Week 9 Descriptive and Comparative Statistics

Question 1

Objectives of Today’s Class

Answer 1

-understanding the role of statistical analysis in health research
-getting familiar with terminology
you must know all terms in ch29 and 30
-essential for correct interpretation of health research results
note: today class is only for introducing the concepts you will learn (much more) in a biostatistics class

Question 2

Research process

Answer 2

Question 3

Descriptive Statistics

Answer 3

Definions need to know in ch

Question 4

Biostatistics

Answer 4

is the science of analyzing data and interpreting the results so that they can be applied to solving problems related to biology, health or related fields

Question 5

Univariate analysis

Answer 5

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

Question 6

Bivariable analysis

Answer 6

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

Question 7

Multivariable analysis

Answer 7

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

Question 8

Advanced statistics should be used only when

Answer 8

they are appropriate for the study question and the analyst knows how to use and interpret them correctly

Question 9

Link to Study Design

Answer 9

Question 10

What is a Variable?

Answer 10

• 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
  -to describes characteristic of a person, place, thing, or idea
  We measure variables when an experiment is carried out or an observation is made (week5-2)

Question 11

THE BIG PICTURE

Answer 11

VMDSI

Question 12

WHAT are the types of variables

Answer 12

Qn-DC
Ql-NO

Question 13

Types of Variables (1)Nominal

Answer 13

-No intrinsic or logical order or value
* university programs, countries, types of fruits
-You can assign numbers to different categories (like assigning a number to a pear) but they do not have any other numeric properties
-doing arithmetic (e.g., 1+2= 3) IS NONSENSICAL

Question 14

Types of Variables (1)ORDINAL

Answer 14

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

Legitimate to say: 1 ≠ 2; 5 > 4 > 3 > 2 > 1
But in terms of the attribute being measured, we cannot say
(4-3) = (3-2) = (2-1)
4 is not two times larger than 2

Question 15

Displaying Qualitative (nominal, ordinal) Data

Answer 15

-Pie chart
-Bar chart

Question 16

Florence Nightingale

Answer 16

Question 17

Displaying Qualitative (nominal, ordinal) Data

Answer 17

Question 18

Types of Variables_Quantitative (Numeric)

Answer 18

Meaningful numeric scales

Age, blood pressure, # of friends, temperature

Assigned numbers have total mathematical meaning

1 ≠ 2; 2 ≠ 3
5 > 4 > 3 > 2 > 1
4 is indeed two times larger than 2
(4-3) = (3-2) = (2-1)

Question 19

Classification of QUANTITATIVE VARIABLES
Continuous vs Discrete

Answer 19

Question 20

Classification of QUANTITATIVE VARIABLES
Interval vs Ratio

Answer 20

Question 21

Numeric Variables; Measures of Central Tendency: 1- Mean

Answer 21

A sample MEAN is 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
Find the mean for the set of measurements:
2, 9, 11, 6, 6, 26
Solution: x̅=(2+9+11+6+6+26)/6=10

Question 22

Numeric Variables; Measures of Central Tendency: 2-Median

Answer 22

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
Find the median for the set of measurements: 9, 5, 11, 6, 6, 26
Solution:
Rank the measurements from smallest to largest: 5, 6, 6, 9, 11, 26
Find the middle observation(s)
Choose a value between the two middle observations
Median = (6+9) = 7.5
2

Question 23

Numeric Variables; Measures of Central Tendency: 3-Mode

Answer 23

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

Find the mode for the set of measurements:
2 9 11 6 6 26

Question 24

Displaying Distributions: Histogram

Answer 24

important to manage the intervals
-remember histograms is one bar that includes a group such as 70-80

Question 25

Shape of the Histogram Normal Distribution

Answer 25

Positively skewed looks like a P on his back.

Question 26

Numeric Variables: Measures of Variability (Spread, dispersion)

Answer 26

-The range for a variable is the difference between the minimum (lowest) and the maximum (highest) values in the data set
-Quartiles mark the three values that divide a data set into four equal parts
The interquartile range (IQR) captures the middle 50% of values for a numeric variable

Question 27

Boxplot: Display of Distribution

Answer 27

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

Question 28

Variance (σ2)

Answer 28

-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

-The standard deviation (σ) is the square root of the variance
-The 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 that number

Question 29

Mean (µ) and SD (σ) in a Normal distribution

Answer 29

-About 68% of area (population) within μ±1σ;
-95% of area within μ±2σ;
-99.7% of area within μ±3σ
If μ=20 and σ=5, then 68% of subjects are measured between 15 (20-5) and 25 (20+5)
The probability of observing a value between 15 and 25=0.68

between 10 and 30=0.95

between 5 and 35 =0.997

Question 30

Confidence Intervals (CI)

Answer 30

-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 95% confidence interval is usually reported for statistical estimates, which means that 5% of the time the confidence interval is expected to miss capturing the true value of a measure in the source population
–Example: mean systolic blood pressure of a sample is 120 mmHg; 95%CI: 110-130
-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

Question 31

Comparative Statistics

Answer 31

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)

Question 32

Inferential Statistics

Answer 32

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

Question 33

Hypothesis Testing

Answer 33

Question 34

Steps in Hypothesis Testing

Answer 34

1. Take a random sample from the population of interest
2. Set up two competing hypotheses (based on research questions)
   Null Hypthesis (H0); no effect, no difference between sample and the original population
   Alternative Hypothesis (H1 or Ha), there is an effect (a difference)
3. Use sample statistics (mean, frequency) to decide whether to support or reject the null
   By calculation of a test statistics
   Note: Tests are developed (specific formula) for different types of data and research questions (Figures 30-12 to 30-15 of the textbook)
4. Determine if the null hypothesis is really true, what the observed sample statistics will be
   How?

Question 35

Idea of (Probability) p. Value

Answer 35

Introduced by Fisher to determine whether the 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

Question 36

Idea of (Probability) p. Value

Answer 36

Is calculated from observed data based on a pertinent test statistic
The probability that the observed sample will produce a value of the test statistics as or more extreme than the observed test statistic in a universe in which we know that null in true
If 0.01 it means if in the real-world null is true (no difference) there is only 1% chance that the data produce results on a difference
Small chance, we can safely reject the null
The significance level (α) is the p value at which the null hypothesis is rejected, usually 0.05 in health research

Question 37

A parametric test

Answer 37

assumes the variables being examined have particular distributions
Inferential methods are based on types of distributions (mostly normal)

Question 38

A nonparametric test

Answer 38

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