Week 9: Descriptive and comparative statistics

Biostatistics

The science of analyzing data and interpreting results so they can be applied to biology, health, environmental problems

Univariate analysis

one variable in a data set using simple statistics like counts (frequencies), proportions, and averages

Bivariable analysis

uses rate ratios, odds ratios, and other comparative statistical tests to examine the associations between two variables (mostly exposure and outcome)

Multivariable analysis

encompasses statistical tests such as multiple regression models that examine the relationships among three or more variable

Describe the population study = ________ analysis

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Compare groups = ________ analysis

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Regression and other advanced analysis = ________ analysis

Univariate analysis
Bivariate analysis
Multivariate analysis

What is a variable?

- Any quantity that varies from one entity to another (sometime within an entity over time)
- Any attribute, phenomenon, or event that can have different values

Qualitative variables

nominal
Ordinal

Quantitative variables

Discrete
Continuous
Internal
Ratio

Nominal Variables

No intrinsic or logical order or value
eg,
- University programs
- Countries
- Types of fruits

numbers can be assigned to different categories

Ordinal Variables

Intrinsic value but with no clear or equal differences between levels (a set of ordered categories)
eg,
- Primary vs. secondary vs. university education
- Mild vs. moderate vs. severe pain
- Rating scales (assigning numbers)

How to display Qualitative data

Pie Charts
Bar charts
Frequency tables

Numeric Variables

Meaningful numeric scales

Age, blood pressure, # of friends, temperature

Assigned numbers have total mathematical meaning

eg. Continuous and Discrete

Continuous Variables

- can take any value
- blood pressure
- temperature
- can be plotted as a line

Discrete Variables

Can take a finite or limited number of values
- age in year
- # of drinks
- can be plotted as dots

Interval Variables

Difference is meaningful
no natural zero
arbitrary zero

Ratio variables

Ratio is meaningful
zero means absence of attribute (is natural)

Mean

calculated by adding up all the values for a particular variable and dividing that sum by the total number of individuals with a value for the variable = arithmetic average

Median

The median is the value in the middle when you rank the data in ascending or descending order
- divides the data into 2 equal parts

Mode

The most frequently occurring value for a particular variable in a data set

Histogram

*not to be confused with Bar Chart
- important to manage the intervals

Histogram normal distribution

Range

The range for a variable is the difference between the minimum (lowest) and the maximum (highest) values in the data set

Quartiles

mark the 3 values that divide a data set into 4 equal parts
- the interquartile range (IQR) captures the middle 50% of values for a numeric variable

Boxplot

A simple visual depiction of an intuitive way to explore the data

variance: σ2

The extent of deviation from the average value of that variable in the data set

- Calculated by adding together the squares of the differences between each observation and the sample mean (µ) and then dividing by the total number of observations

Standard deviation: σ

the square root of the variance

Standard error

Standard error of the mean adjusts for the number of observations in the data set by dividing the variance by the total number of observations and then taking the square root of the number

Mean and standard deviation

Confidence intervals (CI)

Provide information about the expected value of a measure in a source population based on the value of that measure in a study population
- A larger sample size will yield a narrower confidence interval

A confidence interval is usually: __%

95%
meaning, 5% of the time, the confidence interval is expected to miss capturing the true value of a measure in the source population

eg,
We are 95% confident that the real average is between 110-130; 5% chance that the true value of mean is either larger than 130 or smaller than 110

Comparative statistics

Comparing main factors between exposed and unexposed in cohort studies

Average age of exposed=Average age of unexposed
% male in exposed=% male in unexposed

Testing if randomization was effective in experimental studies
Comparing the outcome status
We can NOT just look at the calculated values (these are estimates from samples, subject to random sampling error)

Inferential statistics

Techniques that use statistics from a random sample of a population to make evidence-based assumptions (inference) about the values of parameters in the population as a whole

Decision about parameters via information obtained from a sample is via hypothesis testing

Hypothesis testing

Aim:
- To test an explicit statement or a ‘hypothesis’ about a population parameter

The null hypothesis (H0)

there is no difference between the two or more values being compared

The alternative hypothesis (Ha)

there is a difference between the two or more populations being compared

Idea of probability - p. value

observed sample supports the null

Between 0.1 and 0.9: no reason to suspect null is false
<0.02 sufficiently strong evidence to conclude null does not reflect the state of nature, unlikely to be true
“The value for which P=0.05, or 1 in 20; it is convenient to take this point as a limit in judging whether a deviation is to be considered significant or not."
0.05 the convention commonly used in health research

*P.value measures how strongly the sample data agrees with the null

Significance level: α

the p value at which the null hypothesis is rejected, usually 0.05 in health research

Parametic test

assumes the variables being examined have particular distributions

- inferential methods are based on types of distributions (mostly normal)

Nonparametic test

does not make assumptions about the distributions of responses

- Nonparametric tests are used for ranked variables and when the distribution of a ratio or interval variable is non-normal