Name: rejection regions and significance in tests
Uploaded: 2023-04-30T12:24:25.000Z
Duration: 1 min 16 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

HIgh School

Biology

BIO.1

BIO.1.d

critical-region-critical-values-and-significance-level

Critical Region, Critical Values and Significance Level

Hypothesis testing requires the sample statistics&#8212;such as proportion, mean, or standard deviation&#8212;to be converted into a value or score known as the test statistics.
Assuming that the null hypothesis is true, the test statistic for each sample statistic is calculated using the following equations.
As samples assume a particular distribution, a given test statistic value would fall into a specific area under the curve with some probability.
Such an area, which includes all the values of a test statistic that indicates that the null hypothesis must be rejected, is termed the rejection region or critical region.
The value that separates a critical region from the rest is termed the critical value. The critical values are the&#160;z, t,&#160;or chi-square values calculated at the desired confidence level.
The probability that the test statistic will fall in the critical region when the null hypothesis is actually true is called the significance level.
In the example of testing the proportion of healthy and scabbed apples, if the sample proportion is 0.9, the hypothesis can be tested as follows.

critical region, critical values and significance level

The critical region, critical value, and significance level are interdependent concepts crucial in hypothesis testing.
In hypothesis testing, a sample statistic is converted to a test statistic using z, t, or chi-square distribution. A critical region is an area under the curve in&#160; probability distributions demarcated by the critical value. When the test statistic falls in this region, it suggests that the null hypothesis must be rejected. As this region contains all those values of the test statistic (calculated using the sample data) that suggest rejecting the null hypothesis, it is also known as the rejection region or region of rejection. The critical region may fall at the right, left, or both tails of the distribution based on the direction indicated in the alternative hypothesis and the calculated critical value.
A critical value is calculated using the z, t, or chi-square distribution table at a specific significance level. It is a fixed value for the given sample size and the significance level. The critical value creates a demarcation between all those values that suggest rejection of the null hypothesis and all those other values that indicate the opposite. A critical value is&#160; based on a pre-decided significance level.
A significance level or level of significance or statistical significance is defined as the probability that the calculated test statistic will fall in the critical region. In other words, it is a statistical measure that indicates that the evidence for rejecting a true null hypothesis is strong enough. The significance level is indicated by &#945;, and it is commonly 0.05 or 0.01.

The critical region, critical value, and significance level are interdependent concepts crucial in hypothesis testing.
In hypothesis testing, a sample ...

Education

JoVE Core

Statistics

Unit 1

Hypothesis Testing

KEY TERMS AND CONCEPTS

rejection regions and significance in tests

Rejection regions and significance level help decide whether to reject the null hypothesis in hypothesis testing. A sample statistic is first turned into a test statistic using the z, t, or chi-square distribution. The critical region is the part of the probability curve where the test statistic leads to rejection of the null hypothesis.

This region is also called the rejection region or region of rejection. It can appear in the right tail, left tail, or both tails of the distribution. The location depends on the direction stated in the alternative hypothesis and on the critical value.

A critical value is the fixed cutoff found from the z, t, or chi-square table for a chosen significance level. It depends on the sample size and the pre-decided level of significance. This value separates test results that suggest rejecting the null hypothesis from those that do not.

The significance level, written as alpha, is the probability that the test statistic falls in the critical region. It shows how strong the evidence must be before a true null hypothesis is rejected. Common significance levels are 0.05 and 0.01.

Rejection Regions and Significance in Tests

rejection-regions-and-significance-in-tests

what is a hypothesis?

Testing a Hypothesis with Sample Data

A hypothesis is a statement about a population property or a phenomenon seen in an observation or experiment. It can describe something that is expected or predicted for a group. In statistics, it is a claim that can be tested with data. A hypothesis should be general, but not vague. It should not make a claim with a definite number, quantity, or measurement for a population property. A hypothesis is not judged as right or wrong on its own. It must be examined through data collection and an...

null and alternative hypotheses

Comparing Hypotheses in Statistical Tests

Statistical hypothesis testing starts by comparing two opposing claims. These are the null hypothesis and the alternative hypothesis. They give researchers a way to judge sample data before making a decision. The null hypothesis, written as H0, says there is no difference between the variables. It also says the variables are not related. This idea is often treated as the status quo. The alternative hypothesis, written as H1 or Ha, makes a claim that conflicts with H0. It is the statement the...

Rejection regions and significance level help decide whether to reject the null hypothesis in hypothesis testing. A sample statistic is first turned into a test statistic using the z, t, or chi-square distribution. The critical region is the part of the probability curve where the test statistic leads to rejection of the null hypothesis. This region is also called the rejection region or region of rejection. It can appear in the right tail, left tail, or both tails of the distribution. The...

p-value

P-Value in Hypothesis Testing

P-value is a key idea in statistics and hypothesis testing. It stands for probability value. It helps show how likely the observed sample results are if the null hypothesis is true. More exactly, p-value is the probability that another randomly selected sample will produce results as extreme or more extreme than the results from the given sample, assuming the null hypothesis is true. A large p-value suggests that the null hypothesis should not be rejected. However, a larger p-value does not...

types of hypothesis testing

Tail Direction in Hypothesis Tests

Hypothesis tests are classified by the direction of the alternative hypothesis. The null hypothesis is a neutral statement, and the alternative hypothesis is the claim being tested against it. If the null hypothesis says p = 0.5, the alternative can be written as p &gt; 0.5, p 0.5, the critical region lies on the right side of the probability distribution curve. A right-tailed hypothesis test is used in that case. When the claim is p &lt; 0.5, the critical region lies on the left side of the...

decision making: p-value method

Hypothesis Test Results with P-Values

Hypothesis testing with the P-value method uses sample data to judge a claim about a population parameter. The process starts with a clear research question and a simple statement about the population. An opposing statement is also written so the claim can be tested fairly. These statements become the null hypothesis and the alternative hypothesis. The null hypothesis is a neutral statement, while the alternative hypothesis can have a direction. In some cases, the original claim is the...

decision making: traditional method

Hypothesis Tests Using Critical Values

Hypothesis tests using critical values follow a traditional decision process in statistics. Students first state a claim about a population parameter and then write the opposite statement. These become the null hypothesis and the alternative hypothesis. The null hypothesis is neutral, while the alternative hypothesis can show a direction. After the hypotheses are set, they are written in symbols. By convention, the null hypothesis includes the equality symbol. The alternative hypothesis may...

hypothesis: accept or fail to reject?

Fail to Reject the Null Hypothesis

Hypothesis testing helps scientists decide whether to reject or fail to reject the null hypothesis. The decision comes from the data, the test statistic, the confidence level, the critical values, and the P-value. These parts work together to show whether the evidence is strong enough to support the alternative hypothesis. When the evidence is weak, it is not correct to say that the null hypothesis has been accepted as true. In statistics, that wording can suggest the null hypothesis has been...

errors in hypothesis tests

Type I, Type II, and Test Power

Hypothesis testing can lead to four outcomes based on the true state of the null hypothesis and the choice to reject or not reject it. If the null hypothesis is true and the decision is not to reject it, that is a correct decision. If the null hypothesis is true but it is rejected, that is a Type I error. A Type II error happens when the null hypothesis is false, but it is not rejected. This is also an incorrect decision. The correct decision when the null hypothesis is false is to reject it.

testing a claim about population proportion

testing-a-claim-about-population-proportion

Population Proportion Tests with z and Binomial

Population proportion tests use hypothesis testing to check a claim about a binomial result. The data must come from random and unbiased samples. The variable must also have only two outcomes, such as success or failure, selected or not selected, or true or false. One common method uses the sample proportion and a normal approximation to the binomial distribution. This approach works when the sample is large enough, the proportion is close to 0.5, and np is greater than 5. Here, p is the...

testing a claim about mean: known population sd

testing-a-claim-about-mean-known-population-sd

Z Test for Mean with Known SD

The z test for a population mean uses a known population standard deviation and a normal distribution. It is used when random samples are collected without sampling bias. The sample size should be greater than 30, and the population standard deviation must already be known. In many real situations, the population standard deviation is unknown. In the rare cases when it is known, the claim about the population mean can be tested with the normality assumption and the z distribution. The null...

testing a claim about mean: unknown population sd

testing-a-claim-about-mean-unknown-population-sd

Using the t Test for a Population Mean

Testing a population mean with an unknown standard deviation uses the t test. This method helps estimate a mean when the population standard deviation is not known. It is common in real situations, so the sample standard deviation is used instead. The data should come from randomly selected samples with no sampling bias. The samples should also be approximately normally distributed. There is no specific requirement for sample size, but a different approach is used when the sample size is less...

testing a claim about standard deviation

Chi-Square Test for Standard Deviation Claims

Chi-square hypothesis testing is used to check a claim about population standard deviation or population variance. The data and samples must be random and unbiased. The population distribution must also be normal. The test starts by stating the null and alternative hypotheses clearly and in symbolic form. The claim usually gives a specific value for the population standard deviation or variance. A sample standard deviation or variance is then used to calculate the test statistic. The critical...

key terms and concepts

Learn how rejection regions, critical values, and significance level work together in hypothesis testing using z, t, and chi-square distributions.

Rejection Regions and Significance in Tests | JoVE K12

statistics

JoVE Core Statistics introduces the concepts and application of the collection, analysis, presentation, and interpretation of data to students. These animated lessons provide an understanding of statistics beneficial to students from a wide range of disciplines. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide

Chemistry

CH.1

CH.1.d

Texas Essential Knowledge and Skills

High School

CHEM.1

CHEM.1.H

The Scientific Method

The scientific method is a detailed, empirical problem-solving process used by biologists and other scientists. This iterative approach involves ...

Inductive Reasoning

Inductive reasoning is a form of logical thinking that uses related observations to arrive at a general conclusion. It is uncertain and operates in ...

Deductive Reasoning

Deductive reasoning, or deduction, is the type of logic used in hypothesis-based science. In deductive reasoning, the pattern of thinking moves in the ...

Correlation and Causation

Correlation and CausationStatistical tests can calculate whether there is a relationship, or correlation, between independent and dependent variables. A ...

The student will demonstrate an understanding of scientific and engineering practices by asking questions and defining problems
• ask questions that arise from careful observation of phenomena and/or
organisms, from examining models and theories, and/or to seek additional
information
• determine which questions can be investigated within the scope of the
school laboratory or field to determine relationships between independent
and dependent variables
• generate hypotheses based on research and scientific principles
• make hypotheses that specify what happens to a dependent variable when
an independent variable is manipulated

BIO.1.a

Case Studies

There are many research methods available to psychologists in their efforts to understand, describe, and explain behavior and the cognitive and biological ...

Naturalistic Observations

If you want to understand how behavior occurs, one of the best ways to gain information is to simply observe the behavior in its natural context. However, ...

Surveys

Often, psychologists develop surveys as a means of gathering data. Surveys are lists of questions to be answered by research participants, and can be ...

Archival Research

Some researchers gain access to large amounts of data without interacting with a single research participant. Instead, they use existing records to answer ...

Longitudinal Research

Sometimes we want to see how people change over time, as in studies of human development and lifespan. When we test the same group of individuals ...

Cross-Sectional Research

In cross-sectional research, a researcher compares multiple segments of the population at the same time. If they were interested in people&#39;s dietary ...

Group Design

The most basic experimental design involves two groups: the experimental group and the control group. The two groups are designed to be the same except ...

Factorial Design

Factorial Analysis is an experimental design that applies Analysis of Variance (ANOVA) statistical procedures to examine a change in a dependent variable ...

The Placebo Effect

The placebo effect occurs when people&#39;s expectations or beliefs influence or determine their experience in a given situation. In other words, simply ...

Blind Procedures

Ideally, the people who observe and record the children&rsquo;s behavior are unaware of who was assigned to the experimental or control group, in order to ...

Ethics in Research

Today, scientists agree that good research is ethical in nature and is guided by a basic respect for human dignity and safety. However, this has not ...

The student will demonstrate an understanding of scientific and engineering practices by planning and carrying out investigations
 • individually and collaboratively plan and conduct observational and experimental investigations 
 • plan and conduct investigations or test design solutions in a safe and ethical manner including considerations of environmental, social, and personal effects
• determine appropriate sample size and techniques 
 • select and use appropriate tools and technology to collect, record, analyze, and evaluate data

BIO.1.b

Introduction to Statistics

The science of statistics involves collecting, analyzing, interpreting, and presenting data. The method of collecting, organizing, and summarizing data is ...

How Data are Classified: Categorical Data

A variable, usually notated by capital letters such as X and Y, is a characteristic or measurement that can be determined for each member of a population. ...

How Data are Classified: Numerical Data

Data that are countable or measurable in specific units are called numerical or quantitative data. Quantitative data are always numbers. Quantitative data ...

Ogive Graph

An ogive graph is sometimes called a cumulative frequency polygon. It is one type of frequency polygon that shows cumulative frequency. In other words, ...

Histogram

The histogram is a graphical representation in the x-y form of data distribution in a data set. The horizontal x-axis is labeled with what the data ...

Relative Frequency Histogram

The relative frequency depicts the proportion of data points that have each value. The frequency tells the number of data points that have each value. ...

Scatter Plot

The most common and easiest way to display the relationship between two variables, x and y, is a scatter plot. A scatter plot shows the direction of a ...

Time-Series Graph

A time-series graph is a line graph with repeated measurements taken at successive intervals of time. It is also called a time series chart. To construct ...

Bar Graph

A bar graph is also called a bar chart and consists of bars that are separated from each other. It either uses horizontal or vertical bars to show ...

Multiple Bar Graph

As the name suggests, a multiple bar graph is the same as a bar graph but has multiple bars to depict relationships between different data values. One can ...

Pareto Chart

A Pareto chart is a bar graph or a combination of both line and bar graphs. The bar lengths represent the individual values or the frequency, while the ...

Pie Chart

A pie chart (or a pie graph) is a circular graphical chart or a pictorial representation of categorical data. It is divided into slices of pie each ...

What is Central Tendency?

Descriptive statistics describe or summarize relevant characteristics of a sample and aid in the analysis of data of interest. When analyzing large ...

Arithmetic Mean

The arithmetic mean is the most commonly used measure of the central tendency of a data set. It is defined as the sum of all the elements constituting the ...

Mean From a Frequency Distribution

Sometimes, data gathered from an experiment on a large sample or population are organized into concise tables. In such cases, the frequency of the ...

What is a Mode?

The mode is one of the commonly used measures of a central tendency. It is defined as the most frequent value in a data set.
There can be more than one ...

Bias

Bias refers to any tendency that prevents a question from being considered unprejudiced. In research, bias occurs when one outcome or answer is selected ...

Median

Besides mean, the median is a widely used measure of central tendency. Typically, median is defined as the central or middle value of a data set, measured ...

Blinding

Blinding is a commonly used method of not telling participants which treatment a subject is receiving. Blinding is a critical part of a randomized control ...

Midrange

A somewhat easy to compute quantitative estimate of a data set&#8217;s central tendency is its midrange, which is defined as the mean of the minimum and ...

Clinical Trials

Clinical trials are prospective experimental studies conducted on humans to determine the safety and efficacy of treatments, drugs, diet methods, and ...

What is Variation?

Apart from the measures of central tendency, distribution, outliers, and the changing characteristics of data with time, an important characteristic of ...

Range

The range is one of the measures of variation. It can be defined as the difference between a dataset&#39;s highest and lowest values. For example, in the ...

Standard Deviation

The most commonly used measure of variation is the standard deviation. It is a numerical value measuring how far data values are from their mean. The ...

Standard Error of the Mean

The sampling variability of a statistic is defined as how much the statistic varies from one sample to another. The sampling variability of a statistic is ...

Calculating Standard Deviation

The standard deviation is the most common measure of variation. It is a value that tells us how far a data value is from the mean value in a dataset. ...

Crossover Experiments

Crossover experiments, also called the repeated-measurements design, is a study design in which all experimental units are exposed to all treatments in ...

Controls in Experiments

When conducting an experiment, it is crucial to have control to reduce bias and accurately measure the dependent variables. It also marks the results more ...

The student will demonstrate an understanding of scientific and engineering practices by interpreting, analyzing, and evaluating data 
 • construct and interpret data tables showing independent and dependent variables, repeated trials, and means
 • construct, analyze, and interpret graphical displays of data
 • use data in building and revising models, supporting an explanation for phenomena, or testing solutions to problems
 • analyze data using tools, technologies, and/or models to make valid and reliable scientific claims or determine an optimal design solution

BIO.1.c

What is a Hypothesis?

A hypothesis can be a simple sentence or statement about a property or any phenomenon observed or predicted for a population. It is usually a claim about ...

Null and Alternative Hypotheses

The actual hypothesis testing begins by considering two hypotheses. They are termed&#160; the null hypothesis and the alternative hypothesis. These ...

P-value

P-value is one of the most crucial concepts in statistics.
P-value stands for the probability value. &#160;P-value is the probability that, if the null ...

Types of Hypothesis Testing

There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed.
When the null and alternative hypotheses are stated, it is observed ...

The student will demonstrate an understanding of scientific and engineering practices by  constructing and critiquing conclusions and explanations
• make quantitative and/or qualitative claims regarding the relationship between dependent and independent variables 
• construct and revise explanations based on valid and reliable evidence obtained from a variety of sources including students' own investigations, models, theories, simulations, and peer review 
• apply scientific ideas, principles, and/or evidence to provide an explanation of phenomena and design solutions 
• compare and evaluate competing arguments or design solutions in light of currently accepted explanations and new scientific evidence
• construct arguments or counterarguments based on data and evidence differentiate between a scientific hypothesis and theory

Dimensional Analysis

Dimensional analysis helps simplify fluid flow problems by using dimensionless groups, reducing complex variables into simpler terms that are easier to ...

Modeling and Similitude

A scaled model of a dam is tested in a controlled environment to observe how it will manage water flow, turbulence, and pressure.
This setup predicts the ...

Typical Model Studies

Typical model studies analyze scaled-down systems to predict fluid behavior, focusing on interactions with free surfaces and flow around immersed bodies.
...

The student will demonstrate an understanding of scientific and engineering practices by  developing and using models
• evaluate the merits and limitations of models
• develop, revise, and/or use models based on evidence to illustrate or predict relationships 
• develop and/or use models to generate data to support explanations, predict phenomena, analyze systems, and/or solve problems

BIO.1.e

Communication Process

The communication process is the transmission and reception of messages or information from one sender to the receiver.
It involves the sender encoding an ...

Communication Objectives

Marketing communication objectives refer to the strategic goals that guide promotional activities.
They set the stage for messaging strategies, content ...

The student will demonstrate an understanding of scientific and engineering practices by  obtaining, evaluating, and communicating information 
• compare, integrate, and evaluate sources of information presented in different media or formats to address a scientific question or solve a problem
• gather, read, and evaluate scientific and/or technical information from multiple authoritative sources, assessing the evidence and credibility of each source
• communicate scientific and/or technical information about phenomena in multiple formats

BIO.1.f

Rejection Regions and Significance in Tests

Description

Transcript

Tags

More videos by Standards