Intro to statistics

• Statistics


  A way to get information from data and a tool for creating new understanding from a set of numbers
• Types of statistics


  • Descriptive statistics
  • Inferential statistics
• Descriptive statistics


  • Involve summarizing data, such as calculating averages, ranges, and frequencies
• Techniques of descriptive statistics

  • Graphical techniques
  • Numerical techniques
• Numerical techniques of descriptive statistics include mean, median, and range
• Inferential statistics


  Involves making inferences and drawing conclusions about a population based on a sample
• Population


  Very large group
• Sample


  Smaller group
• Parameter


  Characteristic of the population
• Statistic


  Characteristic of the sample
• In inferential statistics, we use a sample to draw conclusions about the parameters that might be true or might not be true
• Statistical inference is the process of making an estimate about a population based on a sample
• We use statistics to make inferences (predictions) about parameters because it is easier and sometimes less expensive, but it is not always correct
• Measures used in statistical inference

  • Confidence level
  • Significance level
• Confidence level is the proportion of times that an estimate will be correct, while significance level is the proportion of times that an estimate will be wrong
• The range is the difference between the highest and lowest values, and the smaller the range, the more accurate the prediction
• The significance level is represented by the Greek letter alpha (α)
• Classes


  Series of intervals that has a range of observations
• Interpreting classes


  Histogram (bar chart)
• Sturge's formula


  1+3.3log(n) - to determine how many classes should be defined
• Shapes of histograms


  • Symmetric
  • Positively skewed
  • Negatively skewed
  • Unimodal (one peak)
  • Bell-shaped
• Cross-sectioned data


  Observations measured at the same point in time (regardless of the time)
• Time series data


  Observations measured at successive points in time (attention of the time)
• Modality


  Unimodal & Bimodal
• Frequency and relative frequency tables and cross-classification table (Contingency) are used to identify patterns in data
• Interval data


  Scatter diagram is used to understand how two interval variables are related
• Scatter diagrams


  Show the relationship between two variables
• Ogive


  Classifying data into intervals
• Positive linear trend
• Negative linear trend