STA 490H1S Initial Examination of Data
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1 Initial Examination of Data Alison L. Department of Statistics University of Toronto Winter 2011
2 Course mantra It s OK not to know. Expressing ignorance is encouraged. It s not OK to not have a willingness to learn.
3 Initial Examination of Data Purpose: Understand the structure of the data.
4 Initial Examination of Data Purpose: Understand the structure of the data. Types of variables: Quantitiative: continuous or discrete Categorical: nominal, ordinal (e.g., Likert scales or binned quantitative), binary
5 Initial Examination of Data Purpose: Understand the structure of the data. Types of variables: Quantitiative: continuous or discrete Categorical: nominal, ordinal (e.g., Likert scales or binned quantitative), binary Check the quality of the data. Find errors (data cleaning). Check for credibility, consistency, completeness. Identify potential outliers. Are there missing observations?
6 Initial Examination of Data Purpose: Understand the structure of the data. Types of variables: Quantitiative: continuous or discrete Categorical: nominal, ordinal (e.g., Likert scales or binned quantitative), binary Check the quality of the data. Find errors (data cleaning). Check for credibility, consistency, completeness. Identify potential outliers. Are there missing observations? Clear up any problems.
7 Initial Examination of Data Purpose: Understand the structure of the data. Types of variables: Quantitiative: continuous or discrete Categorical: nominal, ordinal (e.g., Likert scales or binned quantitative), binary Check the quality of the data. Find errors (data cleaning). Check for credibility, consistency, completeness. Identify potential outliers. Are there missing observations? Clear up any problems.
8 Initial Examination of Data Purpose: Understand the structure of the data. Types of variables: Quantitiative: continuous or discrete Categorical: nominal, ordinal (e.g., Likert scales or binned quantitative), binary Check the quality of the data. Find errors (data cleaning). Check for credibility, consistency, completeness. Identify potential outliers. Are there missing observations? Clear up any problems. Get ideas for more sophisticated analyses.
9 Initial Examination of Data Purpose: Understand the structure of the data. Types of variables: Quantitiative: continuous or discrete Categorical: nominal, ordinal (e.g., Likert scales or binned quantitative), binary Check the quality of the data. Find errors (data cleaning). Check for credibility, consistency, completeness. Identify potential outliers. Are there missing observations? Clear up any problems. Get ideas for more sophisticated analyses. Check on whether or not assumptions of more sophisticated analyses seem reasonable.
10 IDA Should be motivated by original research questions.
11 IDA Should be motivated by original research questions. Avoid data dredging. (Look long enough and you ll find some meaningless pattern.)
12 IDA Should be motivated by original research questions. Avoid data dredging. (Look long enough and you ll find some meaningless pattern.) Trivial? Requires judgment and common sense.
13 Types of Missing Data 1. Missing Completely At Random (MCAR) The probability that a data value is missing does not depend on the missing value, nor on the values of all other variables.
14 Types of Missing Data 1. Missing Completely At Random (MCAR) The probability that a data value is missing does not depend on the missing value, nor on the values of all other variables. 2. Missing At Random (MAR) The probability that a data value is missing, conditional on the values of the other variables for the observation, is not related to the missing value.
15 Types of Missing Data 1. Missing Completely At Random (MCAR) The probability that a data value is missing does not depend on the missing value, nor on the values of all other variables. 2. Missing At Random (MAR) The probability that a data value is missing, conditional on the values of the other variables for the observation, is not related to the missing value. 3. Informative / Non-ignorable (NMAR) Difficult to deal with.
16 Tools for IDA 5 number summary (for all data and for subsets).
17 Tools for IDA 5 number summary (for all data and for subsets). Other summary statistics, e.g., mean and s.d.
18 Tools for IDA 5 number summary (for all data and for subsets). Other summary statistics, e.g., mean and s.d. Histograms / stem-and-leaf plots.
19 Tools for IDA 5 number summary (for all data and for subsets). Other summary statistics, e.g., mean and s.d. Histograms / stem-and-leaf plots. Frequency tables (1- and 2-way) for categorical variables
20 Tools for IDA 5 number summary (for all data and for subsets). Other summary statistics, e.g., mean and s.d. Histograms / stem-and-leaf plots. Frequency tables (1- and 2-way) for categorical variables Scatterplots.
21 Tools for IDA 5 number summary (for all data and for subsets). Other summary statistics, e.g., mean and s.d. Histograms / stem-and-leaf plots. Frequency tables (1- and 2-way) for categorical variables Scatterplots. Correlations.
22 Some More Sophisticated Tools for IDA
23 Some More Sophisticated Tools for IDA Kernel Density Estimation Smoothed function to estimate the density function. Amount of smoothing controlled by the bandwidth. Non-parametric (that is, doesn t make an assumption about the distribution).
24 Some More Sophisticated Tools for IDA Kernel Density Estimation Smoothed function to estimate the density function. Amount of smoothing controlled by the bandwidth. Non-parametric (that is, doesn t make an assumption about the distribution). LOWESS (LOESS): Locally Weighted Scatterplot Smoothing Idea: fit a simple polynomial using regression on a small ranges of the independent variable, and smoothly join up the pieces. Amount of smoothing controlled by a smoothing parameter.
25 Course mantra It s OK not to know. Expressing ignorance is encouraged. It s not OK to not have a willingness to learn.
26 For Thursday: Hand in your meeting summary to your TA advisor. Be ready for a discussion about a plan for the project: Data cleaning / IDA What methods of analysis might be appropriate.
27 For next class (Tuesday, February 1) Read Chapters 11 and 12 in Chatfield. Bring the text to class.
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