terms

• Statistics


  The science of collecting, classifying, and interpreting data
• Observational Study


  Observe a group and measure quantities of interest. This is passive data collection in that one does not attempt to influence the group. The purpose of the study is to describe the group
• Experiment


  Deliberately impose treatments on groups in order to observe responses. The purpose is to study whether the treatments cause a change in their responses.
• Population


  Entire group of interest
• Sample


  A part of the population selected to draw conclusions about the entire population
• Census


  A sample that attempts to include the entire population
• Parameter


  A concept that describes the population (mean, median, stdev, variance)
• Statistic


  A number produced from a sample that estimates a population parameter
• Experimental Group


  A collection of experimental units subjected to a difference in treatment, imposed by the experimenter
• Control Group


  A collection of experimental units subjected to the same conditions as those in an experimental group except that no treatment is imposed
• Confounding Effects


  When you have multiple factors in a study and you can't tell which factor causes a change in the variable of interest
• Variable


  Any characteristic or quantity to be measured on units in a study
• Categorical Variable


  Places a unit into one of several categories (examples: gender, race, political party)
• Quantitative Variable


  Takes on numerical values for which arithmetic makes sense (examples: SAT score, number of siblings, cost of textbooks)
• Univariate


  Data has one variable
• Bivariate


  Data has two variables
• Multivariate


  Data has three or more variables
• Frequency


  Number of times the value occurs in the data
• Relative frequency


  Proportion of the data with the value
• "Typical" Concentration


  Generally characterized by the center of the data (the mean of the sample/population)
• Spread


  Wide vs. narrow, describes how much "stuff" is under the curve
• Histogram


  Bar graph of binned or grouped data where the height of the bar above each bin denotes the frequency (relative frequency of values in the bin)
• How do you choose the number of histogram bins?

  # of bins = sqrt(number of observations)
• Symmetric data


  Has roughly the same mirror image on each side of a center value
• Skewed data


  One side (either left or right) which is much longer than the other relative to the mode (peak value).

  
  

  It is skewed in the direction that you'd think the skier on a slope would fall.

  
  

  Example: hump on left, right-skewed.
• Multi-modal data


  Data has more than one mode
• Measures of Central Tendency

  Sample median and sample mean
• Sample Median


  Middle observation if the values are arranged in increasing order
• Sample mean


  The average of n observations, aka the sum of the values divided by the number "n" observations.
• First Quartile (Q1)


  25th percentile of the data
• Second Quartile (Q2)


  50th percentile of the data (median)
• Third Quartile (Q3)


  75th percentile of the data
• 5-number summary


  Min, Q1, Q2, Q3, and Max values
• Boxplots


  Graphically displaying the 5-number summary
• Measures of Spread


  Interquartile range, sample variance, and sample standard deviation
• Interquartile Range


  IQR = Q3 - Q1 = range of the middle 50% of the data
• Sample Variance


  Sum of squared deviations from the sample mean divided by n-1

  
  

  The n-1 term is essentially degrees of freedom.
• Sample Standard Deviation


  Square root of the variance, where the variance is the sum of squared deviations from the sample mean divided by n-1.
• Random Process


  A process whose outcome cannot be predicted with certainty
• Sample Space


  The collection of all possible outcomes to a random process