introduction to statistics - chapter 3-5 notes (2)

8/12/2019 Introduction to Statistics - Chapter 3-5 Notes (2)

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Introduction to Statistics

Lecture Notes

Chapters 3-5

Please sign in (SIGNATURES) as you come in to class. It will savemy voice instead of my taking attendance (this is only to settle the

class roster).



What’s up with the powerpoint?

I don’t usually use slides, but am going to try to usethese to save my voice somewhat.

Notes: Still working on getting the class roster

settled. Has been some movement on the waitlist,will keep in touch as things develop. Be sure you’ve

signed in!

First homework is posted (on our course website),

but isn’t due until next Friday (the 4th). Theadditional problem is NOT optional, that just means it

is not a book problem.



Handouts for Today

There is one handout on graphs/descriptive statisticsgoing around. Save this to use tomorrow in class.

There is a second handout – the anonymous survey

largely designed by the class on Monday. Please goahead and take a few minutes to fill this out (no

names!) and get it back to me. We’ll take a look at

this data next week in lab.

If you missed class Monday, I have extra course

syllabuses at the front as well.



The “W”’s of a Data Set

Who – the observations (population – set of all objectsyou are interested in obtaining the value of some

parameter for – since we usually can’t observe all

objects, we take a sample of objects – a subset of the

overall population of objects to observe) Note: There is NO such thing as a population sample or

sample population.

What – the variables

Why – why was the data collected

How – how was the data collected (related to

design/sampling in chapters 12-13)

When/Where – more information that could be relevant



Chapters 3-5 Overview

Covers basic graphs and descriptive statistics forboth categorical and quantitative variables

This is what you would do as a “preliminary analysis”

for a variable.

Recall: a data set can have multiple variables in it.

These chapters focus on mostly univariate (single

variable) analyses. There is one comparative graph

– a side-by-side boxplot in Chapter 5.



3 Rules of Data Analysis

Rule 1- Make a picture Rule 2 – Make a picture (really, before you do

anything else)

Rule 3 – Make a picture (really, we mean a well-

chosen picture for your variables)



Categorical Variable Prelim Analysis

Frequency tables (one variable) – summarize countsby category

Contingency tables (2 or more variables) –

summarize counts by category for multiple variables

Bar charts Pie charts



Frequency

What is f requency ? Frequency is the number of objects/cases per category

You can also look at relat ive frequ ency .

Relative frequency is the number of objects/cases per

category divided by the total number of objects. Hence it gives proportions for each category out of the

total.

It is often converted to %.



Bar Charts

One bar per category – height is determined byfrequency or relative frequency

Order of categories is arbitrary.

Does NOT let you talk about the shape of a

distribution.

“Area” principle – areas are supposed to be relative.

This is often violated when people try to make

graphs “cool” and go 3-D, etc. (see Example passed

around).



Pie Charts

Take 100% of cases and divide up 360 degreesbased on relative frequencies.

We will look at bar charts over pie charts.

Note that for bar charts you do not need to create

bars for 100% of the cases. You could look at the top

three risk factors for a disease, etc. However, we

usually do have 100% of cases shown.



Contingency Tables - Example

See first page of Handout Totals for rows/columns give marginal dis t r ibut ion s

for each variable.

You can also look at condi t ional dis t r ibut ions . Fix

a row or column and work solely within that row orcolumn.

Concept of independence (will formalize later):

If the distribution of one variable is the same for all

categories of another variable, then the two variables are

independent.



On Your Own

Text has some discussion of segmented bar-chartsand side-by-side (feel free to read or skip)



Simpson’s Paradox

Something that can happen when you aggregatecategorical data

Looking at overall averages or % can be misleading

Can get different results looking at breakdown

Berkeley Discrimination Data Example (see bottom of

page one of the handout) Claims of Sexual Discrimination in1973 Graduate School

Admissions Overall, 44.28% of males who applied were admitted, while

only 34.58% of females were admitted. Look what happens when you breakdown by the 6 largest

departments though! (try this on your own or with a partner). Isthere evidence of discrimination against females at the dept.level? What is going on?



Quantitative Variables Preliminary Analysis

Graphs Dot plot – won’t use much – read about on your own

Stem and leaf – won’t use much – read about on your own

Histogram

Boxplot (chapter 5) Qqplot (Friday or next week)

Time plot (Friday or next week)

Descriptive statistics

Measures of center: mean, median Measures of spread: standard deviation, IQR, range



Describing the distribution of a quantitative

variable

You should focus on three things when describingthe distribution of a quantitative variable:

Shape – unimodal (one peak), bimodal (two peaks),

multimodal (many peaks), bell-shaped, skewed left (tail to

the left), skewed right (tail to the right), symmetric,

uniform (no peaks, basically flat)

Center – estimate the center (or use a descriptive

statistic)

If multiple peaks, report the peak locations

Spread – estimate the spread (can use a descriptivestatistic)



Dot Plot – On Your Own

Most basic quantitative graph Use for a low number of observations (<50)

Basically use a number line and place a dot above it

for each value you have observed.

Example from wikipedia:



Stem and Leaf – On Your Own

Your book discusses lots of options for these,including split leaves (which is something R/Rcmdr

will do).

Basics: You take your values and set a stem –

maybe tens. Then the leaves are the ones place. Foreach stem, you list the leaves that coincide in

numeric order.

Usually works decently for fewer than 100

observations Try it. Suppose you have scores on a pre-test for an

at-risk youth group as follows:

5, 11, 13, 21, 34, 36, 45, 47, 48, 48, 49



Histogram

Take the quantitative variable and break it up into “piles”or “bins” (usually the same width).

Count the number of observations in each bin or pile.

Plot the frequencies per bin.

Usually no spaces between bins (if there is, it is a gap –

NOT like a bar chart). You DO need to know the boundaries. (5,10], (10,15] as

bins IS different from [5,10),[10,15). (If anyone needs meto explain open/closed brackets, please ask).

Technology lets us vary the width of bins (effectively thenumber)

You can also use unequal bin widths but then you needsomething called densi ty , not frequency.



Examples

See page 2 of the handout Try to describe the shape of each histogram

Then see page 3 of the handout We’re going to create a histogram by hand if there is time

If no time, you can do this on your own.



Cookie Lab

Time Permitting (otherwise, Friday)

The last page (to turn in) is not due till the end of

class tomorrow. So don’t worry if we don’t get to it

today. You can look at it tonight or tomorrow in class(I’ll give last five minutes of class for you to work on

it).

introduction to statistics - chapter 3-5 notes (2)

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