statistics david pieper, ph.d. [email protected]
TRANSCRIPT
Types of Variables Categorical Variables
• Organized into category• No necessary order• No quantitative measure• Examples
• male, female• race• marital status• treatment A and treatment B
Types of Variables Ordinal Data
• Ranked or ordered
• Examples:– strongly agree, agree, disagree– worse, no change, better– 1st place, 2nd place, 3rd place
Types of Variables Continuous Variables
• Have specific order• Examples:
– weight– temperature– blood pressure– time
• May be converted to categorical or ordinal
Types of Statistics
• Descriptive– summarize data for clearer understanding
• Inferential– generalize results from sample to
population– make probability decisions
Descriptive Statistics• Measures of central tendency
– mean – mode– median
• Measures of variability– range– variance– standard deviation– standard error
Research Hypothesis
• Null hypothesis: relationship among phenomena does not exist
• Example: kids who attend daycare have no greater incidence of colds than kids who do not attend daycare
Probability and p Values
• p < 0.05– 1 in 20 or 5% chance groups are not
different when we say groups are significantly different
• p < 0.01 – 1 in 100 or 1% chance of error
• p < 0.001– 1 in 1000 or .1% chance of error
Type of Statistical Test to Use
• Continuous variable as end point
– 2 groups: t-test
– 3 or more groups: ANOVA
• Relation between 2 categorical variables:
– Chi-square test
– Fisher’s Exact test (2 x 2)
• Relation between 2 continuous variables:
– Regression analysis or correlation
T-test• When comparing 2 independent
groups and end-point variable (dependent variable) is continuous
• Purpose is determine if the difference between the 2 groups is unlikely due to chance
• May be paired or unpaired
T-test
• Example:
• Blood pressure before and after exercise program (paired t-test)
• Compare blood pressure in a group undergoing cardiac rehab to a control group not undergoing rehab (unpaired t-test)
Analysis of Variance (ANOVA)
When comparing 3 or more groups (independent variables) and end-point (dependent variable) is continuous.
Analysis of Variance (ANOVA)
Treatment A Treatment B Treatmnet C
Patient 1 25 10 23
Patient 2 30 13 28
Patient 3 32 15 30
Patient 4 26 14 32
Patient 5 24 15 25
Analysis of Variance (ANOVA)
Treatment A Treatment B Treatmnet C
mean SE
27.4 1.5 13.4 0.9 27.6 1.6
p < 0.001 overall there is a difference between groups - does not tell us which groups are different from one another
Post-hoc analysis with Tukey’s multiple comparison test
A vs B p < 0.001A vs C p > 0.05 (not significantly different)
B vs C p < 0.001
Chi-square Test
• When comparing 2 or more groups and the dependent variable is categorical
• Minimum frequency in any cell must be at least 5
• If less than 5 and a 2 x 2 analysis - use Fisher’s Exact Test
Is there a relationship between hypertension and gender?Chi square analysis - p < 0.001
Correlation or Regression
• When determining if there is a linear relationship between 2 continuous variables
• Ranges from -1 to 1
• Assumptions:
– Relationship is linear
– Random variables
Pearson’s Correlation CoefficientDiastolic BP (mm) Weight (kg)
90 82
140 114
68 56
110 62
100 83
95 110
Is Diastolic BP related to Weight?
r = 0.805 p < 0.01
Pearson’s Correlation Coefficient
• r = 0.805 does not mean weight gain causes increase in BP or vice versa
• Correlation does not prove cause and effect
Type of Variable Descriptive Statistics Compare Groups Relationship of Groups
Nominal (Categorical)
(Non-parametric)
Central Variability Tendency Mode
1 or 2 groups 3 groups
2
Fisher’s Exact Test
2
Ordinal (Ranks)
Mode Range Median
Mann-Whitney Kruskal-Wallis Wilcoxon
Spearman’s Rank Order
Interval or
Ratio
(Continuous) (Parametric)
Mode Standard deviation Median Standard Mean error Confidence Variance Interval Range
t-test ANOVA
Pearson’s r
Regression
Name the Statistical Test
Do students improve their knowledge after a lecture, as measured by the number of correct answers on a
quiz before and after the lecture?
a. ANOVA
b. Chi-Square
c. Paired t-test *
d. Unpaired t-test
Name the Statistical Test
Is there an association between smoking status and 3 levels of socioeconomic status?
a. Mann-Whitney U-test
b. Pearson’s correlation
c. Turkey’s test
d. Chi-Square *
Name the Statistical Test
Is there a relationship between length of hospitalization and number of medications
prescribed when patient is discharged?
a. Logistic regression
b. Pearson’s correlation *
c. Repeated measures ANOVA
d. Chi-Square
Free Statistics Software
http://freestatistics.altervista.org/click/fclick.php?fid=4
Illustrations• Graphs - not tables
• Replace keys with direct labels
• Use color
• Each axis must have a label with units
• Each graph must have a legend
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Jan Feb Mar April
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core
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) Girls
Boys