Statistics and Sampling Quiz

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Questions and Answers

Which type of measurement is exemplified by asking, 'How many cigarettes did you smoke in the last 3 days?'

Ordinal

Interval

Ratio (correct)

Nominal

What is the primary purpose of a census?

To analyze sample means

To collect sample statistics

To collect data from the entire population (correct)

To provide an estimate of parameters

What distinguishes parameters from statistics?

Parameters are derived from samples, statistics from populations

Parameters can be directly observed, statistics cannot

Statistics are constants, parameters are variables

Parameters describe populations, statistics describe samples (correct)

Which of the following methods fall under Descriptive Statistics?

Organizing and summarizing data Signup and view all the answers

The symbols µ and σ represent which of the following in statistics?

Population mean and population standard deviation Signup and view all the answers

What is the role of inferential statistics?

To use sample data to make predictions about population parameters Signup and view all the answers

Which measure is NOT considered a central tendency measure?

Percentile Signup and view all the answers

Which of the following is a characteristic of statistics as a branch of applied mathematics?

It aims to interpret data to make informed decisions Signup and view all the answers

What is necessary for all methods of probability sampling?

Every unit must have an equal chance of selection Signup and view all the answers

In systematic sampling, how is the starting point chosen?

By selecting a random unit from the sampling frame Signup and view all the answers

Which of the following accurately describes stratified sampling?

The sampling frame must be split into distinct strata before sampling occurs. Signup and view all the answers

What is the main characteristic of cluster sampling?

It involves selecting all subjects within a certain cluster. Signup and view all the answers

What is a significant requirement for simple random sampling?

Creation of a complete, numbered list of the population Signup and view all the answers

What is the purpose of stratifying a sampling frame in research?

To enable comparisons across different characteristics accurately Signup and view all the answers

What does the sampling frame represent in a study population?

It is the list of all units constituting the study population. Signup and view all the answers

How is the sampling fraction determined in systematic sampling?

By calculating the ratio of sample size to the total population Signup and view all the answers

What does a qualitative variable lack when compared to a quantitative variable?

The ability to be measured Signup and view all the answers

Which level of measurement allows for the calculation of the mean?

Interval Signup and view all the answers

In the context of levels of measurement, which example represents the highest level?

Weight measured in pounds or kilograms Signup and view all the answers

Which statistic would be inappropriate to use for nominal level data?

Average Signup and view all the answers

What defines an independent variable in research?

The presumed cause of a dependent variable Signup and view all the answers

Which characteristic is associated with ordinal level measurement?

Indicates ordering without specifying the exact differences Signup and view all the answers

What is a critical feature of the ratio level of measurement?

A true zero point indicating absence of the quantity measured Signup and view all the answers

Regarding variables, which statement is true?

Independent variables can influence dependent variables. Signup and view all the answers

What is a key advantage of using cluster sampling in interventional studies?

It eliminates the need for a sampling frame entirely. Signup and view all the answers

Which sampling method does not require an initial sampling frame of the whole population?

Multistage sampling Signup and view all the answers

What is a common characteristic of nonprobability sampling methods?

The sample may be biased and limits generalization. Signup and view all the answers

In snowball sampling, what role do the subjects play?

They assist by referring additional potential subjects. Signup and view all the answers

Which of the following sampling methods involves selecting a sample based on certain characteristics of the population?

Quota sampling Signup and view all the answers

The purpose of purposive sampling is primarily to select subjects who are:

Judged to be typical or expert in the research area. Signup and view all the answers

What is a significant drawback of convenience sampling?

It often produces biased samples that may not reflect the population. Signup and view all the answers

What best describes the use of multistage sampling in community-based studies?

Selects participants through multiple layers and stages. Signup and view all the answers

What does the null hypothesis (H0) represent in statistical testing?

The hypothesized parameter value that is compared with the sample value. Signup and view all the answers

What happens when a statistical test results in rejecting the null hypothesis (H0) when it is actually true?

A Type I error occurs. Signup and view all the answers

Which statement regarding the alternative hypothesis (H1) is correct?

It represents a hypothesis that contradicts the null hypothesis. Signup and view all the answers

What does the significance level (α) indicate in hypothesis testing?

The probability of rejecting H0 when it is actually true. Signup and view all the answers

When committing a Type II error (β), what conclusion is mistakenly reached?

Accepting the null hypothesis when it is actually false. Signup and view all the answers

What is a key step that must be performed after computing the test statistic?

Establish the critical value needed to make a decision. Signup and view all the answers

Which of the following best describes the validity of H0 after a hypothesis test?

You can only state there is insufficient evidence to reject H0. Signup and view all the answers

What is the typical significance level (α) commonly used in hypothesis testing?

0.01 or 0.05 Signup and view all the answers

Which of the following measures is a measure of dispersion?

Interquartile range Signup and view all the answers

Which scenario describes a negatively skewed distribution?

Mean < Median Signup and view all the answers

What is the primary purpose of inferential statistics?

To make predictions about population characteristics based on a sample Signup and view all the answers

A research hypothesis must always involve which of the following?

Two or more variables Signup and view all the answers

Which of the following is an example of a nonparametric statistical test suitable for nominal data?

Chi-Square Goodness-of-Fit Test Signup and view all the answers

Which criterion is NOT part of the requirements for writing a research hypothesis?

It must be written in past tense Signup and view all the answers

What does the coefficient of variation primarily measure?

The relative variability of a dataset Signup and view all the answers

In which situation should a one-sample t-test be applied?

When testing a hypothesis about the mean of one group against a known value Signup and view all the answers

Study Notes

Biostatistics Introduction

Biostatistics is the application of mathematical statistics to biological sciences and medicine involving data collection, organization, summarization, and analysis.
It's a growing field with numerous applications in areas like epidemiology, medical sciences, health sciences, educational research, and environmental sciences.
A key concern for biostatistics is the collection, organization, summarization, and analysis of data to draw inferences about a larger body of data even when only a portion is observed.

Purposes of Statistics

Statistics is used to describe and summarize information, reducing it down to more meaningful sets of data.
Statistics enables predictions about occurrences based on observations.
Identifying relationships and differences between observations is another important function of statistics.

Data

Data consists of measurements or counted values.
Biostatistics centers around interpreting the data and communicating information derived from the data.

Populations and Samples

A population is the complete set of values a variable can take.
A sample is a part of a larger population.
Samples are used to analyze the population, and are used effectively in cases where a population is too large for an analysis.

Population and Sampling

Sampling is the process of choosing a portion of the population for study.
Representativeness is a major characteristic of a good sample that ensures the sample characteristics closely match those of its larger population.
Sampling bias occurs when a subject is excluded from the sample without a sound scientific rationale, or it fails to fulfill the major inclusion and exclusion criteria.

Example

Studying self-esteem and academic achievement among college students.
Population: all college level students.
Sample: students from the University of Jordan.

What is Sampling?

Sampling is the process of selecting a group of study units or subjects from a larger, defined population.
It is a key element in efficient, cost-effective research.

Questions to Consider

The reference population for the research.
The group of people used for drawing the sample.
The size needed for the sample.
The appropriate method needed for selecting the sample.

Sampling - Populations

A reference population is the complete population being or potentially being studied
A study population is a manageable subset of the reference population that will be studied
A sampling frame is a list of all members in the study population.

Sampling

An element is a single member of a population being studied.
Sampling frame is a list of all elements in the population.
Example: list of all medical students at the University of Jordan for the years 2014-2016.

Sampling Methods

Sampling relies heavily on the sampling frame.
The sampling frame is a list of every unit that belongs to the study population.

Types of Sampling Methods

Probability sampling methods uses random selection to sample. Subtypes include simple random sampling, systematic sampling, stratified sampling, cluster sampling, and multistage sampling.
Non-probability sampling methods do not employ random selection. This could cause bias. Subtypes include convenience sampling, snowball sampling, quota sampling, and purposive sampling.

Probability Sampling Methods

Random selection is used to ensure that every unit in the study population has an equal or known chance of being included in a sample.
All units in the study population must have an equal or a known chance of being included in the sample.
A sampling frame is required.

Simple Random Sampling

This is the simplest probability sampling method.
Create a numbered list of all units in the population.
Decide on the sample size.
Select the required number of units via the lottery method or random numbers.

Systematic Sampling

Choose individuals at regular intervals from the sampling frame.
A starting point is randomly selected.
Individuals are selected at specified intervals.
Example: Every 5th household, every 10th woman attending an ANC, etc.

Stratified Sampling

Divide units into categories (strata) based on characteristics
Ensures strata proportions in the sample mirror the larger population.
Example: Samples are divided into strata based on socioeconomic class or race to ensure the representation of the sample mirrors that of the complete population.

Cluster Sampling

Select study units (clusters) instead of individuals.
All units in the cluster meet the criteria and are included.
Useful for geographic units (schools, villages).
It is helpful when the sampling frame isn't readily available or studying a population that is scattered over a large area.

Multistage Sampling

More than one sampling method is used, often in phases.
Sampling frame for entire population isn't necessary but individual clusters need a sampling frame.
Helpful for studying a population spread over a huge area

Nonprobability Sampling Methods

Sample elements aren't randomly selected.
It is more likely to occur or lead to biased samples.
Often used for convenience and to utilize available subjects. This could lead to bias.

Convenience Sampling

Selects people who are easily available.
People may or may not be typical of the population.
A convenient way in health research.
An advantage of this technique is that it is quick and cost-effective.

Snowball Sampling

Study subjects refer to others who fit the sample criteria.
Useful for populations that are hard to reach.
Example: Drug users, AIDS patients.

Quota Sampling

Ensures specific groups (strata) are represented in sample based on their proportions in the population.
The sample is selected by convenience - e.g. the first 50% of males and 50% of females.

Purposive Sampling

The subjects are handpicked because they represent the accessible population or they are experts in the field who can add value to the research.

Variables

A variable is an object, characteristic, or property that can take on different values.
A quantitative variable can be measured; a qualitative variable can be categorized.

Types of Variables

Independent variable: presumed cause.
Dependent variable: presumed effect.
- example: Smoking (IV) Lung cancer (DV)

Levels of Measurement

Nominal: categories with no particular order (gender, blood type).
Ordinal: categories with an order (pain severity).
Interval: equal intervals, but no true zero (temperature).
Ratio: equal intervals and a true zero (weight, height).

What Type of Data To Collect?

The goal of the researcher is to collect data using the highest possible level of measurement (ratio).
Using a lower level would restrict the analyses that can be performed.

Parameter and Statistic

A parameter is a numerical value measured from a complete population.
A statistic is a numerical value computed from a sample.

Statistics

Statistics is the science of collecting, organizing, and interpreting data.
Descriptive statistics: organizes, summarizes, and displays data.
Inferential statistics: makes predictions from samples about a larger population.

Descriptive Statistics

Measures of location: Mean, median, mode.
Measures of dispersion: Interquartile range, variance, standard deviation, coefficient of variation.
Measures of shape: Skewness

Statistical Inference

Making conclusions about a population using sample data.

Inferential Statistics

Used to test hypotheses about relationships between variables in a population.
Techniques involve prediction of population characteristics based on sample data.
Reports the likely accuracy (confidence) of samples.