Week 9: Descriptive and Comparative Statistics

Question 1

Research Process

Answer 1

Question 2

Descriptive Statistics

Question 3

Biostatistics

Answer 3

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 4

Univariate analysis

Answer 4

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

Question 5

Bivaraible analysis

Answer 5

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

Question 6

Multivariable analysis

Answer 6

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

Question 7

Advanced statistics should be used only when…

Answer 7

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

Question 8

Link to Study Design

Answer 8

Question 9

What is a Variable?

Answer 9

-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
  ØTo describes characteristic of a person, place, thing, or idea
  We measure variables when an experiment is carried out or an observation is made (week 5-2)

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
  ØTo describes characteristic of a person, place, thing, or idea
  We measure variables when an experiment is carried out or an observation is made (week 5-2)

Question 11

What is The Big Picture?

Answer 11

Question 12

Types of Variables

Answer 12

Quant.dis.con

Qual.no.or

Question 13

(Qualitative)
Types of Variables

Nominal

Answer 13

ØNo intrinsic or logical order or value
-University programs
-Countries
ØTypes of fruits
ØYou can assign numbers to different categories
Ø1=apple
Ø2=peach
Ø3=pair
ØBut they do not have any other numeric properties
Ø
ØDoing arithmetic (e.g., 1 + 2 = 3) is nonsensical

Question 14

(Qualitative)
Types of Variables

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
Ø (4-3) = (3-2) = (2-1)
Ø 4 is not two times larger than 2

Question 15

How can you display qualitative(nominal, ordinal) data ?

Answer 15

Question 16

Who in the absolute fuck is Florence Nightingale

Answer 16

the lady with the pie chart

Question 17

How else can we display qualitative (nominal, ordinal) data?

Answer 17

-Frequency tables

Question 18

Classification of Quantitative Variables
What is the difference between Continuous and Discrete

Answer 18

Question 19

Quantitative Variables: Interval vs Ratio
What is the difference?

Answer 19

Question 20

Numeric Variables; Measures of Central Tendency:
Mean

Answer 20

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 21

Median

Answer 21

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

Question 22

Mode

Answer 22

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 23

Displaying Distributions: H

Answer 23

Histograms
-important to manage the intervals

Question 24

Shape of the histogram: Normal Distribution

Answer 24

Question 25

Number Variables: Measures of Variability (Spread, dispersion)

Answer 25

-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 26

Boxplot: Display of Distribution

Answer 26

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

Question 27

Variance (σ2)

Answer 27

standard error of the mean ADJUSTS FOR THE NUMBER OF OBSERVATIONS

Question 28

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

Answer 28

Question 29

Confidence Intervals (CI)

Answer 29

-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 30

Comparative Statistics
what are we comparing and in what type of studies?

Answer 30

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 31

Inferential Statistics

Answer 31

ØTechniques 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
ØDecision about parameters via information obtained from a sample is via hypothesis testing

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

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

Question 34

What are the four steps for 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 and Alternative
3.Use sample statistics (mean, frequency) to decide whether to support or reject the null
By calculation of a TEST STATISTICS
4. DET IF the null hyp is really true, what the observed sample statistics will be

Question 35

Steps for Hypothesis Testing
1

Answer 35

1. Take a random sample from the population of interest

Question 36

Steps for Hypothesis Testing
2

Answer 36

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)

Question 37

Steps for Hypothesis Testing
3

Answer 37

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)

Question 38

Steps for Hypothesis Testing
4

Answer 38

4. Determine if the null hypothesis is really true, what the observed sample statistics will be
   How?
   Idea of (Probability) p. Value
   ØIntroduced by Fisher to determine whether the observed sample supports the null
   ØBetween 0.1 and 0.9: no reason to suspect null is false
   Ø<0.02 sufficiently strong evidence to conclude null does not reflect the state of nature, unlikely to be true
   Ø“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.”
   Ø0.05 the convention commonly used in health research
   * P.value measures how strongly the sample data agrees with the null
   ØIs calculated from observed data based on a pertinent test statistic
   ØThe 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
   ØIf 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
   ØSmall chance, we can safely reject the null
   ØThe significance level (α) is the p value at which the null hypothesis is rejected, usually 0.05 in health research