ST 351 - Statistical Methods (Learning Paths 1-5)

Non-Response Bias

Would exist if the responses of those that did participate are different than the responses of those who did not participate

Statistics starts with a ____ ___ ____

question of interest

Voluntary Response Sample vs. Convenience Sample

• Convenience sample - researcher decides who is in sample • Voluntary response sample - researcher has no control over who is in sample

Sample size has no effect on whether or not which three types of bias exists?

• Sampling Bias • Response Bias • Non-response bias

Explanatory Variable

The variable that might explain the differences observed in the response variable

Six components of an experiment:

1. Treatment 2. Experimental Unit 3. Control Group 4. Replication 5. Randomization 6. Control

Six steps in the Statistical Process

1. Write question of interest 2. Design a proper study 3. Collect and record the data 4. Explore the data through summary information, graphical displays 5. Perform a statistical analysis of data 6. Answer the question of interest

Undercoverage

Exists when certain cases in a population are not eligible to be part of sample or not part of selection process

Sampling Bias

Exists when the method of selecting cases to be part of sample leads to an over/under representation of certain groups in the population

Causation

Implies that the observed differences in the response variable between the categories of the explanatory variable are directly related to the explanatory variable

Association

Implies that there are differences in responses between the different categories of the explanatory variable

Prospective Observational Study

Investigator identifies cases in the different groups (the explanatory variable) that the investigator thinks may be explaining certain outcomes and follows these cases for a period of time to see what outcome (the response variable) occurs

Retrospective Observational Study

Investigator identifies cases that already have certain outcomes (the response variable) and looks back into their past to see what may be explaining these outcomes (the explanatory variable)

Data

Is information

Statistical Inference

Making a conclusion or generalization about the population based on information collected from the sample

Double-Blinded

Neither the subjects nor the administrators and participants know to which group the subject belongs • Best method to ensure that none of the patients will know to which group they're in

Blinding

Not letting a subject know which comparison group they belong to

Replication

Performing the experiment on more than one experimental unit; repeat entire experiment on different set of experimental units; important for validity

Cluster Random Sample

Population divided into clusters (not based on similar characteristics), randomly select predetermined number of clusters, all in cluster are part of sample

Case

The object or individual on which data is collected

Experimental Unit

The object that receives the treatment or standard treatment

Quantitative (numerical) Variables

The piece of each information recorded on each case is a number Ex. weight, points scored in a game, time texting each day

Categorical (qualitative) Variables

The piece of information recorded on each case falls into one of several categories - descriptive Ex. Yes/No, hair color, ethnicity, military ranks

Placebo Effect

The psychological effect of feeling better because you think you are getting a treatment that is supposed to make you feel better

Sampling

The selection of a subset (statistical sample) of individuals from within a statistical population

Statistical Process

The six step scientific method followed in statistics

Randomized Block Design

To balance a known confounding variable; a completely randomized design is performed within each block

Control

To make sure all experimental units are exposed to the same conditions

Main goal of sampling

To obtain a representative sample of the population

Response Bias

When an individual selected to be part of a sample does not answer the survey questions honestly, either intentionally or not knowing the answer

Non-Response

When an individual who was selected to be part of the sample does not participate in the sample either because they cannot be contacted or they decide not to

A professor wanted to determine the proportion of students that supported a certain issue at their school. She sampled 25 students and asked each if they support the issue or not. What is the variable in this example?

Whether or not a student supported the issue

First step in the statistical process

Write a research question or question of interest

An advantage of Matched-Pairs design is that it is a better way to control for ______ variables

confounding

Major League Baseball tests players to see whether they are using performance-enhancing drugs. Officials select a team at random, and a drug-testing crew shows up unannounced to test all 40 players on the team. Each testing day can be considered a study of drug use in Major League Baseball. What kind of study is described? a) Simple random sample b) Stratified random sample c) Systematic random sample d) Cluster random sample

d) Cluster random sample

Second step in the Statistical Process is to ____ ___ ____

design a study

A professor wanted to determine the proportion of students that supported a certain issue at their school. She sampled 25 students and asked each if they support the issue or not. What is a case in this example?

each student

In observational studies, it is not reasonable to say that the _____ variable caused the association

explanatory

The idea of statistics: we cannot collect data on the whole ________, therefore we collect data on a ______

population of interest, sample

Only _____ balances all possible confounding variables between comparison groups.

randomization

In a completely _______ design, researchers randomly assign experimental units to receive each treatment.

randomized

Only in a _____ experiment can we say that the _____variable caused the observed difference in the response variable.

randomized, explanatory

Association is not about individuals, association is about the _____

trend

The difference between an Experiment and an Observational Study:

• Experiment - the researcher gets to decide which individuals receive the treatment and which do not • Observational Study - the researcher has no control over which group the cases are in

Four Steps That Can Reduce Response Bias:

• Phrasing questions precisely, succinctly without words that elicit a certain response • Using written surveys instead of oral • Keeping number of questions on survey limited • Provide an exhaustive set of answer options

What is the difference between statistics (small "s") and Statistics (capital "S")?

• statistics with a small s refers to numerical summaries of data. • Statistics with a capital S refers to the process of collecting, recording, organizing, analyzing, and interpreting the data.

Randomization

The most important component of an experiment; randomly assigning treatments • All confounding variables should be balanced between comparison groups

Convenience Samples

A method of selecting cases that are close in proximity or convenient to you • Often leads to sampling bias

A properly written research question should contain two details:

1. A well defined variable of interest 2. The population of interest

To remove a placebo effect from a study:

1. Incorporate a placebo 2. Include blinding in the study

Two ways of collecting data:

1. Observational Studies 2. Experiments

Two types of observational studies:

1. Retrospective 2. Prospective

How sensitive to changes in water temperature are coral reefs? To find out, we can measure the growth of corals in aquariums where the water temperature is controlled at different levels. Growth is measured by weighing the coral before and after the experiment. 1. What is the response variable? 2. What is the explanatory variable?

1. The response variable is: growth of coral 2. The explanatory variable is: changes in water temperature

State if each of the following are part of the definition of statistics (small s) or Statistics (capital S): 1. average body temperature 2. collecting data 3. analyzing data 4. proportion of adults who own at least one pet 5. number of elementary students who chose pizza as their favorite food 6. interpreting data 7. the percent of students in favor of having ice cream at the end of lecture

1. average body temperature (small s) 2. collecting data (capital S) 3. analyzing data (capital S) 4. proportion of adults who own at least one pet (small s) 5. number of elementary students who chose pizza as their favorite food (small s) 6. interpreting data (capital S) 7. the percent of students in favor of having ice cream at the end of lecture (small s)

The Super Yummy Candy Company offers a discount card to all of its customers. Everyone who signs up for this card receives a 10% discount on all purchases in the store, but in order to sign up for the card customers must provide information which is recorded in a large data set. Identify each variable as either categorical or quantitative. 1. gender 2. age (years) 3. whether or not there are kids under the age of 10 in the household 4. On a scale of 1-10, how much the customers loves candy (10 = REALLY loves candy)

1. gender categorical 2. age (years) quantitative 3. whether or not there are kids under the age of 10 in the household categorical 4. On a scale of 1-10, how much the customers loves candy (10 = REALLY loves candy!) quantitative

An article in the USA Today (October 19, 2010) described a study of how toddlers ages 1 to 2 years old learn. Sixty-four toddlers between 1 and 2 years old were allowed to play in a lab equipped with toys which also had a robot hidden behind a screen. After allowing the toddlers playtime, the team removed the screen and let the children see the robot. In some tests, an adult talked to the robot and played with it. In other tests, the adult ignored the robot. After the adult left the room, the robot beeped and then turned its head to look at a toy to the side of the toddler. In the cases where the adult had played with the robot, the toddler was four times more likely to follow the robot's gaze to the toy. State if the variable listed is the response variable, the explanatory variable, or neither the response or explanatory variable in the scenario given. 1. whether or not an adult talked and played with the robot 2. the age of the toddler 3. whether or not the toddler followed the robot's gaze to the toy 4. the number of toddlers that followed the robot's gaze to the toy 5. the amount of playtime

1. whether or not an adult talked and played with the robot explanatory 2. the age of the toddler neither 3. whether or not the toddler followed the robot's gaze to the toy response 4. the number of toddlers that followed the robot's gaze to the toy neither 5. the amount of playtime neither

Placebo

A "treatment" that is exactly the same in nature (looks, taste, texture, etc.) as those in the treatment group get except it doesn't contain an active ingredient

Multi-Stage Sampling Designs

A combination of random sampling designs

Block

A group of similar experimental units Ex. Two plots next to a river

Biased

A sample that is not representative of the population

Experiment

A study where the investigator deliberately imposes some condition (treatment) on the cases (experimental units)

Observational Study

A study where the investigator passively observes and records information on cases; investigator does not actively have any control over what a case does or values collected

Confounding Variable

A variable not being studied but is directly related to the explanatory variable and is also associated with the response variable

Consider the following research question, "What percent of American adults are left-handed?" What is the population of interest based on this question of interest?

All American adults

Clinical Trial

An experiment performed on human subjects involving medicine or medical procedures

Matched-Pairs Design

An experiment where two cases are matched together on similar characteristics - one assigned to treatment group, one to control group • Another method - case appears in both treatment and control group

Variable

Any characteristic that is recorded for each case

Consider the following research question, "What percent of American adults are left-handed?" What is the variable of interest?

Dominant hand (left or right)

Completely Randomized Experiment

Each case (experimental unit) is randomly assigned to one of the comparison groups

Stratified Random Sample

Cases in population divided into groups (strata) based on similar characteristics; take simple random sample within each strata • useful when there is a characteristic in the population that you may want to account for when selecting individuals

Voluntary Response Samples

Cases in the population decide for themselves if they want to be part of sample • May lead to bias because those that do respond may have different opinion than those not responding

Ordinal Variable

Categorical variables that have an inherent order to the categories Ex. military ranks

Tests of gene therapy on laboratory rats have raised hopes of stopping the degeneration of tissue that characterizes chronic heart failure. Researchers at the University of California, San Diego, used hamsters with cardiac disease, randomly assigning 30 to receive the gene therapy and leaving the other 28 untreated. Five weeks after treatment the gene therapy group's heart muscles stabilized, while those of the untreated hamsters continued to weaken. (Source: Science News, July 27, 2002) What kind of study is described?

Completely Randomized Experiment

Two Variable Types

Quantitative and Categorical

The method that best guarantees obtaining a representative sample; only way to be sure sampling is without bias

Random Sample

Systematic Random Sample

Randomly select a starting case to be part of sample, then every K'th case selected to be part of sample • Useful for situations where you may have an ordered list of the population. It is also used as a technique to sample items coming off of an assembly line

Sample

Subset from a population on which data will be collected

Treatment

The experimental treatment that is being investigated

Response Variable

The focus of the study; what researcher is studying; outcome variable

Control Group

The group of cases that do not receive the receive the standard treatment; needed for comparison purposes • Can tell you if the treatment is working

Population

The group of cases to which we want to make a conclusion

Simple Random Sample (SRS)

The most basic random sample design ; all cases in population have same chance of being selected as part of sample

A college Statistics class conducted a survey concerning community attitudes about the college's large homecoming celebration. That survey drew its sample in the following manner: Telephone numbers were generated at random by selecting one of the local telephone exchanges (first three digits) at random and then generating a random four-digit number to follow the exchange. If a person answered the phone and the call was to a residence, then that person was taken to be the subject for interview. (Undergraduate students and those under voting age were excluded, as was anyone who could not speak English.) Calls were placed until a sample of 200 eligible respondents had been reached. What kind of study is this? a) Simple random sample b) Stratified sample c) Systematic sample

a) Simple random sample

Administrators at Texas A&M University were interested in estimating the percentage of students who are the first in their family to go to college. The A&M student body has about 46,000 members. How might the administrators answer their question by applying the three Big Ideas? For each scenario below, identify the study (systematic, cluster, or stratified) used by the university administrators: a) Select several dormitories at random and contact everyone living in the selected dorms. b) Using a computer-based list of registered students, contact 200 freshmen, 200 sophomores, 200 juniors, and 200 seniors selected at random from each class. c) Using a computer-based alphabetical list of registered students, select one of the first 25 on the list by random and then contact the student whose name is 50 names later, and then every 50 names beyond that.

a) This is a cluster sample, with each selected dormitory as a cluster. b) This is a stratified sample, stratified by class year. c) This systematic sample, with a randomized starting point.

If variable of interest is quantitative, the research question may ask about the ______ for the population a. average or mean b. percent or proportion c. mode

a. average or mean

A dog food company wants to compare a new lower calorie food with their standard dog food to see if it's effective in helping inactive dogs maintain a healthy weight. They have found several dog owners willing to participate in the trial. The dogs have been classified as small, medium, or large breeds, and the company will supply some owners of each size of dog with one of the two foods. The owners have agreed not to feed their dogs anything else for a period of 6 months, after which the dogs' weights will be checked. We assumed that dogs are randomly assigned to different treatment groups. What kind of study is described? a) Matched-pairs design b) Randomized block design

b) Randomized block design

The manager of a dairy factory wants to determine how accurate all of the machines in his factory are, on average. He identifies all containers that are made by each of the 5 machines and then randomly selects 50 containers from each machine and weighs them. What sampling method did the manager use? a) Simple random sample b) Stratified random sample c) Cluster sample d) Matched-pairs sample

b) Stratified random sample

When spending large amounts to purchase advertising time, companies want to know what audience they'll reach. In January 2011, a poll asked 600 American male adults and 400 female adults whether they planned to watch the upcoming Super Bowl. Men and women were asked separately whether they were looking forward more to the football game or to watching the commercials. Among the men, 16% were planning to watch and were looking forward primarily to the commercials. Among women, 30% were looking forward primarily to the commercials. What kind of study is described? a) Simple random sample b) Stratified random sample c) Systematic random sample d) Cluster random sample

b) Stratified random sample

If variable of interest is categorical, the research question may ask about the ______ of individuals in one of the categories a. average or mean b. percent or proportion c. mode

b. percent or proportion

In a randomized ________ design, the random assignment of experimental units to treatments is carried out separately within each block.

block

Never infer _____ in an observational study

causation

A health specialist wants to examine the relationship between type of exercise among adults between 25 and 40 years old who exercise regularly and frequency of injuries. She has defined certain types of regular exercise as "high impact" (such as running) and other types as "low impact" (such as swimming). She obtains lists of active members at local health and fitness clubs, running clubs, bicycling clubs, and other athletic clubs. After classifying each member as either a "high impact" exerciser or "low impact" exerciser, she randomly selects some from each category and follows them for one year, recording whether or not an exerciser had to cease exercise due to an injury. Identify each of the following: response variable, explanatory variable What type of observational study is being described?

explanatory - type of exercise ("high impact" and "low impact") response - Whether or not the exerciser had to cease exercise due to an injury prospective

Sample is used because...

it is usually too time consuming, costly to gather information about an entire population

As long as a study is properly designed we can..

make a valid conclusion about the population of interest based on sample data

In a _______ design, there is a "connection" between an observation in the treatment group and an observation in the control group. This design is generally done with human subjects, but can be done on other objects as well.

matched-pairs