week 2 - data wrangling

Question 1

Statistics & Samples

Answer 1

• Types of Data
  
  • Data = measurements of 1/+ variables made on a sample of individuals.

Question 2

Categorical Variables

Answer 2

• Describe membership in a category/group.
• Describe qualitative characteristics of individuals that do not correspond to a degree of diff. on a numerical scale.
• Categorical variables = attribute/qualitative variables.
• E.g. survival (alive or dead),
• Nominal if the diff. categories = no inherent order.
• Nominal = name.
• values of an ordinal categorical variable = ordered.
• Magnitude of the diff betw. consecutive values = not known.
• Ordinal = having an order

Question 3

Numerical Variables

Answer 3

• When measurements of individuals = quantitative & have magnitude.
• Numbers.
• E.g core body temp. (e.g., degrees Celsius [°C])
• Either continuous/discrete.
• Continuous numerical data
  
  • Take on any real-number value within some range.
  • Betw any 2 values of a continuous variable, an infinite number of other values = possible.
  • Continuous data = rounded to a predetermined number of digits, set for convenience
• Discrete numerical data
  
  • Data come = in indivisible units.
  • Often analyzed as though they = continuous, if large # of possible values.
• Numbers might also be used to name categories
• Numerical data = be reduced to categorical data by grouping → result contains less info

Question 4

Explanatory & Response Variables

Answer 4

• To relate 1 variable to another by examining associations betw. variables & differs betw. groups.
• Measuring an association = measuring a difference
• Goal = to assess how well 1 of the variables (explanatory variable) predicts/affects the other variable (response variable).
• Treatment variable = manipulated by the researcher → explanatory variable
• Measured effect of the treatment → response variable.
• Neither variable = manipulated by the researcher → association
• described by the “effect” of 1 of the variables on the other → not direct evidence for causation.
• IV = explanatory
• DV = response

Question 5

Frequency Distributions

Answer 5

• Diff individuals in a sample = diff.
• Measurements → observed by frequency dist.
• Freq. of a specific measurement in a sample = #of observations having a particular value of the measurement.
• Freq. dist shows how often each value of the variable occurs in the sample
• Informs us about the dist of the variable in the pop. it came from.
• Gives intuitive understanding of the variable.

Question 6

Probability Distribution

Answer 6

• Distribution of a variable in the whole pop. = prob dist.
• Real prob in nature = almost never known.
• Researchers → theoretical prob dists to approx the real prob dist.

Question 7

Normal Distribution

Answer 7

• Normal dist = “bell curve.”
• Most important prob. dist. in stats.

Question 8

Describing Data - Sample Mean

Answer 8

• Avg. of the measurements in the sample
• Sum of all observations divided by # observations
• x̄ (symbol)

Question 9

Describing Data - Variance & Standard deviation (SD)

Answer 9

• Used to measure of the spread of a dist
• How far from the avg the observations =
• SD = large → most observations = far from mean
• SD = small → most observations = close to mean
• Calc. from variance
• SD = square root of variance
• SD = better b/c = same units as variable
• Deviation from mean = diff. betw. measurement & mean
• -ve deviations cancel +ve deviations
• Need to avg squared deviations
• Deviations above & below the mean contribute +ly to var
• Never -ve & same units as OG observations
• SD = connected to freq. dist. b/c bell-shaped freq, then ⅔ of observations = lie in 1SD of the mean & 95% = lie 2SD

Question 10

Describing Data - Coefficient of Variations (CV)

Answer 10

• Calcs. the SD as a % of mean
• High CV = more variability
• Low CV = individuals = similar & more relative to mean

Question 11

Median

Answer 11

• Middle observation in data set
• Dividing data set into 2 by sorting from smallest to largest
• Even # of observation find average of middle values

Question 12

IQR

Answer 12

• Dividing data into quarters
• Q1 = middle value lying below the median
• Q2 = median
• Q3 = middle value lying above the median
• IQR = Q3 - Q1

Question 13

Box Plots

Answer 13

• Shows median & IQR
• Lower & upper edges = Q1 & Q3 → span of the box

Question 14

Measuring Spread & Location Comparison - Mean vs median

Answer 14

• Median = middle measurement of a dist.
• Mean = center of all points including to outliers → balance
• Mean = sensitive to extreme outliers
• Median = unaffected
• Mean = displaced from location of normal measurement when freq. dist. = strongly skewed → extreme values

Question 15

Measuring Spread & Location Comparison - SD vs. IQR

Answer 15

• Calc from square of deviations → more sensitive to extreme observations
• IQR = better indicator of spread b/c strongly skewed data due to extreme values
• SD reflects variation among all data points

Question 16

Estimating w/ Uncertainty

Answer 16

• Estimation = process of inferring a pop parameter from sample data.
• All estimates = sampling dist, → prob dist of all the possible values of the estimate that might be obtained under rando sampling w/ given sample size.
• Standard error (SE) of an estimate = SD of its sampling dist.
• SE measures precision.
• Smaller SE = more precise estimate
• SE & CI assume that sampling = rando
• SE of estimate declines w/ increase in sample size
• CI = range of values calced from sample data → likely to contain within its span the value of the target parameter.
• 95% CIs calced from independent random samples = include the value of the parameter 19/20 times
• 2SE rule = rough approx to the 95% CI for a mean.
• Error bars to graphs reps SEs/CIs