Entity Academy Lesson 6 Statistical Inference

.docx

School

Liberty University *

*We aren’t endorsed by this school

Course

BASIC

Subject

Statistics

Date

Jan 9, 2024

Type

docx

Pages

Uploaded by JusticeFogPrairieDog37

Sindy Saintclair Monday, November 28 2021 Lesson 6 – Statistical Inference Learning Objectives and Questions Notes and Answers Sampling Methods Balance Accuracy with Practicality Sampling – when you take a subset of the population and make assertions about the entire population by just observing a small subset of that population. - population: everyone (not as practical) - sample: some (more practical)  The risk involved with this is since you are purposely excluding most of the households in the city, you are obtaining incomplete information. You can take multiple samples and they will all be slightly different, with no way to tell which one is the most accurate.  The advantage is that my workload is dramatically decreased if I decide to sample. Sample Size Sample size is referred to as n. For instance, if you talk to 30 people out of a larger group, this is a sample size of 30, or n=30. Simple Random Sample Everyone has an equal chance of being selected - drawing names out of hat - scientists will assign people a number and will have Excel or Python select someone Cluster Sampling Randomly select a group, not an individual Example Stratified Sampling – usually demographic in nature Population 10,000 Sample: 100 Females: 20% - 2,000 Female: 20% - 20 Males: 80% - 8,000 Males: 80% Systematic Sampling

Convenience Sampling Just sampling those that are easy to sample, for instance only the people closest to you, the smallest file, or the beginning of the alphabet— usually what’s convenient for the scientist. Sample Size: Number of People in the Sample - How many people do you need in your sample? Enough to represent the population accuracy Not too many to be impractical Simple Random Sampling Often referred to as SRS, every potential candidate for data collection has the same probability of being chosen as every other candidate for data collection. Whoever gets selected is random . The best way to do this is to assign all candidates a unique number, and then have a random number generator select which of those candidates should be a part of the sample. This method provides the best samples but may not always be done because it can be logistically difficult or expensive. Sampling Method Examples I work for a healthcare provider. My team is tasked by a federal agency to add to the knowledge base of 10 th grade students by collecting medical information. The population is all 10 th grade students in the state of Ohio. You will collect height, weight, and hearing test data for each child sampled. Simple Random Sampling Example Each 10 th grader in Ohio is assigned a number from 1 to 38,559 (that is the number of 10 th graders in

the state). A random number generator is used to select 3000 of these numbers, with no repeats. Your team will spread out across the state to meet with each of these 3000 students and collect the health data you need. Cluster Sampling Occurs when the population is broken down into groups based on some sort of information such as location, age, or gender. Usually demographic in nature, but not always. Then, a few of the groups, called clusters, are randomly selected, and within each of the chosen clusters, you sample at 100%-- which means that everyone in a chosen cluster becomes part of the sample, and everyone in a non-chosen cluster is not part of the sample. Example – Rather than looking at individual students as sampling candidates, you decide to look at each school as a sampling candidate. There are 270 high schools in Ohio, so you randomly select 18 of these high schools and then sample every 10 th grader at each of these 18 high schools. There will be no data collected from the 10 th graders at the high schools that weren’t selected. Stratified Sampling Occurs when the population is divided into strata, usually based on demographic characteristics, such as gender, age, or education level, and then within each strata candidate are randomly open. The strata are sampled according to their relative size within the population. For example, if the largest strata have 5x as many candidates as the smallest data, then the final sample should have five times as many sampled candidates from the large strata as the small strata. In this image, the population has been stratified or broken into groups based on a particular characteristic (color). However, unlike cluster

sampling, you don’t randomly select the strata and sample everyone in it. Instead, you will randomly sample within the strata at a rate that is proportionate to the how large the strata are. In this image, since the purple strata is the largest, you will randomly select more people from those strata then from either the red or the green strata, which are smaller. Example – There are some huge high schools in Ohio (3500+) students, and there are some smaller schools and charter schools with as few as 50 students. I break the schools into three different strata: schools with 1500 or more students, schools with 400 to 1499 students, and schools with 399 or fewer students. I will label these schools as big, medium, and small schools. The big schools are where 45% of Ohio 10 th grade students are going to school, with 38% going to medium-sized schools, and 17% going to the small schools. I want my total sample size to be 3000 students, so I randomly select 3000 x 45% = 1350 students from the big schools ,3000 x 38% = 1140 students from the medium schools, and 3000 x 17% = 510 students from the small schools. This way, I have broken down the population into stratum and sampled from each strata proportionally so that each is fairly represented in the final sample of 3000 students. Systematic Sampling Systematic sampling happens when a start point is chosen at random, and then every nth item is selected after that. This ultimately makes the sampling as a whole no longer random. Example

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Recommended textbooks for you

Holt Mcdougal Larson Pre-algebra: Student Edition...

Algebra

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Glencoe Algebra 1, Student Edition, 9780079039897...

Algebra

ISBN:9780079039897

Author:Carter

Publisher:McGraw Hill

Big Ideas Math A Bridge To Success Algebra 1: Stu...

Algebra

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:Houghton Mifflin Harcourt

College Algebra (MindTap Course List)

Algebra

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:Cengage Learning

SEE MORE TEXTBOOKS

Recommended textbooks for you

Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning