# coursera statistics

Post on 09-Oct-2015

77 views

Embed Size (px)

TRANSCRIPT

Chapter 1: Introduction to data

OpenIntro Statistics, 2nd Edition

Case study

1 Case study

2 Data basics

3 Overview of data collection principles

4 Observational studies and sampling strategies

5 Experiments

6 Examining numerical data

7 Considering categorical data

8 Case study: Gender discrimination

OpenIntro Statistics, 2nd Edition

Chp 1: Intro. to data

Case study

Treating Chronic Fatigue Syndrome

Objective: Evaluate the effectiveness of cognitive-behaviortherapy for chronic fatigue syndrome.

Participant pool: 142 patients who were recruited from referralsby primary care physicians and consultants to a hospital clinicspecializing in chronic fatigue syndrome.

Actual participants: Only 60 of the 142 referred patients enteredthe study. Some were excluded because they didnt meet thediagnostic criteria, some had other health issues, and somerefused to be a part of the study.

Deale et. al. Cognitive behavior therapy for chronic fatigue syndrome: A randomized controlled trial. The American Journal of

Psychiatry 154.3 (1997).

OpenIntro Statistics, 2nd Edition Chp 1: Intro. to data 2 / 94

Case study

Study design

Patients randomly assigned to treatment and control groups, 30patients in each group:

Treatment: Cognitive behavior therapy collaborative, educative,and with a behavioral emphasis. Patients were shown on howactivity could be increased steadily and safely withoutexacerbating symptoms.Control: Relaxation No advice was given about how activitycould be increased. Instead progressive muscle relaxation,visualization, and rapid relaxation skills were taught.

OpenIntro Statistics, 2nd Edition Chp 1: Intro. to data 3 / 94

Case study

Results

The table below shows the distribution of patients with goodoutcomes at 6-month follow-up. Note that 7 patients dropped out ofthe study: 3 from the treatment and 4 from the control group.

Good outcomeYes No Total

Treatment 19 8 27GroupControl 5 21 26Total 24 29 53

Proportion with good outcomes in treatment group:

19/27 0.70 70%Proportion with good outcomes in control group:

5/26 0.19 19%

OpenIntro Statistics, 2nd Edition Chp 1: Intro. to data 4 / 94

Case study

Results

The table below shows the distribution of patients with goodoutcomes at 6-month follow-up. Note that 7 patients dropped out ofthe study: 3 from the treatment and 4 from the control group.

Good outcomeYes No Total

Treatment 19 8 27GroupControl 5 21 26Total 24 29 53

Proportion with good outcomes in treatment group:

19/27 0.70 70%

Proportion with good outcomes in control group:

5/26 0.19 19%

OpenIntro Statistics, 2nd Edition Chp 1: Intro. to data 4 / 94

Case study

Results

The table below shows the distribution of patients with goodoutcomes at 6-month follow-up. Note that 7 patients dropped out ofthe study: 3 from the treatment and 4 from the control group.

Good outcomeYes No Total

Treatment 19 8 27GroupControl 5 21 26Total 24 29 53

Proportion with good outcomes in treatment group:

19/27 0.70 70%Proportion with good outcomes in control group:

5/26 0.19 19%OpenIntro Statistics, 2nd Edition Chp 1: Intro. to data 4 / 94

Case study

Understanding the results

Do the data show a real difference between the groups?

Suppose you flip a coin 100 times. While the chance a coin landsheads in any given coin flip is 50%, we probably wont observeexactly 50 heads. This type of fluctuation is part of almost anytype of data generating process.

The observed difference between the two groups (70 - 19 =51%) may be real, or may be due to natural variation.

Since the difference is quite large, it is more believable that thedifference is real.

We need statistical tools to determine if the difference is so largethat we should reject the notion that it was due to chance.

OpenIntro Statistics, 2nd Edition Chp 1: Intro. to data 5 / 94

Case study

Understanding the results

Do the data show a real difference between the groups?

Suppose you flip a coin 100 times. While the chance a coin landsheads in any given coin flip is 50%, we probably wont observeexactly 50 heads. This type of fluctuation is part of almost anytype of data generating process.

The observed difference between the two groups (70 - 19 =51%) may be real, or may be due to natural variation.

Since the difference is quite large, it is more believable that thedifference is real.

We need statistical tools to determine if the difference is so largethat we should reject the notion that it was due to chance.

OpenIntro Statistics, 2nd Edition Chp 1: Intro. to data 5 / 94

Case study

Generalizing the results

Are the results of this study generalizable to all patients with chronicfatigue syndrome?

These patients had specific characteristics and volunteered to be apart of this study, therefore they may not be representative of allpatients with chronic fatigue syndrome. While we cannot immediatelygeneralize the results to all patients, this first study is encouraging.The method works for patients with some narrow set ofcharacteristics, and that gives hope that it will work, at least to somedegree, with other patients.

OpenIntro Statistics, 2nd Edition Chp 1: Intro. to data 6 / 94

Case study

Generalizing the results

Are the results of this study generalizable to all patients with chronicfatigue syndrome?

These patients had specific characteristics and volunteered to be apart of this study, therefore they may not be representative of allpatients with chronic fatigue syndrome. While we cannot immediatelygeneralize the results to all patients, this first study is encouraging.The method works for patients with some narrow set ofcharacteristics, and that gives hope that it will work, at least to somedegree, with other patients.

OpenIntro Statistics, 2nd Edition Chp 1: Intro. to data 6 / 94

Data basics

1 Case study

2 Data basicsObservations and variablesTypes of variablesRelationships among variablesAssociated and independent variables

3 Overview of data collection principles

4 Observational studies and sampling strategies

5 Experiments

6 Examining numerical data

7 Considering categorical data

8 Case study: Gender discrimination

OpenIntro Statistics, 2nd Edition

Chp 1: Intro. to data

Data basics Observations and variables

Data matrix

Data collected on students in a statistics class on a variety ofvariables:

variable

Stu. gender intro extra dread1 male extravert 32 female extravert 23 female introvert 4 4 female extravert 2 observation...

......

......

86 male extravert 3

OpenIntro Statistics, 2nd Edition Chp 1: Intro. to data 7 / 94

Data basics Types of variables

Types of variables

all variables

numerical categorical

continuous discrete regularcategorical ordinal

OpenIntro Statistics, 2nd Edition Chp 1: Intro. to data 8 / 94

Data basics Types of variables

Types of variables (cont.)

gender sleep bedtime countries dread

1 male 5 12-2 13 32 female 7 10-12 7 23 female 5.5 12-2 1 44 female 7 12-2 25 female 3 12-2 1 36 female 3 12-2 9 4

gender:

sleep:

bedtime:

countries:

dread:

OpenIntro Statistics, 2nd Edition Chp 1: Intro. to data 9 / 94

Data basics Types of variables

Types of variables (cont.)

gender sleep bedtime countries dread

1 male 5 12-2 13 32 female 7 10-12 7 23 female 5.5 12-2 1 44 female 7 12-2 25 female 3 12-2 1 36 female 3 12-2 9 4

gender: categorical

sleep:

bedtime:

countries:

dread:

OpenIntro Statistics, 2nd Edition Chp 1: Intro. to data 9 / 94

Data basics Types of variables

Types of variables (cont.)

gender sleep bedtime countries dread

1 male 5 12-2 13 32 female 7 10-12 7 23 female 5.5 12-2 1 44 female 7 12-2 25 female 3 12-2 1 36 female 3 12-2 9 4

gender: categorical

sleep:

bedtime:

countries:

dread:

OpenIntro Statistics, 2nd Edition Chp 1: Intro. to data 9 / 94

Data basics Types of variables

Types of variables (cont.)

gender sleep bedtime countries dread

gender: categorical

sleep: numerical, continuous

bedtime:

countries:

dread:

OpenIntro Statistics, 2nd Edition Chp 1: Intro. to data 9 / 94

Data basics Types of variables

Types of variables (cont.)

gender sleep bedtime countries dread

gender: categorical

sleep: numerical, continuous

bedtime:

countries:

dread:

OpenIntro Statistics, 2nd Edition Chp 1: Intro. to data 9 / 94

Data basics Types of variables

Types of variables (cont.)

gender sleep bedtime countries dread

gender: categorical

sleep: numerical, continuous

bedtime: categorical, ordinal

countries:

dread:

OpenIntro Statistics, 2nd Edition Chp 1: Intro. to data 9 / 94

Data basics Types of variables

Types of variables (cont.)

gender sleep bedtime countries drea