优秀大学统计学授课ppt讲义statistics

Literary Digest had been conducting successful presidential election polls since 1916 They had correctly predicted the outcomes of the 1916, 1920, 1924, 1928, and 1932 elections by conducting polls. These polls were a lucrative venture for the magazine: readers liked them; newspapers played them up; and each “ballot” included a subscription blank.
Types of Data

Continuous

height, age, time # of days worked this week, # leaves on a tree {Good, O.K., Bad} {Yes/No}, {Teacher/Chemist/Haberda

Ordinal


Nominal

Picturing The Data
Pie Charts

Nominal/Ordinal Only suitable for data that adds up to 1 Hard to compare values in the chart


Bar Charts
Overview



General Statistics The Normal Distribution Z-Tests Confidence Intervals T-Tests
General Statistics
~ THE GOLDEN RULE ~ Statistics NEVER replace the judgment of the expert.
Terminology


Population: is a set of entities concerning which statistical inferences are to be drawn. Sample: a number of independent observations from the same probability distribution Parameter: the distribution of a random variable as belonging to a family of probability distributions, distinguished from each other by the values of a finite number of parameters Bias: a factor that causes a statistical sample of a population to have some examples of the population less represented than others.
Outliers (and their treatment)

An "outlier" is an observation that does not fit the pattern in the rest of the data
Check the data Check with the measurer If reason to believe it is NOT real, change it if possible, otherwise leave it out (but note). If reason to believe it is real, leave it out and note.
Time-Series Plots

Time related Data e.g. Stock Prices
Question 1
In a telephone survey of 68 households, when asked do they have pets, the following were the responses :
Question 1 - Solution
How many? It must be (60 - 52) = 8 people No pets = 16 Dogs = 20 Cats = 24 Both = 8 ------------------------Total = 68
Question 1 - Solution
The Literary Digest Poll



Response rate: approximately 25%, or 2,376,523 responses Result: Landon in a landslide (predicted 57% of the vote, Roosevelt predicted 40%) Election result: Roosevelt received approximately 60% of the vote

Nominal/Ordinal Easier to compare values than pie chart Suitable for a wider range of data


Dot Plots

Nominal/Ordinal Represents all the data


Difficult to read
(Basically the same as all other research)
Hypothesis Testing
H0 : Null Hypothesis, status quo HA : Alternative Hypothesis, research question
So, either : "The data does not support H0" or "We fail to reject H0"
The Literary Digest Poll

POSSIBLE CAUSES OF ERROR Selection Bias: By taking names and addresses from telephone directories, survey systematically excluded poor voters. Republicans were markedly overrepresented in 1936, Democrats did not have as many phones, not as likely to drive cars, and did not read the Literary Digest “Sampling Frame” is the actual population of individuals from which a sample is drawn: Selection bias results when sampling frame is not representative of the population of interest


The Mean


The Mean (Arithmetic) The mean is defined as the sum of all the elements, divided by the number of elements. The statistical mean of a set of observations is the average of the measurements in a set of data
The Literary Digest Poll

POSSIBLE CAUSES OF ERROR Non-response Bias: Because only 20% of 10 million people returned surveys, nonrespondents may have different preferences from respondents Indeed, respondents favored Landon Greater response rates reduce the odds of biased samples
Quantitative Data Analysis: Statistics
Sherlock Holmes
"... while man is an insoluble puzzle, in the aggregate he becomes a mathematical certainty. You can, for example, never foretell what any one man will do, but you can say with precision what an average number will be up to. Individuals vary, but percentages remain constant. So says the statistician"
Box Plots

Nominal/Ordinal 1IQR, 3IQR Outliers


Scatter Plots

Excellent for examining association between two variables