Statistics is... a collection of techniques for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data... statistics uses data to gain understanding, to answer questions…or as the textbook says: “the science of learning from data” A dataset is… a collection of information about individuals (or observations) "measured" on variables

A variable is… any characteristic of an individual or observation. a variable takes on different values for different observations… the distribution of a variable tells us what values it takes on and with what frequency or relative frequency. We are interested in analyzing the distributions of variables both graphically and numerically … Variables come in two basic varieties… categorical - puts an individual into categories or into its levels quantitative - takes on numerical values, like measurements or counts or rates

The first 10 observations of Dr. Padgett's dataset are given above. plantno marsh form type flower plantht lleaves totmass bllenavg 132 si un unk no 56.5 8 4.513 33.1625 133 si un unk no 45.8 9 3.591 29.0111111 137 si un unk no 62.5 8 3.2994 20.425 138 si tn tall no 48 4 1.3218 31.8 139 si tn tall no 65.6 9 3.7607 31.4333333 140 si tn tall no 43.2 6 1.9402 22.95 141 si un unk no 26 4 0.583 13.275 142 si tn tall no 36.7 3 1.0668 30.3333333 143 ph tn tall no 111 8 9.935 47.3 144 ph tn tall no 98 6 11.345 47.95 The first 10 observations of Dr. Padgett's dataset are given above. The categorical variables are marsh, form, type and flower. Their values are categories. The quantitative variables are plantht, lleaves, totmass, and bllenavg. Notice that their values are numbers obtained by counting, measuring, or by computing ratios.

Graphical analysis of data Graphs help us visually understand the distribution of a variable… The type of graph used in an analysis depends on the type of variable. For categorical variables, we use bar graphs or pie charts For quantitative variables, we use histograms or stemplots or … In the special circumstance that observations are ordered in time, we can make time plots to look for trends in the variable over time… Analyze the distributions of the variables in Dr. Padgett's dataset, using JMP to see the graphics available there. Make sure you understand what they mean.

Once a graph of the variable is made, we can begin to understand its distribution by looking at the following: look at the overall pattern in the graph and for striking deviations from that overall pattern. Peaks? Gaps? Symmetric? Skewed? describe the overall pattern of the distribution by talking about its shape, center, and spread (or variation). look for possible outliers in the distribution; i.e., those values of the variable that seem to fall outside the overall pattern you see. These features will be important for all types of graphs…

For categorical variables, the best we can do is count the number of observations in each category (and compute the percent in each category). The bar graph plots the counts or percents falling in each of the categories… below is the distribution of the highest educational level of people in the U.S. aged 25-34 years…see 1.1, 2/8 . This variable is categorical but is also called ordinal since its values can be ordered in some sense.

Example: Top 10 causes of death in the United States 2001 Rank Causes of death Counts % of top10 % of total deaths 1 Heart disease 700,142 37% 29% 2 Cancer 553,768 23% 3 Cerebrovascular 163,538 9% 7% 4 Chronic respiratory 123,013 6% 5% 5 Accidents 101,537 4% 6 Diabetes mellitus 71,372 3% 7 Flu and pneumonia 62,034 8 Alzheimer’s disease 53,852 2% 9 Kidney disorders 39,480 10 Septicemia 32,238 1% All other causes 629,967 26% For each individual who died in the United States in 2001, we record what was the cause of death. The table above is a summary of that information. Why are the percentages in the two columns different??

Ways to graph quantitative data Line graphs: time plots Use when there is a meaningful sequence, like time. The line connecting the points helps emphasize any change over time. Histograms and stemplots These are summary graphs for a single variable. They are very useful to understand the pattern of variability in the data. Other graphs to reflect numerical summaries.

Line graphs: time plots In a time plot, time always goes on the horizontal, x axis. We describe time series by looking for an overall pattern and for striking deviations from that pattern. In a time series: A trend is a rise or fall that persist over time, despite small irregularities. A pattern that repeats itself at regular intervals of time is called seasonal variation.

http://www.eia.doe.gov/oil_gas/petroleum/info_glance/petroleum.html For quantitative variables, we'll consider both stemplots and histograms - stemplots are much easier to draw and interpret… see Table 1.2 and consider the female literacy rates in Islamic countries in Ex.1.7 (1.1, 4/8) The tens digit becomes the stem, and the units digit becomes the leaf (see Fig. 1.5)

Histograms break up the range of values of the variable into intervals (on the horizontal axis) and displays (on the vertical axis) the count (or percent) of observations falling into those intervals - choosing the number of intervals and/or the width of the intervals can be problematic… usually histograms are made by computer programs (like JMP). See Fig. 1.7, p. 14 (1.1, 5/8) Data is in table 1.3 (1.1, 5/8).

Homework Carefully read sections 1.1 and 1.2 Work through the examples in those two sections… Work on the following problems: #1.1-1.9 (these are scatted throughout section 1.1), 1.12-1.14, 1.17, 1.18, 1.20, 1.21, 1.23, 1.24, 1.25, 1.27, 1.37 Use JMP or an Applet for the following problems: 1.28-1.32, 1.39, 1.42, 1.43-1.45