Statistics Unit

2.1 Fundamentals of Statistics

POPULATION: the complete set of people or things being studied

SAMPLE: the subset of the population from which the raw data were actually obtained

SAMPLE STATISTICS: a value calculated using the data from a sample

POPULATION PARAMETER: a value calculated using all the data from a population

SAMPLING METHODS:

  1. Simple Random Sampling

    2. Example: The names of 25 employees are chosen out of a hat from a company of 250 employees.

  2. Systematic Sampling

    3. Example: You select every tenth person for an experiment from a list of 10,000 names.

  3. Convenience Sampling

    4. Example: A researcher working at a university chooses students from the university to participate in a study.

  4. Stratified Sampling

    5. A researcher divides the population into subgroups and then randomly selects participants from each subgroup.

  5. Quota sampling

    6. Sampling continues until preset quotas are reached. Example: A researcher wants 40 women and 60 men for a total of 100 respondents to match population characteristics.

  6. Cluster Sampling

    7. The population is divided into clusters and then a sample is chosen by randomly selecting an entire cluster.

  7. Voluntary Response Sampling

    8. Samples are formed using self-selected volunteers like when a radio show asks for listeners to call in to complete a survey.

TYPE OF STUDY:

  1. Treatment group
  2. Control group
  3. Placebo effect
  4. Single blind
  5. Double blind

CONFIDENCE INTERVAL: found by adding AND subtracting the margin of error from the sample statistic

BASIC STEPS IN A STATISTICAL STUDY

  1. Determine the research question for your study.
  2. Choose a representative sample.
  3. Collect the raw data and summarize these data.
  4. Use the sample statistics to infer information about the population.
  5. Draw conclusions.

SAMPLING BIAS: A sampling method is biased if every member of the population does not have equal likelihood of being in the sample.

SAMPLING VARIABILITY: the natural variation of samples

Statistical Studies

70 Percent of College Students Stressed About Finances

“Seven out of 10 college students feel stressed about their personal finances, according to a new national survey.”

“The findings come from the National Student Financial Wellness Study, which surveyed 18,795 undergraduate students at 52 colleges and universities across the country. It included students from four-year and two-year private and public institutions.”

Source: Website Source for Study

Assume students were proportionally selected from 26 two-year institutions, 13 four-year public institutions and 13 four-year private institutions.

Population

All college students

Sample

18,795 undergraduate students

Sample Statistics

7 of 10 college students are stressed about personal finances.

Sampling Methods

Stratified

Type of Study

Observational

Tests of Cholesterol Drugs Offer Hope of Reducing Heart Attacks and Strokes

“A new class of experimental cholesterol drugs might sharply reduce the risk of heart attacks and strokes, researchers reported on Sunday, citing what they described as preliminary evidence.”

“The study of Amgen’s evolocumab involved 4,465 patients with various degrees of risk, two-thirds of whom were randomly chosen to get the drug in addition to the medication they were already taking. After one year, 0.95 percent of those in the group that received the drug had suffered a heart attack, stroke or other cardiovascular problem, compared with 2.18 percent in the group that did not take the drug. By a measure known as the hazard ratio, the risk of cardiovascular events was reduced by 53 percent.

Source: Website Source for Cholesterol Study

Assume the patients were volunteers who responded to an advertisement looking for cases in a drug study.

Population

All people with various degrees of risk for a cardiovascular problem.

Sample

4,465 at-risk patients

Sample Statistics

0.95% of experimental group suffered a cardiovascular problem, 2.18% of control group suffered a cardiovascular problem and there was a 53% reduced risk of a problem

Sampling Methods

Voluntary response

Type of Study

Experimental

Voters Still See America As a Special Place

Wednesday, February 08, 2017

Voters now believe even more strongly that the United States is special among the nations of the world.

A new Rasmussen Reports national telephone and online survey finds that 69% of Likely U.S. Voters think the United States is more exceptional than other nations. This is up significantly from 57% two years ago. Just 20% disagree, while 10% are not sure. (Question wording: Is the United States more exceptional than other nations?)

The survey of 1,000 Likely Voters was conducted on February 6-7, 2017 by Rasmussen Reports. The margin of sampling error is +/- 3 percentage points with a 95% level of confidence. Field work for all Rasmussen Reports surveys is conducted by Pulse Opinion Research, LLC.

Source: Rasmussen Reports Website Source

Population

All registered voters

Sample

1,000 likely voters

Sample Statistics

69% think that the U.S. is more exceptional than other nations, compared to 57% two years ago. 20% disagree. 10% are unsure.

Sampling Methods

Simple random

Type of Study

Observational

Confidence Interval

66% - 72%

Data for Rasmussen Reports survey research is collected using an automated polling methodology. Calls are placed to randomly-selected phone numbers through a process that ensures appropriate geographic representation. Typically, calls are placed from 5 pm to 9 pm local time during the week. Saturday calls are made from 11 am to 6 pm local time and Sunday calls from 1 pm to 9 pm local time. To reach those who have abandoned traditional landline telephones, Rasmussen Reports uses an online survey tool to interview randomly selected participants from a demographically diverse panel.

After the surveys are completed, the raw data is processed through a weighting program to ensure that the sample reflects the overall population in terms of age, race, gender, political party, and other factors. The processing step is required because different segments of the population answer the phone in different ways. For example, women answer the phone more than men, older people are home more and answer more than younger people, and rural residents typically answer the phone more frequently than urban residents.

For surveys of all adults, the population targets are determined by census bureau data.

For political surveys, census bureau data provides a starting point and a series of screening questions are used to determine likely voters. The questions involve voting history, interest in the current campaign, and likely voting intentions.

In a sample of 500 city voters, 45% said they will vote for Mr. Alpha, 51% said they will vote for Ms. Beta and 4% will vote for someone else. If the margin of error is +/-3 percentage points, can we say with confidence that Ms. Beta is ahead?