Hypothesis Testing In Statistics | Hypothesis Testing Explained With Example | Simplilearn

Summary

This video from Simply Learn explores the concept of hypothesis testing, a statistical method for validating claims about population parameters using sample data. It starts with the formulation of a hypothesis from a research question, emphasizing the difference between the two. The video delves into criteria for a good hypothesis, introduces the null and alternative hypotheses, and explains test statistics like t-tests, z-tests, and f-tests. It concludes with the significance level, using an example of students' performance with special learning aids to illustrate the process. The video aims to clarify these statistical concepts, encouraging viewers to engage with the content and subscribe for more.

Takeaways

• 🔍 Hypothesis testing is a statistical method used to test a claim about a population parameter using sample data.
• 📚 A research question is a specific concern derived from a broader research problem and guides the investigation.
• 💡 The hypothesis is a tentative statement predicting the relationship between variables, often starting with a question and supported by background research.
• 🚫 The null hypothesis (H₀) assumes that an event will not occur and is used as a basis for testing against the alternative hypothesis.
• 🌐 The alternative hypothesis is the logical opposite of the null hypothesis and is accepted if the null hypothesis is rejected.
• 📊 Test statistics summarize observed data into a single number to compare against the expected distribution under the null hypothesis.
• 📈 T-tests, Z-tests, and F-tests are common statistical tests used in hypothesis testing, each with specific applications and interpretations.
• 🎓 A hypothesis should be compatible with current knowledge, logically consistent, clearly stated, and testable.
• 📉 The significance level is a threshold for deciding whether the null hypothesis can be rejected; it is often set at 0.05 or 1%.
• 📚 An example given in the script involves testing the impact of special science learning videos on student performance in a competency test.
• 🔔 The video concludes by emphasizing the importance of hypothesis testing in research and encourages viewers to ask questions and subscribe for more content.

Q & A

What is hypothesis testing?

Hypothesis testing, also known as significance testing, is a statistical method used to test a claim or hypothesis about a population parameter using sample data. It checks if there is sufficient statistical evidence to support the hypothesis claimed.

What is the purpose of hypothesis testing?

The purpose of hypothesis testing is to determine whether there is enough statistical evidence to support a hypothesis, thus allowing researchers to make informed decisions about the validity of their claims.

What is the difference between a research question and a hypothesis?

A research question is a specific concern that aims to be answered through research, derived from a broader research problem. A hypothesis, on the other hand, is a tentative statement about the relationship between variables, making predictions about experimental outcomes based on the research question.

What are the criteria for developing a good hypothesis?

A good hypothesis should be compatible with current knowledge, follow logical consistency, be testable, and be stated briefly and clearly.

What is the null hypothesis?

The null hypothesis (H0) is an assumption that there is no effect or relationship between variables being studied. It is used as a basis for comparison against the alternative hypothesis.

What is the alternative hypothesis?

The alternative hypothesis is a logical opposite of the null hypothesis. It represents the research hypothesis that the researcher is trying to support and is accepted if the null hypothesis is rejected.

Can you explain the concept of test statistics in hypothesis testing?

Test statistics is a number calculated from the statistical test of a hypothesis, indicating how closely the observed data matches the expected distribution under the null hypothesis. It summarizes the observed data into a single number using measures such as central tendency, variation, and sample size.

What are the different types of statistical tests mentioned in the script?

The script mentions three types of statistical tests: t-test, z-test, and f-test. The t-test compares the means of two groups, the z-test compares a sample mean with a population mean when population variance is known or sample size is greater than 30, and the f-test assesses the equality of variances or the ratio of two variances.

What is the significance level in hypothesis testing?

The significance level, often denoted as alpha (α), is the probability threshold used to decide whether to reject the null hypothesis. It is typically set at 0.05 (5%), indicating that if the probability of observing the data under the null hypothesis is less than this threshold, the null hypothesis is rejected.

How does the example in the script illustrate the concept of hypothesis testing?

The example in the script involves a study on students receiving special learning aids through online science videos. The research hypothesis predicts that these students will score higher on a science competency test than those who did not receive the videos. The null hypothesis states that there is no impact of the videos on student scores. The significance level is used to determine whether to reject or support the null hypothesis based on the study results.

Outlines

00:00

🔍 Introduction to Hypothesis Testing

This paragraph introduces the concept of hypothesis testing, explaining it as a method for evaluating claims about a population parameter using sample data. It emphasizes the purpose of hypothesis testing, which is to determine if there is sufficient statistical evidence to support a hypothesis. The paragraph also distinguishes between a research question and a hypothesis, highlighting that a hypothesis predicts outcomes while a research question does not. It further outlines the criteria for a good hypothesis, such as compatibility with existing knowledge, logical consistency, clarity, and testability. The discussion then moves to the null hypothesis and alternative hypothesis, explaining their roles in hypothesis testing and providing an example related to the impact of advertisement duration on product sales.

05:02

📊 Exploring Test Statistics and Hypothesis Testing Methods

The second paragraph delves into the specifics of test statistics, which quantify how closely observed data aligns with the expected distribution under the null hypothesis. It outlines three main types of statistical tests: t-tests, which compare group means; z-tests, used when population variance is known or sample size exceeds 30; and f-tests, which assess the ratio of variances. The paragraph explains the null and alternative hypotheses associated with these tests, using the example of a study on the effectiveness of special learning aids in improving science test scores. It concludes by defining the significance level, a threshold for determining whether to reject the null hypothesis, often set at 0.05, and encourages viewers to engage with the channel for further learning opportunities.

Keywords

💡Hypothesis Testing

Hypothesis testing, also known as significance testing, is a statistical method used to evaluate a claim or hypothesis about a population parameter based on sample data. It is central to the video's theme as it provides a framework for determining whether there is sufficient evidence to support a hypothesis. For example, the script discusses the process of hypothesis testing in the context of a research question, explaining how it can be used to check if the duration of TV advertisements is related to product sales.

💡Research Question

A research question is a specific concern that a researcher seeks to answer through their study. It is derived from a broader research problem and is the foundation for formulating a hypothesis. In the video, the research question is used to illustrate the difference between a question and a hypothesis, with examples such as 'how many hours per day a student spends on gaming' and its relation to social alienation.

💡Hypothesis

A hypothesis is a tentative statement about the relationship between variables, which predicts the outcome of a study. It is more than a guess and is based on background research. The video emphasizes that a hypothesis should be testable and makes a prediction, such as the hypothesis that 'students who spend more time on gaming are socially alienated'.

💡Null Hypthesis

The null hypothesis is an assumption that there is no effect or relationship between variables being studied. It serves as a baseline against which the alternative hypothesis is compared. The script uses the example of advertising duration and product sales, stating that the null hypothesis would be 'the duration of the advertisement on TV channels is not related to the sales of the product'.

💡Alternative Hypothesis

The alternative hypothesis is the logical opposite of the null hypothesis and represents the research hypothesis that the study is actually testing. It is accepted if the null hypothesis is rejected. The video explains this concept by stating that if the null hypothesis is about no relationship between advertising duration and sales, the alternative would be that there is a positive relationship.

💡Test Statistics

Test statistics are numerical values calculated from sample data to determine how well the observed data fits with the distribution expected under the null hypothesis. They are crucial in hypothesis testing as they summarize the data into a single number that can be compared to a critical value. The video script mentions test statistics in the context of different statistical tests, such as t-tests, z-tests, and f-tests.

💡T-test

A t-test is a statistical method used to compare the means of two groups to determine if there is a significant difference between them. The video script explains that the null hypothesis for a t-test is that the true difference between group means is zero, while the alternative hypothesis is that the difference is not zero.

💡Z-test

A z-test is a statistical test used to compare a sample mean to a known population mean, assuming the population variance is known or the sample size is large enough. The video script discusses z-tests in the context of hypothesis testing when the population variance is known or when the sample size exceeds 30.

💡F-test

An F-test, or F-statistic, is used to compare the variances of two or more groups. It is a ratio of variances and can be used in various situations, including assessing the equality of variances. The video script explains that the F-test is a flexible test that can be adapted for different statistical models by changing the variances included in the ratio.

💡Significance Level

The significance level is the probability threshold used to decide whether to reject the null hypothesis. It is a key concept in hypothesis testing as it determines the stringency of the test. The video script mentions that the significance level is typically set at 0.05, indicating that if the probability of observing the test statistic under the null hypothesis is less than this value, the null hypothesis is rejected.

Highlights

Hypothesis testing is a method for testing a claim or hypothesis about a parameter in a population using data measured in a sample.

The purpose of hypothesis testing is to check if there is enough statistical evidence in favor of a hypothesis.

A research problem identifies a broad issue to address, while a research question is a specific concern to be answered through research.

A hypothesis makes a prediction about experimental outcomes, whereas a research question does not.

A hypothesis is a tentative statement about the relationship between variables, involving more than a guess and based on background research.

Good criteria for a hypothesis include compatibility with current knowledge, logical consistency, clarity, and testability.

The null hypothesis assumes that an event will not occur, symbolized by H₀.

The alternative hypothesis is the logical opposite of the null hypothesis and is accepted if the null hypothesis is rejected.

Test statistics summarize observed data into a single number to compare with the expected distribution under the null hypothesis.

T-tests are used to compare the means of two groups and determine if a process or treatment affects the population of interest.

Z-tests compare a sample mean with a population mean when either the population variance is known or the sample size is greater than 30.

F-tests assess the equality of variances and are flexible for various situations by changing the variances included in the ratio.

An example study investigates whether special science learning videos improve students' scores on a science competency test.

The significance level is a criterion for judgment based on the probability of obtaining a statistic if the null hypothesis were true.

A commonly set significance level is 0.05, which can be interpreted as a 5% probability threshold for rejecting the null hypothesis.

If the study result indicates a probability lower than the significance level, the null hypothesis can be rejected.

If the study result indicates a probability higher than the significance level, the null hypothesis is supported.

The video concludes with an invitation for questions, subscription, and notification activation for updates.

Transcripts

hi everyone welcome to this exciting

session by simply learn

today we have a really interesting topic

for you

in this video we'll be discussing about

the hypothesis testing

we'll start by talking about the

hypothesis testing and how a research

question can help you come with a good

hypothesis

then we'll look at the hypothesis and

the criteria for developing a good

hypothesis

following that we'll look at the null

hypothesis concept test statistics and

understand it with the help of an

example

finally we conclude this video by

briefing you about the significance

level

so let's get started

what is hypothesis testing

hypothesis testing or significance

testing is a method for testing a claim

or hypothesis about a parameter in a

population using data measured in a

sample

the purpose of the hypothesis testing is

to check if there is enough statistical

evidence in a favor of hypothesis that

we have claimed

now we will move on to the research

question

a research problem is a broad issue that

you would like to address through your

research

it identifies the difficult doubt or

area of concern in the theory or in

practice

that requires thought and investigation

research objectives are clear statements

of what you aim to achieve through your

research there are specific actions that

you will take and act as a milestone

that will help you complete your

research a research question is a

specific concern that you will answer

through research it is derived from a

research problem but is based on a study

design

when you narrow down on a research

problem to a specific idea that points

towards a feasible way to investigate or

address the research problems we'll get

a research question

now

what you should really take care of is

the slight difference between the

research question and the hypothesis

hypothesis makes prediction about

experimental outcome whereas research

question does not

let's understand with the help of an

example suppose your research question

is how many hours per day a student

spends on a giving and you want the

answer for that

another recent question may be

do the college students with more study

hours can achieve the higher gpa than

the students who do not put in more

hours for study

these questions can be answered by

framing a hypothesis so let's understand

what a hypothesis is

a hypothesis is a temptative statement

about the relationship between two or

more variables

it is a specific festival predictions

about what you expect to happen in a

study the hypothesis is a prediction but

it involves more than a guess

most of the time hypothesis begins with

a question which is then explored to a

background research

hypothesis translates the research

question into a prediction of expected

outcomes

unless you are creating an explanatory

study a hypothesis should always explain

what to expect to happen

so as in the previous slide we have

framed the question that how many hours

per student spend on a gaming related to

this question we can create a hypothesis

that students who spend more time on

gaming are socially alienated

so there are some good criteria for a

good hypothesis let's discuss what are

those

a hypothesis should be compatible with

the current knowledge in the area and it

should follow the logical consistency it

should not be inconsistent in places

a good hypothesis must be shaded briefly

and clearly

and it should be testable now we'll

understand what a null hypothesis and

alternative hypothesis is

the null hypothesis is the assumption

that an event will not occur

a null hypothesis has no bearing on the

study's outcome unless it is rejected

h naught is a symbol for null hypothesis

the alternating hypothesis or a research

hypothesis is a logical opposite of the

null hypothesis

the acceptance of the alternative

hypothesis follows the rejection of the

null hypothesis

let's understand the null hypothesis

with the help of an example suppose we

have a research hypothesis the duration

of an advertisement on the tv channels

is positively related to the sales of

the product

the more the duration the more the sales

of that product

so the null hypothesis of this

assumption would be

the duration of the advertisement on the

tv channels are not related to the sales

of the product they're not related at

all now we'll move on to the test

statistics that i frequently discussed

when creating hypothesis testing

the test statistics is a number

calculated from the statistical test of

a hypothesis it shows how close your

observed data matches the distribution

expected under the null hypothesis of

data statistical test

the distribution of the data is how

often each observation occurs and can be

described by central tendency and

variation around the central tendencies

the test statistics summarizes your

observed data into a single number using

the central tendency variation sample

size and the other number of predictable

variables in your statistical model

there are broadly three capsule

statistical tests

different statistical tests have

slightly different ways of calculating

these test statistics but the underlying

hypothesis and interpretation of the

test statistics stay the same

so the first one is a t-test

a t-test is a statistical test that is

used to compare the means of two groups

it is often used in hypothesis testing

to determine whether a process or

treatment actually has an effect on the

population of interest or whether the

two groups are different from one

another the null hypothesis

is that the true difference between

these group means is zero and the

alternative hypothesis is that the true

difference is different from zero

now let's move on to the test

the tests are statistical way of testing

a hypothesis that either we know the

population variance or we don't know the

population variance but our sample size

is greater than 30. we perform the z

test when we want to compare a sample

mean with the population mean

the next is an f test the f test or the

f statistics is simply a ratio of two

variances

variances is a measure of dispersion or

how far the data are scattered from the

mean larger values represent a greater

dispersion despite being a ratio of

variances you can use a f-test in a wide

variety of situation

f-test can assess the equality of

variances however by changing the

variances that are included in the ratio

the f-test became a very flexible test

now that we have discussed all the

theories related to the hypothesis

testing let's take an example to

understand them more clearly

consider a study on a group of students

whether students receive a special

learning aid to the online videos on

science

it is hypothesized that after viewing

these online videos the group of

students who are better than the one who

have not seen the videos

so in this case a research hypothesis

will be students who have received their

special science learning videos will

score high in a science competency test

and its null hypothesis will be the

special science learning videos may no

impact on the scores of the students

now we will discuss what a significance

level is

level of significance or significance

level refers to a criterion of judgment

upon which a decision is made regarding

the values stated in the null hypothesis

this criteria is based on the

probability of obtaining a statistic

measured in a sample if the values

stated in null hypothesis were true

generally the criterion of the level of

significance is typically set at 5

or 0.05

this value of significance level can

also be taken as one percent or 10

depending upon your requirement

if the result obtained from the study

indicates the probability lower than the

significance level so in this case a

researcher can reject null hypothesis

otherwise if the result of the study

indicates a probability higher than the

significance level the researcher can

support the null hypothesis with that we

have come to the end of this video on

hypothesis testing i hope this was

helpful

if you have any questions then please

put them in the comment section also

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