighted sample- Observations that are over-represented are weighted down (weight <1.0) in the analysis so that they represent less than one person the population
- Observations that are under-represented are weighted up (weight >1.0) in the analysis so that they represent more than one person in the population - 59Weighting for non-response- weightings used if some sub-groups have lower response rates than others
- so data of those who answered are given more weight
- non-response weight = 1/probability of response
- Probability of response is estimated by the proportion responding the survey
- this weight is combined with weights due to sampling for analysis - 60Design effect- Shows effect of sampling design on the standard error estimate (clustered vs SRS)
- Depends on sampling design used, amount of "between-cluster" variation, and variable you are analysing - 61Design effect (DEFF)Variance for cluster sampling/variance for SRS
- DEFF tells you how much larger than a SRS sample, your clustered sample needs to be
- Hard to know what DEFF should be. If you don't know, some people assume DEFF = 2. so double sample size
- Having more clusters and less individuals in each, will make DEFF smaller, increasing precision
- = DEFT squared - 62Design factor (DEFT)SE for cluster sampling/SE for SRS
- This is the ratio of SEs
- CIs will increase proportionally with DEFT. So bigger design effects means that CIs in clustered will be wider than those from a SRS
- This is a measure of loss of precision - 63Bradford Hill Criteria for causality- Temporal relationship
- Plausibility
- Strength
- Coherence
- Consistency
- Dose-response
- Specificity
- Reversibility
- Analogy
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- Masters Statistics Flashcards on STEPH Review, created by Mariella Munyuza on 24/05/2016.
- Created by
- Mariella Munyuza · May 2016
- Updated
- Jun 5, 2016
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