This document introduces hypothesis testing, which is used to determine if a treatment has an effect on a population. It involves taking a sample from a population, administering a treatment, measuring the results, and using statistics to decide if any differences are likely due to the treatment or just chance. The null hypothesis states there is no effect, and the alternative hypothesis states there is an effect. Hypothesis tests aim to avoid type 1 and type 2 errors and can measure effect size and test power.
Following points are presented in this presentation.
1. Hypothesis testing is a decision-making process for evaluating claims about a population.
2. NULL HYPOTHESIS & ALTERNATIVE HYPOTHESIS.
3. Types of errors.
Following points are presented in this presentation.
1. Hypothesis testing is a decision-making process for evaluating claims about a population.
2. NULL HYPOTHESIS & ALTERNATIVE HYPOTHESIS.
3. Types of errors.
This slideshow is related to testing of hypothesis and goodness of fit of statistics. This may be useful for students, teachers, managers concerned with bio statistics, bioinformatics, data science, etc.
Hypothesis testing and estimation are used to reach conclusions about a population by examining a sample of that population.
Hypothesis testing is widely used in medicine, dentistry, health care, biology and other fields as a means to draw conclusions about the nature of populations
A non technical overview of sample size calculation and why it is necessary with some brief examples of how to approach the problem and why it is useful to actually think of these calculations.
The error (or disturbance) of an observed value is the deviation of the observed value from the (unobservable) true value of a quantity of interest (for example, a population mean), and the residual of an observed value is the difference between the observed value and the estimated value of the quantity of interest (for example, a sample mean).
Suppose there is a series of observations from a univariate distribution and we want to estimate the mean of that distribution (the so-called location model). In this case, the errors are the deviations of the observations from the population mean, while the residuals are the deviations of the observations from the sample mean.
A statistical error (or disturbance) is the amount by which an observation differs from its expected value, the latter being based on the whole population from which the statistical unit was chosen randomly. For example, if the mean height in a population of 21-year-old men is 1.75 meters, and one randomly chosen man is 1.80 meters tall, then the "error" is 0.05 meters; if the randomly chosen man is 1.70 meters tall, then the "error" is −0.05 meters. The expected value, being the mean of the entire population, is typically not observable, and hence the statistical error cannot be observed either.
Application of statistical tests in Biomedical Research .pptxHalim AS
Here I have tried to show how to select a statistical test for a research project based on the type of data.
initially I have given an idea about the types of data, null hypothesis, p value and the types of error
Hypothesis Testing Definitions A statistical hypothesi.docxwilcockiris
Hypothesis Testing
Definitions:
A statistical hypothesis is a guess about a population parameter. The guess may or not be
true.
The null hypothesis, written H0, is a statistical hypothesis that states that there is no
difference between a parameter and a specific value, or that there is no difference between
two parameters.
The alternative hypothesis, written H1 or HA, is a statistical hypothesis that specifies a
specific difference between a parameter and a specific value, or that there is a difference
between two parameters.
Example 1:
A medical researcher is interested in finding out whether a new medication will have
undesirable side effects. She is particularly concerned with the pulse rate of patients who
take the medication. The research question is, will the pulse rate increase, decrease, or
remain the same after a patient takes the medication?
Since the researcher knows that the mean pulse rate for the population under study is 82
beats per minute, the hypotheses for this study are:
H0: µ = 82
HA: µ ≠ 82
The null hypothesis specifies that the mean will remain unchanged and the alternative
hypothesis states that it will be different. This test is called a two-tailed test since the
possible side effects could be to raise or lower the pulse rate. Notice that this is a non
directional hypothesis. The rejection region lies in both tails. We divide the alpha in two
and place half in each tail.
Example 2:
An entrepreneur invents an additive to increase the life of an automobile battery. If the
mean lifetime of the automobile battery is 36 months, then his hypotheses are:
H0: µ ≤ 36
HA: µ > 36
Here, the entrepreneur is only interested in increasing the lifetime of the batteries, so his
alternative hypothesis is that the mean is greater than 36 months. The null hypothesis is
that the mean is less than or equal to 36 months. This test is one-tailed since the interest
is only in an increased lifetime. Notice that the direction of the inequality in the alternate
hypothesis points to the right, same as the area of the curve that forms the rejection
region.
Example 3:
A landlord who wants to lower heating bills in a large apartment complex is considering
using a new type of insulation. If the current average of the monthly heating bills is $78,
his hypotheses about heating costs with the new insulation are:
H0: µ ≥ 78
HA: µ < 78
This test is also a one-tailed test since the landlord is interested only in lowering heating
costs. Notice that the direction of the inequality in the alternate hypothesis points to the
left, same as the area of the curve that forms the rejection region.
Study Design:
After stating the hypotheses, the researcher’s next step is to design the study. In designing
the study, the researcher selects an appropriate statistical test, chooses a level of
significance, and formulates a plan for conducting the study..
Testing of hypothesis - large sample testParag Shah
Different type of test which are used for large sample has been included in this presentation. Steps for each test and a case study is included for concept clarity and practice.
USDA Loans in California: A Comprehensive Overview.pptxmarketing367770
USDA Loans in California: A Comprehensive Overview
If you're dreaming of owning a home in California's rural or suburban areas, a USDA loan might be the perfect solution. The U.S. Department of Agriculture (USDA) offers these loans to help low-to-moderate-income individuals and families achieve homeownership.
Key Features of USDA Loans:
Zero Down Payment: USDA loans require no down payment, making homeownership more accessible.
Competitive Interest Rates: These loans often come with lower interest rates compared to conventional loans.
Flexible Credit Requirements: USDA loans have more lenient credit score requirements, helping those with less-than-perfect credit.
Guaranteed Loan Program: The USDA guarantees a portion of the loan, reducing risk for lenders and expanding borrowing options.
Eligibility Criteria:
Location: The property must be located in a USDA-designated rural or suburban area. Many areas in California qualify.
Income Limits: Applicants must meet income guidelines, which vary by region and household size.
Primary Residence: The home must be used as the borrower's primary residence.
Application Process:
Find a USDA-Approved Lender: Not all lenders offer USDA loans, so it's essential to choose one approved by the USDA.
Pre-Qualification: Determine your eligibility and the amount you can borrow.
Property Search: Look for properties in eligible rural or suburban areas.
Loan Application: Submit your application, including financial and personal information.
Processing and Approval: The lender and USDA will review your application. If approved, you can proceed to closing.
USDA loans are an excellent option for those looking to buy a home in California's rural and suburban areas. With no down payment and flexible requirements, these loans make homeownership more attainable for many families. Explore your eligibility today and take the first step toward owning your dream home.
This slideshow is related to testing of hypothesis and goodness of fit of statistics. This may be useful for students, teachers, managers concerned with bio statistics, bioinformatics, data science, etc.
Hypothesis testing and estimation are used to reach conclusions about a population by examining a sample of that population.
Hypothesis testing is widely used in medicine, dentistry, health care, biology and other fields as a means to draw conclusions about the nature of populations
A non technical overview of sample size calculation and why it is necessary with some brief examples of how to approach the problem and why it is useful to actually think of these calculations.
The error (or disturbance) of an observed value is the deviation of the observed value from the (unobservable) true value of a quantity of interest (for example, a population mean), and the residual of an observed value is the difference between the observed value and the estimated value of the quantity of interest (for example, a sample mean).
Suppose there is a series of observations from a univariate distribution and we want to estimate the mean of that distribution (the so-called location model). In this case, the errors are the deviations of the observations from the population mean, while the residuals are the deviations of the observations from the sample mean.
A statistical error (or disturbance) is the amount by which an observation differs from its expected value, the latter being based on the whole population from which the statistical unit was chosen randomly. For example, if the mean height in a population of 21-year-old men is 1.75 meters, and one randomly chosen man is 1.80 meters tall, then the "error" is 0.05 meters; if the randomly chosen man is 1.70 meters tall, then the "error" is −0.05 meters. The expected value, being the mean of the entire population, is typically not observable, and hence the statistical error cannot be observed either.
Application of statistical tests in Biomedical Research .pptxHalim AS
Here I have tried to show how to select a statistical test for a research project based on the type of data.
initially I have given an idea about the types of data, null hypothesis, p value and the types of error
Hypothesis Testing Definitions A statistical hypothesi.docxwilcockiris
Hypothesis Testing
Definitions:
A statistical hypothesis is a guess about a population parameter. The guess may or not be
true.
The null hypothesis, written H0, is a statistical hypothesis that states that there is no
difference between a parameter and a specific value, or that there is no difference between
two parameters.
The alternative hypothesis, written H1 or HA, is a statistical hypothesis that specifies a
specific difference between a parameter and a specific value, or that there is a difference
between two parameters.
Example 1:
A medical researcher is interested in finding out whether a new medication will have
undesirable side effects. She is particularly concerned with the pulse rate of patients who
take the medication. The research question is, will the pulse rate increase, decrease, or
remain the same after a patient takes the medication?
Since the researcher knows that the mean pulse rate for the population under study is 82
beats per minute, the hypotheses for this study are:
H0: µ = 82
HA: µ ≠ 82
The null hypothesis specifies that the mean will remain unchanged and the alternative
hypothesis states that it will be different. This test is called a two-tailed test since the
possible side effects could be to raise or lower the pulse rate. Notice that this is a non
directional hypothesis. The rejection region lies in both tails. We divide the alpha in two
and place half in each tail.
Example 2:
An entrepreneur invents an additive to increase the life of an automobile battery. If the
mean lifetime of the automobile battery is 36 months, then his hypotheses are:
H0: µ ≤ 36
HA: µ > 36
Here, the entrepreneur is only interested in increasing the lifetime of the batteries, so his
alternative hypothesis is that the mean is greater than 36 months. The null hypothesis is
that the mean is less than or equal to 36 months. This test is one-tailed since the interest
is only in an increased lifetime. Notice that the direction of the inequality in the alternate
hypothesis points to the right, same as the area of the curve that forms the rejection
region.
Example 3:
A landlord who wants to lower heating bills in a large apartment complex is considering
using a new type of insulation. If the current average of the monthly heating bills is $78,
his hypotheses about heating costs with the new insulation are:
H0: µ ≥ 78
HA: µ < 78
This test is also a one-tailed test since the landlord is interested only in lowering heating
costs. Notice that the direction of the inequality in the alternate hypothesis points to the
left, same as the area of the curve that forms the rejection region.
Study Design:
After stating the hypotheses, the researcher’s next step is to design the study. In designing
the study, the researcher selects an appropriate statistical test, chooses a level of
significance, and formulates a plan for conducting the study..
Testing of hypothesis - large sample testParag Shah
Different type of test which are used for large sample has been included in this presentation. Steps for each test and a case study is included for concept clarity and practice.
USDA Loans in California: A Comprehensive Overview.pptxmarketing367770
USDA Loans in California: A Comprehensive Overview
If you're dreaming of owning a home in California's rural or suburban areas, a USDA loan might be the perfect solution. The U.S. Department of Agriculture (USDA) offers these loans to help low-to-moderate-income individuals and families achieve homeownership.
Key Features of USDA Loans:
Zero Down Payment: USDA loans require no down payment, making homeownership more accessible.
Competitive Interest Rates: These loans often come with lower interest rates compared to conventional loans.
Flexible Credit Requirements: USDA loans have more lenient credit score requirements, helping those with less-than-perfect credit.
Guaranteed Loan Program: The USDA guarantees a portion of the loan, reducing risk for lenders and expanding borrowing options.
Eligibility Criteria:
Location: The property must be located in a USDA-designated rural or suburban area. Many areas in California qualify.
Income Limits: Applicants must meet income guidelines, which vary by region and household size.
Primary Residence: The home must be used as the borrower's primary residence.
Application Process:
Find a USDA-Approved Lender: Not all lenders offer USDA loans, so it's essential to choose one approved by the USDA.
Pre-Qualification: Determine your eligibility and the amount you can borrow.
Property Search: Look for properties in eligible rural or suburban areas.
Loan Application: Submit your application, including financial and personal information.
Processing and Approval: The lender and USDA will review your application. If approved, you can proceed to closing.
USDA loans are an excellent option for those looking to buy a home in California's rural and suburban areas. With no down payment and flexible requirements, these loans make homeownership more attainable for many families. Explore your eligibility today and take the first step toward owning your dream home.
Resume
• Real GDP growth slowed down due to problems with access to electricity caused by the destruction of manoeuvrable electricity generation by Russian drones and missiles.
• Exports and imports continued growing due to better logistics through the Ukrainian sea corridor and road. Polish farmers and drivers stopped blocking borders at the end of April.
• In April, both the Tax and Customs Services over-executed the revenue plan. Moreover, the NBU transferred twice the planned profit to the budget.
• The European side approved the Ukraine Plan, which the government adopted to determine indicators for the Ukraine Facility. That approval will allow Ukraine to receive a EUR 1.9 bn loan from the EU in May. At the same time, the EU provided Ukraine with a EUR 1.5 bn loan in April, as the government fulfilled five indicators under the Ukraine Plan.
• The USA has finally approved an aid package for Ukraine, which includes USD 7.8 bn of budget support; however, the conditions and timing of the assistance are still unknown.
• As in March, annual consumer inflation amounted to 3.2% yoy in April.
• At the April monetary policy meeting, the NBU again reduced the key policy rate from 14.5% to 13.5% per annum.
• Over the past four weeks, the hryvnia exchange rate has stabilized in the UAH 39-40 per USD range.
Falcon stands out as a top-tier P2P Invoice Discounting platform in India, bridging esteemed blue-chip companies and eager investors. Our goal is to transform the investment landscape in India by establishing a comprehensive destination for borrowers and investors with diverse profiles and needs, all while minimizing risk. What sets Falcon apart is the elimination of intermediaries such as commercial banks and depository institutions, allowing investors to enjoy higher yields.
Turin Startup Ecosystem 2024 - Ricerca sulle Startup e il Sistema dell'Innov...Quotidiano Piemontese
Turin Startup Ecosystem 2024
Una ricerca de il Club degli Investitori, in collaborazione con ToTeM Torino Tech Map e con il supporto della ESCP Business School e di Growth Capital
how to sell pi coins in all Africa Countries.DOT TECH
Yes. You can sell your pi network for other cryptocurrencies like Bitcoin, usdt , Ethereum and other currencies And this is done easily with the help from a pi merchant.
What is a pi merchant ?
Since pi is not launched yet in any exchange. The only way you can sell right now is through merchants.
A verified Pi merchant is someone who buys pi network coins from miners and resell them to investors looking forward to hold massive quantities of pi coins before mainnet launch in 2026.
I will leave the telegram contact of my personal pi merchant to trade with.
@Pi_vendor_247
The secret way to sell pi coins effortlessly.DOT TECH
Well as we all know pi isn't launched yet. But you can still sell your pi coins effortlessly because some whales in China are interested in holding massive pi coins. And they are willing to pay good money for it. If you are interested in selling I will leave a contact for you. Just telegram this number below. I sold about 3000 pi coins to him and he paid me immediately.
Telegram: @Pi_vendor_247
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how to sell pi coins effectively (from 50 - 100k pi)DOT TECH
Anywhere in the world, including Africa, America, and Europe, you can sell Pi Network Coins online and receive cash through online payment options.
Pi has not yet been launched on any exchange because we are currently using the confined Mainnet. The planned launch date for Pi is June 28, 2026.
Reselling to investors who want to hold until the mainnet launch in 2026 is currently the sole way to sell.
Consequently, right now. All you need to do is select the right pi network provider.
Who is a pi merchant?
An individual who buys coins from miners on the pi network and resells them to investors hoping to hang onto them until the mainnet is launched is known as a pi merchant.
debuts.
I'll provide you the Telegram username
@Pi_vendor_247
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The unveiling of the IndusInd Bank Poonawalla Fincorp eLITE RuPay Platinum Credit Card marks a notable milestone in the Indian financial landscape, showcasing a successful partnership between two leading institutions, Poonawalla Fincorp and IndusInd Bank. This co-branded credit card not only offers users a plethora of benefits but also reflects a commitment to innovation and adaptation. With a focus on providing value-driven and customer-centric solutions, this launch represents more than just a new product—it signifies a step towards redefining the banking experience for millions. Promising convenience, rewards, and a touch of luxury in everyday financial transactions, this collaboration aims to cater to the evolving needs of customers and set new standards in the industry.
how can i use my minded pi coins I need some funds.DOT TECH
If you are interested in selling your pi coins, i have a verified pi merchant, who buys pi coins and resell them to exchanges looking forward to hold till mainnet launch.
Because the core team has announced that pi network will not be doing any pre-sale. The only way exchanges like huobi, bitmart and hotbit can get pi is by buying from miners.
Now a merchant stands in between these exchanges and the miners. As a link to make transactions smooth. Because right now in the enclosed mainnet you can't sell pi coins your self. You need the help of a merchant,
i will leave the telegram contact of my personal pi merchant below. 👇 I and my friends has traded more than 3000pi coins with him successfully.
@Pi_vendor_247
how to sell pi coins at high rate quickly.DOT TECH
Where can I sell my pi coins at a high rate.
Pi is not launched yet on any exchange. But one can easily sell his or her pi coins to investors who want to hold pi till mainnet launch.
This means crypto whales want to hold pi. And you can get a good rate for selling pi to them. I will leave the telegram contact of my personal pi vendor below.
A vendor is someone who buys from a miner and resell it to a holder or crypto whale.
Here is the telegram contact of my vendor:
@Pi_vendor_247
how to swap pi coins to foreign currency withdrawable.DOT TECH
As of my last update, Pi is still in the testing phase and is not tradable on any exchanges.
However, Pi Network has announced plans to launch its Testnet and Mainnet in the future, which may include listing Pi on exchanges.
The current method for selling pi coins involves exchanging them with a pi vendor who purchases pi coins for investment reasons.
If you want to sell your pi coins, reach out to a pi vendor and sell them to anyone looking to sell pi coins from any country around the globe.
Below is the contact information for my personal pi vendor.
Telegram: @Pi_vendor_247
What website can I sell pi coins securely.DOT TECH
Currently there are no website or exchange that allow buying or selling of pi coins..
But you can still easily sell pi coins, by reselling it to exchanges/crypto whales interested in holding thousands of pi coins before the mainnet launch.
Who is a pi merchant?
A pi merchant is someone who buys pi coins from miners and resell to these crypto whales and holders of pi..
This is because pi network is not doing any pre-sale. The only way exchanges can get pi is by buying from miners and pi merchants stands in between the miners and the exchanges.
How can I sell my pi coins?
Selling pi coins is really easy, but first you need to migrate to mainnet wallet before you can do that. I will leave the telegram contact of my personal pi merchant to trade with.
Tele-gram.
@Pi_vendor_247
how to sell pi coins on Bitmart crypto exchangeDOT TECH
Yes. Pi network coins can be exchanged but not on bitmart exchange. Because pi network is still in the enclosed mainnet. The only way pioneers are able to trade pi coins is by reselling the pi coins to pi verified merchants.
A verified merchant is someone who buys pi network coins and resell it to exchanges looking forward to hold till mainnet launch.
I will leave the telegram contact of my personal pi merchant to trade with.
@Pi_vendor_247
Even tho Pi network is not listed on any exchange yet.
Buying/Selling or investing in pi network coins is highly possible through the help of vendors. You can buy from vendors[ buy directly from the pi network miners and resell it]. I will leave the telegram contact of my personal vendor.
@Pi_vendor_247
2. 2
Hypothesis Testing
• The general goal of a hypothesis test is to
rule out chance (sampling error) as a
plausible explanation for the results from a
research study.
• Hypothesis testing is a technique to help
determine whether a specific treatment
has an effect on the individuals in a
population.
3. 3
Hypothesis Testing
The hypothesis test is used to evaluate the
results from a research study in which
1. A sample is selected from the
population.
2. The treatment is administered to the
sample.
3. After treatment, the individuals in the
sample are measured.
4.
5. 5
Hypothesis Testing (cont.)
• If the individuals in the sample are
noticeably different from the individuals in
the original population, we have evidence
that the treatment has an effect.
• However, it is also possible that the
difference between the sample and the
population is simply sampling error
6.
7. 7
Hypothesis Testing (cont.)
• The purpose of the hypothesis test is to decide
between two explanations:
1. The difference between the sample and
the population can be explained by sampling
error (there does not appear to be a
treatment effect)
2. The difference between the sample and
the population is too large to be
explained by sampling error (there does
appear to be a treatment effect).
8.
9. 9
The Null Hypothesis, the Alpha Level, the
Critical Region, and the Test Statistic
• The following four steps outline the
process of hypothesis testing and
introduce some of the new terminology:
10. 10
Step 1
State the hypotheses and select an α
level. The null hypothesis, H0, always
states that the treatment has no effect (no
change, no difference). According to the
null hypothesis, the population mean after
treatment is the same is it was before
treatment. The α level establishes a
criterion, or "cut-off", for making a decision
about the null hypothesis. The alpha level
also determines the risk of a Type I error.
11.
12. 12
Step 2
Locate the critical region. The critical
region consists of outcomes that are very
unlikely to occur if the null hypothesis is
true. That is, the critical region is defined
by sample means that are almost
impossible to obtain if the treatment has
no effect. The phrase “almost impossible”
means that these samples have a
probability (p) that is less than the alpha
level.
13.
14. 14
Step 3
Compute the test statistic. The test
statistic (in this chapter a z-score) forms a
ratio comparing the obtained difference
between the sample mean and the
hypothesized population mean versus the
amount of difference we would expect
without any treatment effect (the standard
error).
15. 15
Step 4
A large value for the test statistic shows that the
obtained mean difference is more than would be
expected if there is no treatment effect. If it is
large enough to be in the critical region, we
conclude that the difference is significant or
that the treatment has a significant effect. In this
case we reject the null hypothesis. If the mean
difference is relatively small, then the test
statistic will have a low value. In this case, we
conclude that the evidence from the sample is
not sufficient, and the decision is fail to reject the
null hypothesis.
16.
17. 17
Errors in Hypothesis Tests
• Just because the sample mean (following
treatment) is different from the original
population mean does not necessarily
indicate that the treatment has caused a
change.
• You should recall that there usually is
some discrepancy between a sample
mean and the population mean simply as
a result of sampling error.
18. 18
Errors in Hypothesis Tests (cont.)
• Because the hypothesis test relies on
sample data, and because sample data
are not completely reliable, there is always
the risk that misleading data will cause the
hypothesis test to reach a wrong
conclusion.
• Two types of error are possible.
19. 19
Type I Errors
• A Type I error occurs when the sample data appear to
show a treatment effect when, in fact, there is none.
• In this case the researcher will reject the null
hypothesis and falsely conclude that the treatment has
an effect.
• Type I errors are caused by unusual, unrepresentative
samples. Just by chance the researcher selects an
extreme sample with the result that the sample falls in
the critical region even though the treatment has no
effect.
• The hypothesis test is structured so that Type I errors
are very unlikely; specifically, the probability of a Type I
error is equal to the alpha level.
20. 20
Type II Errors
• A Type II error occurs when the sample does
not appear to have been affected by the
treatment when, in fact, the treatment does have
an effect.
• In this case, the researcher will fail to reject the
null hypothesis and falsely conclude that the
treatment does not have an effect.
• Type II errors are commonly the result of a very
small treatment effect. Although the treatment
does have an effect, it is not large enough to
show up in the research study.
21.
22. 22
Directional Tests
• When a research study predicts a specific
direction for the treatment effect (increase
or decrease), it is possible to incorporate
the directional prediction into the
hypothesis test.
• The result is called a directional test or a
one-tailed test. A directional test includes
the directional prediction in the statement
of the hypotheses and in the location of
the critical region.
23. 23
Directional Tests (cont.)
• For example, if the original population has a
mean of μ = 80 and the treatment is predicted to
increase the scores, then the null hypothesis
would state that after treatment:
H0: μ < 80 (there is no increase)
• In this case, the entire critical region would be
located in the right-hand tail of the distribution
because large values for M would demonstrate
that there is an increase and would tend to reject
the null hypothesis.
24. 24
Measuring Effect Size
• A hypothesis test evaluates the statistical
significance of the results from a research study.
• That is, the test determines whether or not it is
likely that the obtained sample mean occurred
without any contribution from a treatment effect.
• The hypothesis test is influenced not only by the
size of the treatment effect but also by the size
of the sample.
• Thus, even a very small effect can be significant
if it is observed in a very large sample.
25. 25
Measuring Effect Size
• Because a significant effect does not necessarily
mean a large effect, it is recommended that the
hypothesis test be accompanied by a measure
of the effect size.
• We use Cohen=s d as a standardized measure
of effect size.
• Much like a z-score, Cohen=s d measures the
size of the mean difference in terms of the
standard deviation.
26.
27. 27
Power of a Hypothesis Test
• The power of a hypothesis test is defined
is the probability that the test will reject the
null hypothesis when the treatment does
have an effect.
• The power of a test depends on a variety
of factors including the size of the
treatment effect and the size of the
sample.