Stats 101 EXAM 1 review

Experimental Study

Research internationally applies one treatment to subjects and then measures a response variable to determine how the treatment affects the response. The purpose is to study whether the treatment causes a change in the response.

Observation Study

observes individuals and measures variables of interest but does not intervene to influence the response. The purpose is to describe some group or situation

not possible to establish cause and effect

What type of study is this?

“Research survey 1,000 adults to record their current exercise habits and blood pressure levels at one point in time

Observation

What type of study is this?

“Scientists randomly assign patients to receive either a new drug or a placebo and track their recovery over 6 months

Experimental

What is a Census?

A special survey that attempts to collect data from every single member of the population.

What the pros and cons of the census?

More accurate since it covers everyone, but takes more time and money.

What is sampling?

The process of selecting a subset of individuals, items. or observation from a larger population to estimate characteristics of the whole population

Convenience Sampling

A bad sampling

A type of sampling where a selection of whichever individuals are easiest to reach rather than at random

What type of sampling is this?

Surveying people in a shopping mall instead of a diverse population.

Convenience Sampling

Voluntary Response Sampling

A bad sampling

Individuals self-select to participate (online polls, call in surveys)

What type of sampling is this?

A Tv show asking viewers to vote on an issue via text messages

Voluntary Response Bias

Simple Random Sample

A good sampling

A sample chosen by a method in which each collection of n population items is equally likely to make up the sample. unbaised

Statified Random Sampling

A good sampling

Where you divide the sample into groups called strata (can be by gender, major, etc) and then take an SRS from each strata

What type is sampling is this

A company wants to survey employee satisfaction across different departments (sales, IT, HR)

We divide employees into strata (sales: 200, It: 150, HR:50) Then randomly selected 20% from each group.

Statified Random Sampling

Cluster Sampling

A good sampling

The population is divided into nonhomogeneous groups called clusters (schools, cities). Entire clusters are randomly selected, and all members within chosen clusters are surveyed.

What type is sampling is this

A researcher wants to study vaccination rates across a country. She randomly selects 5 cities out of 50, and then surveys all residents in those cities.

Cluster Sampling

Systemic Sampling

A sample is drawn by selecting every k-th element from the list (every 10th customer). Requires a random starting point to avoid bias

What type is sampling is this

A factory checks product quality from a production line of 10,000 items. The quality control manager picks a random starting point (item #7), then selects every 100th item until he obtains 50 items and checks for quality

Systemic Sampling

Sampling Variability

Describes how statistics will take different values when you repeat a sample or experiment

Sampling Bias

When a sampling design systematically favors certain individuals over others

How can we reduce bias ?

Using simple random samplings- a sampling where you use a radoms digit table

How can we reduce variability

Using a larger sample

The larger the sample size the ___ the variability

Smaller

Voluntary Response Bias

In particaulr people with strong opinions are more likely to participate

Self-Interest Bias

People who have an interest in the outcome of an experiment have an incentive to use biased methods

Social Acceptability Bias

People are reluctant to admit behavior that may reflect negatively on them

Leading Question Bias

Sometimes questions are worded in a way that suggests a particular response

Non-response Bias

People who refuse to respond to a survey or participate in any study they have been asked.

Sampling Bias

Occurs when some members of the population are more likely to be included in the sample than others.

Sampling Erros

erros caused by the act or process of taking a sample

What are the two types of sampling errros?

Randome and systematic

Random Sampling Error

The deviation (distance) between the statistic and the parameter caused by chance in selecting a random sample

The margin of error in a confidence statement account only for WHICH TYPE of error?

Random Sampling Error

Systematic Sampling Error

Consistent bias in the selection process, leading to under- or overestimating the true population parameter.

caused when the sampling process is biased or flawed in a systematic way

Ways of sampling Systematic Sampling Error

1) unvercoverage

2) poor sampling designs

Undercoverge

Somemembers of the population are inadequately represented in the sample

These is an example of what?

Using a phone directory to sample people (excludes those without a landline)

undercoverge

These is an example of what?

a survey that excludes rural areas when studying national healthcare access.

undercoverge

Poor sampling designs examples

convenience and voluntary response sampling

Nonsampling errors

error not caused by the act of sampling

Sources of nonsampling errors

1) Non-response error

2) response error

3) data entry

4)poorly worded/ misleading questions

5) interviewer bias

What are the two types of non-sampling errors?

Non response and response

Non-response error

Failure to obtain data from an individual selected from a sample.

Most nonresponse occurs when some subjects cannot be contacted or refuse to cooperate

Response Error

Occurs when a subject gives an incorrect response (participant lies about their response)

Way to minimize nonsampling erros

1)Prevention (before data collection)

2)Detection (during and after data collection)

3) Mitigation (after errors occur)

Prevention to minimize nonsampling errors

design a clear survey and instruments

-avoid ambiguous or leading questions

-pilot-test questionnaires to catch errors

train data collection

-ensure interviews, observers, or technicians follow protocols

Detection (during and after data collection) to minimize nonsampling errors

Monitor response rates-high nonresponse? adjust with follow ups or incentives

Mititgation(after erros occur) to minimize nonsampling errors

For nonresponse: substitute other households for the nonresponders

Probability weighting: to weight the response differently

Example for which type of Mitigation

For nonresponse

Example for which type of Mitigation

Probability weighing

What is Margin of Error

a numerical value that quantifies the uncertainty in an estimate

Margin of error formula (MOE)

n= sample size

How does the sample size effect Margin of error formula (MOE)

The larger the sample size, the smaller the margin of error.

How does the confidence interval affect Margin of error (MOE)

The higher the confidence level, the wider the margin of error.

Sampling frame

A sampling frame is a list or database from which a sample is drawn for a research study or survey.

frame errors

When the sampling frame is not a complete representation of the pop. of interest.

Frame erros can lead

under coverage, over coverage, duplication errors

What is the sampling frame?

If you’re studying university students

university office student enrollment list

Population

Statistical studies consist of all elements (individuals, items, or objects) whose characterstics are being studied

Sample

The part or subset of the population, containing individuals that are actually observed.

A university wants to know the average study time of all 20,000 students. It collects data from 400 students who volunteered.

What is the population, and what is the sample?

sample: 400 students

population: ALL 20,000 students

Parameter

A number that describes the population

Statistics

A number that describes a sample

Sampling distribution of statistic

The distribution of values taken
by the statistic in all possible samples of the same size from the same
population.

an example of a sampling distribution

What does P stand for?

Population proportion

What does X stand for?

number of successes in the sample

What does n stand for?

sample size

What does

stand for? also known as “P-Hat”

Sample proportion

Standard Deviation for the sample proportion equation

What is the sample proportion (p-hat)

x/n = 23/50 =0.46

Find the mean of the (all possible) sample

p=.43

Find the standard deviation of (all possible) sample proportions (p-hat)

Find the estimated margin of error for 95% confidence level

Formula for confidence level

What factors affect the confidence level width

sample size

standard deviation

z score

the chosen confidence level

another formula of Margin of error

As the sample size increases, what happens to the confidence interval?

decreases

The larger confidence level,

You have more certainty that the interval contains the true population parameter

larger interval

Formual of confidence interval for proportion

Interpretation of confidence interval statement example.

We are 95% confident that the proportion of parents who believe that music education has a positive effect is between
76.18% and 81.82%.

Randomized Comparative Experiments

A study design where subjects (or experimental units) are randomly assigned to different treatment groups to compare their outcomes

Types of Randomized Comparative Experiments

1) Completely randomized

2) Matched pairs

3) Block Design

Completely randomized design

Experimental units are randomly assigned to different treatment groups.

each subject is assigned one of any of the possible groups at random

What is best suited for Completely randomized design

when experimental units are homogeneous ( similar in all respects that might affect the outcome)

What type of design is this?

Completely randomized design

What type of design is this?

Completely randomized design

Matched pairs design

A randomized block design where each block contains only two subjects or conditions that are matched closely (either the same person under two treatments or two very similar subjects). The pairs form a block

What does the matched pairs design help control?

confounding variables and increase the precision of the experiment by reducing variability between groups

Matched pairs design are appropriate when?

comparing two treatments

Types of examples of Match Pairs Design

1) Before and after study

2) Twins Study

3) Matched subjects, two treatments

4) Same subject, two treatments

Measuring blood pressure before and after a diet intervention on the same individuals is an example of what type of design?

Match Pairs Design: Before and after study

because each individual’s before measurement is paired with their after measurement, controlling for individuals baseline differences

Comparing the effect of two different diets by assigning one diet to one twin and the other diet to the other. Example of what type of design?

Match Pairs Design; twin studies

Twin share genetics and environment, so pairing controls for these factors

Studying the effect of a new teaching method on student performance. Students are paired based on similar GPA and study habits. One from each pair is randomly assigned to the new method, and the other to the traditional method Example of what type of design?

Match Pairs Design; matched subject, two treatments

because students are matched to control for variability in prior academic ability

Testing two types of headache medicine on the same person. The person takes medicine A on one day and Medicine B on another day, and the headache relief is measured after each Example of what type of design?

Match Pairs Design; same subject, two treatments (repeated measures)

because the same person acts as teir own control, so individual differences are eliminated.

Block Design

Dividing subjects into blocks (groups) based on a variable that could affect the outcome of(like age, gender, etc.) to reduce variability within each block Then, within each block, treatments are randomly assigned

Why do we use block design?

1) Reduce variability from nuisance factors (like time, location, or batch)

2) Increase the precision of treatment comparisons (by controlling for the block-to-block variation, you reduce the “noise” - error or fluctuation- in the data, making it easier to detect real differences between treatments

3) Improve the accuracy of the conclusion (since variation due to blocks is accounted for separately, the analysis focuses more accuratley on the treatment effect)

Testing 3 fertilzer on 30 plants, but some are in sun and some in shade. You group them into sun and shade blocks, then randomly assign rach fetlizer within each block

what type of design is this?

block desgin

What is the best type of design for this ?

if you have an experiment that wants to compare the effecttivenessof three television comericals for the same product will between women and man

block design (explantion on page 46 of notes)

What are the principles in experimental designs

1) Randomization

2) control

3) Replication