Statistics for Everyone Workshop Fall 2010

Part 1 Statistics as a Tool in Scientific Research: Summarizing & Graphically Representing Data Statistics for Everyone Workshop Fall 2010 Workshop presented by Linda Henkel and Laura McSweeney of Fairfield University Funded by the Core Integration Initiative and the Center for Academic Excellence at Fairfield University

Types of Research Questions Descriptive (What does X look like?) Correlational (Is there an association between X and Y? As X increases, what does Y do?) Experimental (Do changes in X cause changes in Y?) Different statistical procedures allow us to answer the different kinds of research questions Statistics as a Tool in Scientific Research

 Start with the science and use statistics as a tool to answer the research question Get your students to formulate a research question first: How often does this happen? Did all plants/people/chemicals act the same? What happens when I add more sunlight, give more praise, pour in more water? Statistics as a Tool in Scientific Research

Can collect data in class Can use already collected data (yours or database) Helping students to formulate research question: Ask them to think about what would be interesting to know. What do they want to find out? What do they expect? For example, what research questions might you ask from the survey? Descriptive, correlational, experimental Statistics as a Tool in Scientific Research

Categorical: male/female blood type (A, B, AB, O) Stage 1, Stage 2, Stage 3 melanoma Numerical: weight # of white blood cells mpg Types of Data: Measurement Scales

Categorical: Nominal (name/label) Ordinal (rank order) Numerical: Interval (equal intervals) Ratio (equal intervals and absolute zero) Types of Data: Measurement Scales

Nominal: numbers are arbitrary; 1= male, 2 = female Ordinal: numbers have order (i.e., more or less) but you do not know how much more or less; 1st place runner was faster but you do not know how much faster than 2nd place runner Interval: numbers have order and equal intervals so you know how much more or less; A temperature of 102 is 2 points higher than one of 100 Ratio: same as interval but because there is an absolute zero you can talk meaningfully about twice as much and half as much; Weighing 200 pounds is twice as heavy as 100 pounds Types of Data: Measurement Scales

1. What College are you from? CAS Business Engineering Nursing Other 2. How many years have you been teaching at Fairfield University? How important do you think it is to integrate statistics into your courses? Not at all Somewhat Important Important Very Important 4. How excited are you about integrating statistics into your courses? 1 2 3 4 5 6 7 Not at all Extremely excited excited Types of Data on Questionnaire

Are you male or female? 6. How many hours a week do you watch television on average? 7. How many hours a day do you spend on the internet on average? 8. Of the following reality/game shows, which one would you most like to be on? (a) Dancing With the Stars (b) American Idol (c) Bachelor/Bachelorette (d) The Apprentice 9. Can you roll your tongue? Yes No 10. How many siblings do you have? Types of Data on Questionnaire

Descriptive: Organize and summarize data Inferential: Draw inferences about the relations between variables; use samples to generalize to population Types of Statistical Procedures

The first step is ALWAYS getting to know your data  Summarize and visualize your data It is a big mistake to just throw numbers into the computer and look at the output of a statistical test without any idea what those numbers are trying to tell you or without checking if the assumptions for the test are met. Descriptive Statistics

Numerical Summaries: Frequencies Contingency tables Measures of central tendency Measures of variability Representing numerical summaries in tables Graphical Summaries: Bar graphs or Pie graphs Histograms Scatterplots Time series plot Descriptive Statistics

Frequency = number of times each score occurs in a set of data Relative Frequency = percent or proportion of times each score occurs in a set of data Summarizing and Reporting Categorical Data

Frequency Table

A display to summarize two categorical variables in a table. Each entry in the table represents the number of observations in a sample with a certain outcome for the 2 variables. Contingency Table

Contingency Tables

One categorical variable (e.g., Political party): Bar Chart or Pie Graph Two categorical variables (e.g., Political party vs. Gender): Side-by-side Bar Chart *Notice with 2 variables, one variable may be treated as the dependent variable and one variable may be treated as the independent variable. Choosing the Appropriate Type of Graph

One numerical variable (e.g., Height): Histogram One numerical variable and one categorical variable (e.g., Height vs. Gender): Side-by-side Histograms Two paired numerical variables (e.g., Weight vs. Exercise per week): Scatterplot One numerical variable over time (e.g., Number of Cells vs. Minutes): Time Series Plot *Notice with 2 variables, one variable may be treated as the dependent variable and one variable may be treated as the independent variable. Choosing the Appropriate Type of Graph

Bar Graph (Frequency)

Bar Graph (Relative Frequency)

Pie Chart

Simple Frequency Tables and Bar Graphs

Side by Side Bar Charts

Histogram of Simple Frequency Data

Side by Side Histograms

Scatterplot

Time Series Plot

Normal (approximately symmetric) Skewed Unimodal/Bimodal/Uniform/Other Outliers Shapes of Distributions

The Normal Curve “Bell-shaped” Most scores in center, tapering off symmetrically in both tails Amount of peakedness (kurtosis) can vary

Skew = Asymmetrical distribution Positive/right skew = greater frequency of low scores than high scores (longer tail on high end/right) Negative/left skew = greater frequency of high scores than low scores (longer tail on low end/left) Variations to Normal Distribution

Histogram Showing Positive (Right) Skew

Bimodal distribution:two peaks Rectangular/Uniform:all scores occur with equal frequency Potential Outlier: An observation that is well above or below the overall bulk of the data Important to determine normality (look at the histogram of the data) so you can choose appropriate measures of central tendency and variability Variations to Normal Distribution

Variations to Normal Distribution

Examples of Bad Graphs: What is Wrong With the Picture?

A BETTER Graph

Example of a Bad Graph Graph the distribution of the first digits.

Example of a GOOD Graph Graph the distribution of the first digits.

Example of a Bad Graph Graph the distribution of the number of bacteria in the cultures sampled.

Example of a GOOD Graph Graph the distribution of the number of bacteria in the cultures sampled.

Label both axes and provide a heading to make clear what the graph is representing. Vertical axes should usually start at 0 to help our eyes compare relative sizes. Remove any clutter that isn’t needed or is distracting The axes may need to be resized to remove extra white space Be careful in using unusual bars since it can be easy to get the relative percentages that the figures represent incorrect. Sometimes displaying information for more than one group on the same graph can be difficult especially when the values differ greatly. Consider using relative frequencies or separate graphs instead. Guidelines for Good Graphs

Y axis should be ¾ as tall as X axis When the number of score values on X axis is large, scores should be collapsed so there are at least 5 intervals but no more than 12 The width of each interval on the X axis should be equal Frequency on the Y axis must be continuous and regular Range on the Y axis and X axis must neither unduly compress nor unduly stretch the data Other Guidelines to Making Graphs

Looking at shape of distribution Making graphs Teaching tips: Hands-on practice is important for your students Sometimes working with a partner helps Time to Practice

Statistics for Everyone Workshop Fall 2010