Lab 2

Stat 350 Lab Session GSI: Yizao Wang Section 016 Mon 2pm30-4pm MH 444-D Section 043 Wed 2pm30-4pm MH 444-B

Outline • • • • •

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Two main types of studies Time plots Module 3 Activity 1 QQ plots Module 3 Activity 2 Quizdom Question

Two Main Types of Studies •

Observational studies: simple observation

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Experiments: design, measuring the effect of manipulation on output of interest, comparison

Time Plots & QQ Plots •

In statistical inference, first we need to check some assumptions for the data before inference procedures.

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Ex1: We need random sample. Ex2: We need the population from which the sample is taken to be normally distributed.

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Time Plots & QQ Plots •

Time plots: check randomness of quantitative data collected over time (identically distributed)

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QQ plots: check normality of population

Time/Sequence Plots

Time/Sequence Plots Time plots • Horizontal axis: time (sequence number) • Vertical axis: response or measured variable Distinguish time plots from histograms

Time/Sequence Plots •

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Purpose: check the identically distributed aspect of a random sample How: looking for evidence of stability Stability = no patterns

If the data is not stable, histograms and numerical summaries may not be meaningful.

Time/Sequence Plots Overall patterns: • Trend: a persistent, long-term rise or fall • Seasonal variation: a pattern that repeats itself at regular intervals of time • A persistent, long-term increase (or decrease) in the variation of the observations.

Time/Sequence Plots

Increasing trend

Time/Sequence Plots

Seasonal variation

Time/Sequence Plots

Increasing trend, seasonal variation and increase in the variation

Module 3 Activity 1 •

Background 1: death rate (number of deaths per 100 million miles driven) from 1960 to 2004 p14 or deathrate.sav

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Task: What do you see? Would it make sense to make a histogram of the death rates?

Module 3 Activity 1 •

Background 1: death rate (number of deaths per 100 million miles driven) from 1960 to 2004 p14 or deathrate.sav

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Task: What do you see? Would it make sense to make a histogram of the death rates? From the sequence plot we see that overall the death rate appears to be decreasing over time. It wouldn't make sense to make a histogram of the death rates because the time series is not stationary because of the decreasing trend.

Module 3 Activity 1 •

Background 2: observed passenger flow (number of passengers flying a given flight) of a certain airline company over many years airline.sav

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Task: What do you see? Is there any pattern?

Module 3 Activity 1 •

Background 2: observed passenger flow (number of passengers flying a given flight) of a certain airline company over many years airline.sav

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Task: What do you see? Is there any pattern? We see a seasonal variation here. We also see that both the overall mean and the overall variation appear to be increasing over time. One possible reason for this seasonal variation is that much more people go on vacation during the summer time than in any other season of a year.

Module 3 Activity 1 •

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Interpretations-words should not be too strong. Not: The mean is increasing. Better: There is evidence of an increasing mean, based on the data. Not: The variance decreased. Better: The variability in the response appears to be decreasing over time. Time plots do not tell the shape of a distribution.

QQ Plots •

You need to know how to check normality using QQ plot

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You don’t need to know how to produce a QQ plot by yourself. (A plot of the percentiles of a standard normal distribution against the corresponding percentiles of the observed data.)

QQ Plots Normal Q -Q Plot of A C T 40

30

20

10

0 0

10

Obser ved Value

20

30

40

QQ Plots •

Purpose: QQ plot is a graphic tool to check normality. (Why/when we need normality?)

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How to check: look at how the points fall… Approximately Normal: approximately along a straight line with a positive slope Not Normal: deviations from the line

QQ Plots

Module 3 Activity 2 •

Task 1: Use the iq.sav dataset and examine the distribution of iq by creating a histogram and QQ plot. Describe the shape of the IQ distribution.

Module 3 Activity 2 •

Task 1: Use the iq.sav dataset and examine the distribution of iq by creating a histogram and QQ plot. Describe the shape of the IQ distribution.

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From the histogram, we see that the distribution of IQ is unimodal, centered around 105-110. It appears to be very slightly skewed left, but is basically symmetric.

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With the Q-Q plot, we do see points falling roughly along a straight line with a positive slope, which would indicate that the bell-curve normal distribution is a reasonable model.

Module 3 Activity 2 •

Task 2: Use the employee data.sav dataset and create the histogram for the variable salary (current salary). Then create a QQ plot for salary. Comments?

Module 3 Activity 2 Task 2: Use the employee data.sav dataset and create the histogram for the variable salary (current salary). Then create a QQ plot for salary. Comments? Normal Q-Q Plot of Current Salary 120

100,000 100

Expected Normal Value

80,000

80

Frequency

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60

40

20

60,000

40,000

20,000

0 Mean = $34,419.57 Std. Dev. = $17,075.661 N = 474

0 $20,000

$40,000

$60,000

$80,000

$100,000 $120,000

Current Salary

-20,000 0

50,000

Observed Value

100,000

Module 3 Activity 2 •

The histogram reveals that the distribution for current salary is definitely not symmetric. It is strongly skewed right. However, it is unimodal, with a peak at around 25000. The mean will be much higher than the median due to the right skewness.

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The QQ plot clearly shows that the distribution for current salary cannot be considered normal, since it does not follow a straight line.

Review of lab 2 • • •

Experiments and observational studies Time/sequence plots Randomness and stability QQ plots Normality of population

Any questions?

Before we finish…

Qwizdom questions