Lec 1 & TB

Question 1

2 main types of data

Answer 1

• Continuous
• Discrete

Question 2

• Define discrete data or 2 types of discrete data
  
  • 3 types of categorical data

Answer 2

Discrete data:

• counts, # of times smth happens
• Categorical: put in categories
  
  • Binary (0/1)
  • Ordered/ordinal: the order is meaningful; but the distance b/w each is not
    
    • E.g. S,M,L; agree, n0, disagree
    • IOW: no meaningful distance b/w S to M
  • Unordered/nominal: names; no logical order
    
    • race, sex

Question 3

Define continuous data

• 2 types of cont data

Answer 3

• Cont data: measured quantities that can be measured to infinite prevision (eg height, weight, BP); difference b/w the intervals are meaningful
• Sometimes data are technically discrete are treated like cont data (eg SF-26 QoL instrument)
  
  • Eg: likert scale is ordinal
    
    • Goal: add them up -> total #
    • Since the stuff you add up are diff v, it ends up LIKE a cont v
• 2 types of cont data
  
  • Ratio: has TRUE meaningful zero (eg height, weight)
  • Interval: zero is arbitrary (eg scale data, temp)
    
    • Eg 0 in dC: freezing pt h2o
    • Eg 0 in dF: freezing pt of salt h2o

Question 4

define “X”

Answer 4

• “X”: variable of interest
• “xi”: the subscript number is a specific item in the data set
• N: number in pop
• “n”: lower case is # in sample
• fi = frequency of xi
• f = total # of observations in an interval
• ∑ = sum
• X
• Greek letters represent pop characteristics (parameters)
  
  • µ = pop mean
  • σ² = pop variance
  • σ = pop SD
• Roman letters rep sample characteristics (stats)
  
  • x̄ = sample mean
  • s²: sample variance
  • s = sample sd

Question 5

Type of data described by descriptive statistics

What does the distribution of data tells us?

Answer 5

• Descriptive stats describe characteristics relating to distribution of data
• The most appropriate descriptive stats depend on data distribution
• Distribution of data = pattern of observations

Question 6

mean

• Where is the mean if the graph is right skewed?
• Where is the mean if the graph is left skewed?
• Geometric mean
• Arithmetic mean

median

• define
• odd vs even # of observations

mode

Answer 6

mean = avg

• -ve or right skewed, mean is shifted to right
• +Ve or left skewed, mean is shifted to left
• Geometric mean: multiple then root
• Arithmetic mean: add then divide

Median

• (Q2): middle data value
• Odd # of observations: median = middle #
• Even # of observations: median = avg of 2 middle vales

Mode

• The # is most frequently occurring in the data set

Question 7

• 5 number summary
• How to get Q1 and Q3

Answer 7

• 5 # summary: min, Q1, Q2, Q3, max
• Quartiles
  
  • Sort the data
  • Q1 = (n+1)/4 th ordered observation
  • Q3: 3(n+1)/4 th ordered observation

Question 8

Formulas

• sample variance
• coefficient of variation

Answer 8

Sample variance: Right formula of image

Sample standard deviation: s = √s2

Interquartile range: IQR = Q3 − Q1

Range: Max − Min

Coefficient of variation: CV = (s/x)(100)% (Only valid for ratio data)

Question 9

degree of freedom

Why do we √ the variance

When is the empirical rules used?

Empirical rule

x

How do we determine outliers if data is asymmetrical, not normally distributed

Answer 9

Degrees of freedom

• df of an estimate is the # of independent pieces of info used to obtain the estimate
• x
• √ the variance gives us the sd, and restores the original unit
• X
• If the freq distribution is symmetrical and bell-shaped = normal distribution; empirical rule is used
• Empirical rule: for a normal distribution, all the data lies in 3 sd of the mean
  
  • 68% of data lie w/in interval µ +/- σ
  • 95% of data in µ +/- 2σ
  • 99.7% in µ +/- 3σ
• IOW: 0.3% of data are outliers
• x
• When we do not have a normal distribution/ data distribution is asymmetric, outliers are identified as
  
  • < Q1 – (1.5 x IQR)
  • > Q3 + (1.5 x IQR)

Question 10

Graphs that show distribution

Graph that show association

Models for inferences

Answer 10

• distributional: histogram, density plot, box-whisker plot, quantile-quantile (Q-Q) plot
• Association: scatter plot
• Inferences
  
  • t-tests (parametric), Wilcoxon (non-parametric)
  • Linear regression, analysis of variance (ANOVA)

Question 11

Graphs

• con
• most common graph

Descriptive stats

• what is displayed
• how do we display relationships

Answer 11

• Graphs
  
  • Challenging to display at times
  • Usually use dotplots
• Descriptive stats
  
  • # or prop (%) of each category
  • Crosstabulations b/w categorical v (have multiple v) to display relationships

Question 12

Inference and stat models

• binomial test
• fischer’s exact or X^2 test

Answer 12

Inference and stat methods

• Binary data: Binomial (prop) test (single sample)
• Fischer’s exact or X^2 test (chi-square test) (comparing samples)
• More than 2 categories, use chi-squared

Question 13

• Population
• Population parameters
• Sample
• Sample stats

Answer 13

Population vs samples

• Pop
  
  • Collection of all possible subjects
  • Parameters:
    
    • µ = mean[AL1]
    • sigma sq: variance
    • π = proportion w/ characteristic
  • Parameters: unknown constant to estimate
• Sample
  
  • Subset of pop (estimates of pop using sample)
    
    • x bar = mean
    • s^2 = sample variance
    • p = proportion in the sample w/ characteristic
  • Sample stats: variable b/c it depends on a particular sample
    
    • Used to estimate pop parameters

[AL1]“m” “mu” “mean”

“s” “sigma” “sd”

“p” “pi” “prop”

Question 14

Describe box plot

Answer 14

Box whisker