SlideShare a Scribd company logo
1 of 41
Download to read offline
HYPOTHESIS TESTING
What is a Hypothesis Test?
• A hypothesis test is a statistical method that uses
sample data to evaluate a hypothesis about a population
• A standardized methodology we use to answer a research question
of interest
• The most commonly utilized inferential procedure
• Incorporates the concepts of z-scores, probability, and the
distribution of sample means
• The general goal of the hypothesis test:
• To rule out chance (sampling error) as a plausible explanation for
the results from a research study
The Logic of Hypothesis Testing
1. We have a hypothesis about a population
• Typically about a population parameter: μ = 50
2. Based on our hypothesis, we predict the characteristics
our sample should have
• M should be around 50
3. Obtain a random sample from the population
• Sample n = 20 from the population and compute their M
4. Compare the sample statistic with our hypothesis about
the population
• If the values are consistent, the hypothesis is reasonable
• If there is a large discrepancy, we decide the hypothesis is
unreasonable
The Unknown Population
• Typically, research involves an unknown population
• After we administer “tutoring treatment” to our sample of
students, what is the new μ?
• Remember, σ should remain the same
• The focus of our hypothesis is the unknown population
The Research Study Sample
• Theoretically:
• We would treat the entire population, randomly sample from the
treated population, and evaluate the M
• Realistically:
• We sample from the original population, treat the sample only, and
evaluate the M
The Purpose of the Hypothesis Test
1.
There does not appear
to be a treatment effect
The difference between the
sample and the population
can be explained by
sampling error
2.
There does appear to
be a treatment effect
The difference between the
sample and the population
is too large to be explained
by sampling error
To decide between two explanations:
The Hypothesis Test: Step 1
State the hypothesis about
the unknown population
• The null hypothesis (H0)
• States that there is no change in the general population before and
after an intervention.
• In the context of an experiment, H0 predicts that the independent
variable (IV) will have no effect on the dependent variable
• The scientific/alternative hypothesis (H1)
• States that there is a change in the general population following an
intervention
• In the context of an experiment, H1 predicts that the independent
variable (IV) will have an effect on the dependent variable
SAT Example
• Population parameters of a normally distributed variable
are μ = 500 and σ = 50
• I believe my prep course will have some effect on this
mean value
• My hypotheses:
• Null (H0): Even with treatment, the mean
SAT score will remain at 500
• Alternative (H1): With treatment, the mean
SAT score will be different from* 500
*Note: Here we do not specify a direction (increase/decrease); just some difference
500:
500:
1
0


SAT
SAT
H
H


The Hypothesis Test: Step 2
Set the criteria for a decision
• Determine before the experiment what sample means are
inconsistent with the null hypothesis
• The sampling distribution of the mean for the population
is divided into two parts:
1. Sample means likely to be obtained
if H0 is true (sample means close to
the null value)
2. Sample means that are very
unlikely to be obtained if H0
is true (sample means that
are very different from the
null value)
The Alpha
(α) Level
a.k.a. the Level of
Significance
The α level establishes the criterion, or “cut-off”, for making a
decision about the null hypothesis. The alpha level also
determines the risk of a Type I error (TBD in next section)
• How we define which
sample means have
“high” or “low”
probabilities
• Typically set at:
• α = 0.05,
• α = 0.01
• α = 0.001
• Separates the typical
values from the
extreme, unlikely-to-
occur values (in the
critical region)
The Hypothesis Test: Step 3
Collect data and compute sample statistics
• After we state they hypotheses and establish our critical
regions:
• Randomly sample from the population
• Give the sample the treatment/intervention
• Summarize the sample with the appropriate statistic (e.g.: the M)
• Compute the test statistic
M
M
z



The z-score (the test statistic) 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)
The Hypothesis Test: Step 4
Make a decision
•Use the z-score obtained for the sample statistic and make
a decision about the null hypothesis (H0) based on the
critical region. Either:
• Reject the null hypothesis
• The sample data fall in the critical region
• This event is unlikely if the null hypothesis is true, so we conclude to
reject the null
• This does NOT mean that we have proven the alternative
• Fail to reject the null hypothesis (retain the null)
• The sample data do not fall in the critical region
• We do not have enough evidence to show that the null hypothesis is
incorrect (NOT that the null hypothesis is “true”)
Making your
decision:
One mo’ time!
• Use the z-score obtained for the sample
statistic and make a decision about the null
hypothesis (H0) based on the critical region
IF: My sample mean has a
corresponding z = 0.87
• My treatment effect is
not convincing. I do not
have enough evidence
and fail to reject the null.
IF: My sample mean has a
corresponding z = -2.50
• This is an unlikely event
if the null is true, so I
reject the null. I have
convincing evidence my
treatment works and has
an effect.
Fail to reject H0
Reject H0 Reject H0
An Analogy for Hypothesis Testing
Research Study
1. H0: There is no treatment effect
2. Researchers gather evidence to
show that the treatment actually
does have an effect
3. If there is enough evidence, the
researchers reject H0 and conclude
that there is a treatment effect
4. If there is not enough evidence, the
researcher fails to reject H0
Jury Trial
1. H0: Defendant did not commit a crime
2. Police gathers evidence to show that
the defendant really did commit a
crime
3. If there is enough evidence, the jury
rejects H0 and concludes that the
defendant is guilty of the crime
4. If there is not enough evidence, the
jury fails to find the defendant guilty
Both are trying to refute the null hypothesis (H0)
They are not concluding that there is
no treatment effect; simply that there
is not enough evidence to conclude
there is an effect
They are not concluding that the
defendant is innocent; simply that
there is not enough evidence for a
guilty verdict
Statistical Significance
A result is statistically significant if it is unlikely to occur
when the null hypothesis (H0) is true
(Sufficient to reject the null hypothesis [H0])
• An effect is significant if we decide to reject the null
hypothesis after conducting a hypothesis test
• Z = 0.87, p > 0.05
does not fall in the critical region, fail to reject the null
• Z = -2.50, p < 0.05
falls in the critical region, reject the null
The z-Score as a Test Statistic
• A Test Statistic = A single, specific statistic (converted
from sample data) that is used to test the hypothesis
• The z-score formula as a recipe
• Make a hypothesis about the value of µ. This is H0.
• Plug the hypothesized value in the formula along with the other
values
• If the results is a z-score near zero (where z-scores are supposed
to be), fail to reject H0.
M
M
z



The z-Score Formula as a Ratio
If z is large, the obtained difference is larger than expected
by chance
• For example:
z = 3 indicates the obtained difference is three times
larger than what would be expected by chance



M
M
z

 Sample mean – hypothesized population mean
Standard error between M and µ
Obtained difference
Difference due to chance
OR
3
1
3

Uncertainty and Errors in Hypothesis Testing
Type I Errors (α)
• A Type I error occurs when the sample data appear to
show a treatment effect when, in fact, there is none
• We reject a null hypothesis (H0) that is actually true
• We falsely conclude that the treatment has an effect
• Caused by unusual, unrepresentative samples that fall
into the critical region despite a null effect of treatment
• Type I errors are very unlikely
Type II Errors (β)
• A Type II error occurs when the sample does not appear
to have been affected by the treatment when, in fact, it
has (the treatment does have an effect)
• We fail to reject the null hypothesis (H0) that is actually false
• We falsely conclude that the treatment had no effect
• 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 our data
The Relationship Between α & Errors
• The alpha (α) level is the probability that the test will lead to a
Type I error
• If α = .05: The probability that the test will lead to a Type I error is 5%
• If α = .01: The probability that the test will lead to a Type I error is 1%
• How does changing α influence Type II errors?
• As we make α smaller, we decrease the chance of making a Type I error.
• However, we also make it harder to reject the null; thus increasing the
risk of a Type II error
Critical Region Boundaries
If α = .05, z = +/-1.96 If α = .01, z = +/-2.58 If α = .001, z = +/-3.30
THE HYPOTHESIS TEST
An Example
The Study:
Prenatal alcohol exposure on birth weights
A random sample of n = 16 pregnant rats is obtained. The mother rats
are given a daily dose of alcohol. At birth, one pup is selected from
each litter to produce a sample of n = 16 newborn rats. The average
weight for the sample is M = 15 grams. It is known that regular newborn
rats have an average weight of μ = 18 grams, with σ = 4
Step 1
State the hypotheses and select the alpha (α) level
• For this test, we will use an alpha level of α = .05
• We are taking a 5% risk of committing a Type I error
H0 :malcoholexp =18
H1 :malcoholexp ¹18
Even with alcohol exposure, the rats still average 18 grams at birth
or
Alcohol exposure does not have an effect on birth weight
Alcohol exposure will change birth weight
Step 2
Set the decision criteria by locating the critical region
• The 3-step process:
If we obtain a sample mean that is in the
critical region, we conclude that the sample
is not compatible with the null hypothesis
and we reject H0
Step 3
• Collect the data, and compute the test statistic
• In this case, the z-score:
z =
M -m
sM
=
15-18
4
16
æ
è
ç
ö
ø
÷
=
-3
4
4
æ
è
ç
ö
ø
÷
=
-3
1
= -3.00
Step 4
Make a decision
• Our z-score (-3.00) exceeds the critical value of +/-1.96
• It is in the critical region
• Our interpretation:
• This event is unlikely if the null is true
Reject the null hypothesis.
Alcohol does have a significant
effect on the birth weight of rats.
Things to Keep In Mind
• State the hypotheses:
• Your hypotheses lays out the whole point of the test
• Phrased in terms of the population parameters
• When setting critical values:
• What are they?
• Are they positive? Negative? Both?
• Results
• What do we conclude about the null?
• State your results in scientific language:
The treatment with alcohol had a significant effect on the birth
weight of newborn rats, z = -3.00, p < .05.
• Conclusions
• What do we conclude about the point of the study?
Factors Influencing a Hypothesis Test
1. The size of difference between M and μ
• Numerator of z-score
• Bigger difference, more likely to reject
2. The variability of the scores (σ)
• Denominator of z-score (standard error)
• More variability, less accurate, less likely to reject
1. The number of scores in the sample (n)
• Denominator of z-score (standard error)
• Bigger sample, more accurate, more likely to reject
Assumptions of Hypothesis Testing
with z-Scores
1. Random sampling
• Ensures a representative sample
2. Independent observations
• No consistent relationship between observations
• The occurrence of the first has no bearing on the second
3. The value of σ is unchanged by the treatment
• In effect, the treatment adds/subtracts a constant from every value
in the distribution
• Remember, when this occurs, the mean will change but not the SD
4. Normal sampling distribution (n > 30 or normal population)
• To justify using the Unit Normal Table
DIRECTIONAL (1-TAILED)
HYPOTHESIS TESTS
• Two-tailed test
• Critical region involves
means that are either
higher or lower than
expected by chance
• There are two “tails” to
this distribution
• One-tailed test
• Critical region involves
only the area you specify
• Specifies an increase or
decrease
• There is one “tail” to this
distribution
• One-tailed test: • Two-tailed test:
H0 :m £100
H1 :m >100 100:
100:
1
0




H
H
CONCERNS ABOUT
HYPOTHESIS TESTING
Measuring effect size
Effect Size
Intended to provide a measurement of the absolute
magnitude of a treatment effect, independent of the size of
the sample(s) being used.
• Statistical significance does not necessarily mean the
difference is substantial or meaningful
• It allows us to conclude the null hypothesis is unlikely and offers
support for the alternative hypothesis
• BUT cannot make any real claims about the treatment effect found
• If the standard error is very small, even a very small treatment
effect may result in rejecting the null hypothesis
• With a large enough sample, you will find a significant effect for
almost any sized difference
Measuring Effect Size
• (0.0 < d < 0.2) = Small effect size
• (0.2 < d < 0.8) = Medium effect size
• (d > 0.8) = Large effect size
Cohen's d =
mean difference
standard deviation
=
mtreatment -mno.treatment
s
We don’t
know this
estimated Cohen's d =
mean difference
standard deviation
=
Mtreatment -mno.treatment
s
so we
use this
Cohen’s d uses σ to measure effect size
estimated Cohen's d =
mean difference
standard deviation
=
Mtreatment -mno.treatment
s
(let's just call this) Cohen's d =
15
100
= 0.15
Cohen’s d uses σ to measure effect size
estimated Cohen's d =
mean difference
standard deviation
=
Mtreatment -mno.treatment
s
(let's just call this) Cohen's d =
15
15
=1.00
STATISTICAL POWER
Power
The probability that the test will correctly reject a false null
hypothesis.
•Will identify a treatment effect if one truly exists
•Factors that affect power:
• Effect size
• A larger effect size  more likely to reject H0  power increases
• Sample size
• Larger sample size  more likely to reject H0  increased power
• Alpha level
• Lower α  less likely to reject H0  less power
• One- versus two-tailed test
• One-tailed  more likely to reject H0  more power

More Related Content

What's hot

non parametric statistics
non parametric statisticsnon parametric statistics
non parametric statisticsAnchal Garg
 
Estimation and hypothesis testing 1 (graduate statistics2)
Estimation and hypothesis testing 1 (graduate statistics2)Estimation and hypothesis testing 1 (graduate statistics2)
Estimation and hypothesis testing 1 (graduate statistics2)Harve Abella
 
The sampling distribution
The sampling distributionThe sampling distribution
The sampling distributionHarve Abella
 
Point and Interval Estimation
Point and Interval EstimationPoint and Interval Estimation
Point and Interval EstimationShubham Mehta
 
Types of error in hypothesis
Types of error in hypothesisTypes of error in hypothesis
Types of error in hypothesisShaifali Pandey
 
Probability distribution
Probability distributionProbability distribution
Probability distributionRohit kumar
 
Statistics: Probability
Statistics: ProbabilityStatistics: Probability
Statistics: ProbabilitySultan Mahmood
 
Sampling distribution
Sampling distributionSampling distribution
Sampling distributionswarna dey
 
Population & sample lecture 04
Population & sample lecture 04Population & sample lecture 04
Population & sample lecture 04DrZahid Khan
 
Testing of hypothesis and tests of significance
Testing of hypothesis and tests of significanceTesting of hypothesis and tests of significance
Testing of hypothesis and tests of significanceSudha Rameshwari
 
Hypothesis testing an introduction
Hypothesis testing an introductionHypothesis testing an introduction
Hypothesis testing an introductionGeetika Gulyani
 
Lecture 6. univariate and bivariate analysis
Lecture 6. univariate and bivariate analysisLecture 6. univariate and bivariate analysis
Lecture 6. univariate and bivariate analysisDr Rajeev Kumar
 

What's hot (20)

non parametric statistics
non parametric statisticsnon parametric statistics
non parametric statistics
 
Hypothesis testing
Hypothesis testingHypothesis testing
Hypothesis testing
 
Estimation and hypothesis testing 1 (graduate statistics2)
Estimation and hypothesis testing 1 (graduate statistics2)Estimation and hypothesis testing 1 (graduate statistics2)
Estimation and hypothesis testing 1 (graduate statistics2)
 
The sampling distribution
The sampling distributionThe sampling distribution
The sampling distribution
 
Point and Interval Estimation
Point and Interval EstimationPoint and Interval Estimation
Point and Interval Estimation
 
Types of error in hypothesis
Types of error in hypothesisTypes of error in hypothesis
Types of error in hypothesis
 
Sampling Distribution
Sampling DistributionSampling Distribution
Sampling Distribution
 
Probability distribution
Probability distributionProbability distribution
Probability distribution
 
Inferential Statistics
Inferential StatisticsInferential Statistics
Inferential Statistics
 
Statistics: Probability
Statistics: ProbabilityStatistics: Probability
Statistics: Probability
 
Sampling distribution
Sampling distributionSampling distribution
Sampling distribution
 
Hypothesis
HypothesisHypothesis
Hypothesis
 
Population & sample lecture 04
Population & sample lecture 04Population & sample lecture 04
Population & sample lecture 04
 
Testing of hypothesis and tests of significance
Testing of hypothesis and tests of significanceTesting of hypothesis and tests of significance
Testing of hypothesis and tests of significance
 
Sampling distribution
Sampling distributionSampling distribution
Sampling distribution
 
Confidence Intervals
Confidence IntervalsConfidence Intervals
Confidence Intervals
 
Parametric vs Non-Parametric
Parametric vs Non-ParametricParametric vs Non-Parametric
Parametric vs Non-Parametric
 
Non-Parametric Tests
Non-Parametric TestsNon-Parametric Tests
Non-Parametric Tests
 
Hypothesis testing an introduction
Hypothesis testing an introductionHypothesis testing an introduction
Hypothesis testing an introduction
 
Lecture 6. univariate and bivariate analysis
Lecture 6. univariate and bivariate analysisLecture 6. univariate and bivariate analysis
Lecture 6. univariate and bivariate analysis
 

Viewers also liked

The T-Test, by Geoff Browne
The T-Test, by Geoff BrowneThe T-Test, by Geoff Browne
The T-Test, by Geoff BrowneStephen Taylor
 
Anesthesia powerpoint
Anesthesia powerpointAnesthesia powerpoint
Anesthesia powerpointJoanBelleman
 
S5 w1 hypothesis testing & t test
S5 w1 hypothesis testing & t testS5 w1 hypothesis testing & t test
S5 w1 hypothesis testing & t testRachel Chung
 
Hypothesis
HypothesisHypothesis
Hypothesis17somya
 
Reporting a single sample t-test
Reporting a single sample t-testReporting a single sample t-test
Reporting a single sample t-testKen Plummer
 
Research hypothesis
Research hypothesisResearch hypothesis
Research hypothesisNursing Path
 
Hypothesis testing ppt final
Hypothesis testing ppt finalHypothesis testing ppt final
Hypothesis testing ppt finalpiyushdhaker
 
Test of hypothesis
Test of hypothesisTest of hypothesis
Test of hypothesisvikramlawand
 
Hypothesis testing; z test, t-test. f-test
Hypothesis testing; z test, t-test. f-testHypothesis testing; z test, t-test. f-test
Hypothesis testing; z test, t-test. f-testShakehand with Life
 

Viewers also liked (11)

The T-Test, by Geoff Browne
The T-Test, by Geoff BrowneThe T-Test, by Geoff Browne
The T-Test, by Geoff Browne
 
Anesthesia powerpoint
Anesthesia powerpointAnesthesia powerpoint
Anesthesia powerpoint
 
S5 w1 hypothesis testing & t test
S5 w1 hypothesis testing & t testS5 w1 hypothesis testing & t test
S5 w1 hypothesis testing & t test
 
Choosing the right statistics
Choosing the right statisticsChoosing the right statistics
Choosing the right statistics
 
Hypothesis
HypothesisHypothesis
Hypothesis
 
Reporting a single sample t-test
Reporting a single sample t-testReporting a single sample t-test
Reporting a single sample t-test
 
Research hypothesis
Research hypothesisResearch hypothesis
Research hypothesis
 
Hypothesis testing ppt final
Hypothesis testing ppt finalHypothesis testing ppt final
Hypothesis testing ppt final
 
Statistical Analysis
Statistical AnalysisStatistical Analysis
Statistical Analysis
 
Test of hypothesis
Test of hypothesisTest of hypothesis
Test of hypothesis
 
Hypothesis testing; z test, t-test. f-test
Hypothesis testing; z test, t-test. f-testHypothesis testing; z test, t-test. f-test
Hypothesis testing; z test, t-test. f-test
 

Similar to Hypothesis testing

Hypothesis testing.ppt
Hypothesis testing.pptHypothesis testing.ppt
Hypothesis testing.pptSteevanTellis1
 
Topic 7 stat inference
Topic 7 stat inferenceTopic 7 stat inference
Topic 7 stat inferenceSizwan Ahammed
 
Chapter 18 Hypothesis testing (1).pptx
Chapter 18 Hypothesis testing (1).pptxChapter 18 Hypothesis testing (1).pptx
Chapter 18 Hypothesis testing (1).pptxNELVINNOOL1
 
Chapter 9 Fundamental of Hypothesis Testing.ppt
Chapter 9 Fundamental of Hypothesis Testing.pptChapter 9 Fundamental of Hypothesis Testing.ppt
Chapter 9 Fundamental of Hypothesis Testing.pptHasanGilani3
 
Introduction to Hypothesis Testing
Introduction to Hypothesis TestingIntroduction to Hypothesis Testing
Introduction to Hypothesis Testingjasondroesch
 
20200519073328de6dca404c.pdfkshhjejhehdhd
20200519073328de6dca404c.pdfkshhjejhehdhd20200519073328de6dca404c.pdfkshhjejhehdhd
20200519073328de6dca404c.pdfkshhjejhehdhdHimanshuSharma723273
 
hypothesis testing
hypothesis testinghypothesis testing
hypothesis testingilona50
 
Inferential statistics hand out (2)
Inferential statistics hand out (2)Inferential statistics hand out (2)
Inferential statistics hand out (2)Kimberly Ann Yabut
 
Hypothesis testing1
Hypothesis testing1Hypothesis testing1
Hypothesis testing1HanaaBayomy
 
Testing Of Hypothesis
Testing Of HypothesisTesting Of Hypothesis
Testing Of HypothesisSWATI SINGH
 
Class 5 Hypothesis & Normal Disdribution.pptx
Class 5 Hypothesis & Normal Disdribution.pptxClass 5 Hypothesis & Normal Disdribution.pptx
Class 5 Hypothesis & Normal Disdribution.pptxCallplanetsDeveloper
 
hypothesis test
 hypothesis test hypothesis test
hypothesis testUnsa Shakir
 
Hypothesis testing- Fundamentals to upload.pptx
Hypothesis testing- Fundamentals to upload.pptxHypothesis testing- Fundamentals to upload.pptx
Hypothesis testing- Fundamentals to upload.pptxarathi
 
TOPIC- HYPOTHESIS TESTING RMS.pptx
TOPIC- HYPOTHESIS TESTING  RMS.pptxTOPIC- HYPOTHESIS TESTING  RMS.pptx
TOPIC- HYPOTHESIS TESTING RMS.pptxanamikamishra29
 

Similar to Hypothesis testing (20)

Hypothesis testing.ppt
Hypothesis testing.pptHypothesis testing.ppt
Hypothesis testing.ppt
 
Topic 7 stat inference
Topic 7 stat inferenceTopic 7 stat inference
Topic 7 stat inference
 
chapter8.ppt
chapter8.pptchapter8.ppt
chapter8.ppt
 
chapter8.ppt
chapter8.pptchapter8.ppt
chapter8.ppt
 
Chapter8
Chapter8Chapter8
Chapter8
 
Chapter 18 Hypothesis testing (1).pptx
Chapter 18 Hypothesis testing (1).pptxChapter 18 Hypothesis testing (1).pptx
Chapter 18 Hypothesis testing (1).pptx
 
Chapter 9 Fundamental of Hypothesis Testing.ppt
Chapter 9 Fundamental of Hypothesis Testing.pptChapter 9 Fundamental of Hypothesis Testing.ppt
Chapter 9 Fundamental of Hypothesis Testing.ppt
 
Hypothesis
HypothesisHypothesis
Hypothesis
 
Introduction to Hypothesis Testing
Introduction to Hypothesis TestingIntroduction to Hypothesis Testing
Introduction to Hypothesis Testing
 
20200519073328de6dca404c.pdfkshhjejhehdhd
20200519073328de6dca404c.pdfkshhjejhehdhd20200519073328de6dca404c.pdfkshhjejhehdhd
20200519073328de6dca404c.pdfkshhjejhehdhd
 
hypothesis testing
hypothesis testinghypothesis testing
hypothesis testing
 
Hypothesis testing
Hypothesis testingHypothesis testing
Hypothesis testing
 
Inferential statistics hand out (2)
Inferential statistics hand out (2)Inferential statistics hand out (2)
Inferential statistics hand out (2)
 
Hypothesis testing1
Hypothesis testing1Hypothesis testing1
Hypothesis testing1
 
Testing Of Hypothesis
Testing Of HypothesisTesting Of Hypothesis
Testing Of Hypothesis
 
7 hypothesis testing
7 hypothesis testing7 hypothesis testing
7 hypothesis testing
 
Class 5 Hypothesis & Normal Disdribution.pptx
Class 5 Hypothesis & Normal Disdribution.pptxClass 5 Hypothesis & Normal Disdribution.pptx
Class 5 Hypothesis & Normal Disdribution.pptx
 
hypothesis test
 hypothesis test hypothesis test
hypothesis test
 
Hypothesis testing- Fundamentals to upload.pptx
Hypothesis testing- Fundamentals to upload.pptxHypothesis testing- Fundamentals to upload.pptx
Hypothesis testing- Fundamentals to upload.pptx
 
TOPIC- HYPOTHESIS TESTING RMS.pptx
TOPIC- HYPOTHESIS TESTING  RMS.pptxTOPIC- HYPOTHESIS TESTING  RMS.pptx
TOPIC- HYPOTHESIS TESTING RMS.pptx
 

More from Kaori Kubo Germano, PhD (16)

Probablity
ProbablityProbablity
Probablity
 
Probability & Samples
Probability & SamplesProbability & Samples
Probability & Samples
 
z-scores
z-scoresz-scores
z-scores
 
Chi square
Chi squareChi square
Chi square
 
regression
regressionregression
regression
 
Correlations
CorrelationsCorrelations
Correlations
 
Factorial ANOVA
Factorial ANOVAFactorial ANOVA
Factorial ANOVA
 
Analysis of Variance
Analysis of VarianceAnalysis of Variance
Analysis of Variance
 
Repeated Measures ANOVA
Repeated Measures ANOVARepeated Measures ANOVA
Repeated Measures ANOVA
 
Repeated Measures t-test
Repeated Measures t-testRepeated Measures t-test
Repeated Measures t-test
 
Independent samples t-test
Independent samples t-testIndependent samples t-test
Independent samples t-test
 
Introduction to the t-test
Introduction to the t-testIntroduction to the t-test
Introduction to the t-test
 
Central Tendency
Central TendencyCentral Tendency
Central Tendency
 
Variability
VariabilityVariability
Variability
 
Frequency Distributions
Frequency DistributionsFrequency Distributions
Frequency Distributions
 
Behavioral Statistics Intro lecture
Behavioral Statistics Intro lectureBehavioral Statistics Intro lecture
Behavioral Statistics Intro lecture
 

Recently uploaded

Satirical Depths - A Study of Gabriel Okara's Poem - 'You Laughed and Laughed...
Satirical Depths - A Study of Gabriel Okara's Poem - 'You Laughed and Laughed...Satirical Depths - A Study of Gabriel Okara's Poem - 'You Laughed and Laughed...
Satirical Depths - A Study of Gabriel Okara's Poem - 'You Laughed and Laughed...HetalPathak10
 
How to Fix XML SyntaxError in Odoo the 17
How to Fix XML SyntaxError in Odoo the 17How to Fix XML SyntaxError in Odoo the 17
How to Fix XML SyntaxError in Odoo the 17Celine George
 
4.9.24 Social Capital and Social Exclusion.pptx
4.9.24 Social Capital and Social Exclusion.pptx4.9.24 Social Capital and Social Exclusion.pptx
4.9.24 Social Capital and Social Exclusion.pptxmary850239
 
Transaction Management in Database Management System
Transaction Management in Database Management SystemTransaction Management in Database Management System
Transaction Management in Database Management SystemChristalin Nelson
 
Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...
Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...
Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...Osopher
 
ICS 2208 Lecture Slide Notes for Topic 6
ICS 2208 Lecture Slide Notes for Topic 6ICS 2208 Lecture Slide Notes for Topic 6
ICS 2208 Lecture Slide Notes for Topic 6Vanessa Camilleri
 
Tree View Decoration Attribute in the Odoo 17
Tree View Decoration Attribute in the Odoo 17Tree View Decoration Attribute in the Odoo 17
Tree View Decoration Attribute in the Odoo 17Celine George
 
Integumentary System SMP B. Pharm Sem I.ppt
Integumentary System SMP B. Pharm Sem I.pptIntegumentary System SMP B. Pharm Sem I.ppt
Integumentary System SMP B. Pharm Sem I.pptshraddhaparab530
 
Objectives n learning outcoms - MD 20240404.pptx
Objectives n learning outcoms - MD 20240404.pptxObjectives n learning outcoms - MD 20240404.pptx
Objectives n learning outcoms - MD 20240404.pptxMadhavi Dharankar
 
6 ways Samsung’s Interactive Display powered by Android changes the classroom
6 ways Samsung’s Interactive Display powered by Android changes the classroom6 ways Samsung’s Interactive Display powered by Android changes the classroom
6 ways Samsung’s Interactive Display powered by Android changes the classroomSamsung Business USA
 
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 - I-LEARN SMART WORLD - CẢ NĂM - CÓ FILE NGHE (BẢN...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 - I-LEARN SMART WORLD - CẢ NĂM - CÓ FILE NGHE (BẢN...BÀI TẬP BỔ TRỢ TIẾNG ANH 8 - I-LEARN SMART WORLD - CẢ NĂM - CÓ FILE NGHE (BẢN...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 - I-LEARN SMART WORLD - CẢ NĂM - CÓ FILE NGHE (BẢN...Nguyen Thanh Tu Collection
 
Narcotic and Non Narcotic Analgesic..pdf
Narcotic and Non Narcotic Analgesic..pdfNarcotic and Non Narcotic Analgesic..pdf
Narcotic and Non Narcotic Analgesic..pdfPrerana Jadhav
 
Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...
Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...
Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...DhatriParmar
 
Decoding the Tweet _ Practical Criticism in the Age of Hashtag.pptx
Decoding the Tweet _ Practical Criticism in the Age of Hashtag.pptxDecoding the Tweet _ Practical Criticism in the Age of Hashtag.pptx
Decoding the Tweet _ Practical Criticism in the Age of Hashtag.pptxDhatriParmar
 
How to Manage Buy 3 Get 1 Free in Odoo 17
How to Manage Buy 3 Get 1 Free in Odoo 17How to Manage Buy 3 Get 1 Free in Odoo 17
How to Manage Buy 3 Get 1 Free in Odoo 17Celine George
 
Q-Factor General Quiz-7th April 2024, Quiz Club NITW
Q-Factor General Quiz-7th April 2024, Quiz Club NITWQ-Factor General Quiz-7th April 2024, Quiz Club NITW
Q-Factor General Quiz-7th April 2024, Quiz Club NITWQuiz Club NITW
 
ARTERIAL BLOOD GAS ANALYSIS........pptx
ARTERIAL BLOOD  GAS ANALYSIS........pptxARTERIAL BLOOD  GAS ANALYSIS........pptx
ARTERIAL BLOOD GAS ANALYSIS........pptxAneriPatwari
 

Recently uploaded (20)

Introduction to Research ,Need for research, Need for design of Experiments, ...
Introduction to Research ,Need for research, Need for design of Experiments, ...Introduction to Research ,Need for research, Need for design of Experiments, ...
Introduction to Research ,Need for research, Need for design of Experiments, ...
 
Satirical Depths - A Study of Gabriel Okara's Poem - 'You Laughed and Laughed...
Satirical Depths - A Study of Gabriel Okara's Poem - 'You Laughed and Laughed...Satirical Depths - A Study of Gabriel Okara's Poem - 'You Laughed and Laughed...
Satirical Depths - A Study of Gabriel Okara's Poem - 'You Laughed and Laughed...
 
How to Fix XML SyntaxError in Odoo the 17
How to Fix XML SyntaxError in Odoo the 17How to Fix XML SyntaxError in Odoo the 17
How to Fix XML SyntaxError in Odoo the 17
 
4.9.24 Social Capital and Social Exclusion.pptx
4.9.24 Social Capital and Social Exclusion.pptx4.9.24 Social Capital and Social Exclusion.pptx
4.9.24 Social Capital and Social Exclusion.pptx
 
Transaction Management in Database Management System
Transaction Management in Database Management SystemTransaction Management in Database Management System
Transaction Management in Database Management System
 
Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...
Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...
Healthy Minds, Flourishing Lives: A Philosophical Approach to Mental Health a...
 
ICS 2208 Lecture Slide Notes for Topic 6
ICS 2208 Lecture Slide Notes for Topic 6ICS 2208 Lecture Slide Notes for Topic 6
ICS 2208 Lecture Slide Notes for Topic 6
 
Tree View Decoration Attribute in the Odoo 17
Tree View Decoration Attribute in the Odoo 17Tree View Decoration Attribute in the Odoo 17
Tree View Decoration Attribute in the Odoo 17
 
Integumentary System SMP B. Pharm Sem I.ppt
Integumentary System SMP B. Pharm Sem I.pptIntegumentary System SMP B. Pharm Sem I.ppt
Integumentary System SMP B. Pharm Sem I.ppt
 
Mattingly "AI & Prompt Design: Large Language Models"
Mattingly "AI & Prompt Design: Large Language Models"Mattingly "AI & Prompt Design: Large Language Models"
Mattingly "AI & Prompt Design: Large Language Models"
 
Objectives n learning outcoms - MD 20240404.pptx
Objectives n learning outcoms - MD 20240404.pptxObjectives n learning outcoms - MD 20240404.pptx
Objectives n learning outcoms - MD 20240404.pptx
 
6 ways Samsung’s Interactive Display powered by Android changes the classroom
6 ways Samsung’s Interactive Display powered by Android changes the classroom6 ways Samsung’s Interactive Display powered by Android changes the classroom
6 ways Samsung’s Interactive Display powered by Android changes the classroom
 
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 - I-LEARN SMART WORLD - CẢ NĂM - CÓ FILE NGHE (BẢN...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 - I-LEARN SMART WORLD - CẢ NĂM - CÓ FILE NGHE (BẢN...BÀI TẬP BỔ TRỢ TIẾNG ANH 8 - I-LEARN SMART WORLD - CẢ NĂM - CÓ FILE NGHE (BẢN...
BÀI TẬP BỔ TRỢ TIẾNG ANH 8 - I-LEARN SMART WORLD - CẢ NĂM - CÓ FILE NGHE (BẢN...
 
Narcotic and Non Narcotic Analgesic..pdf
Narcotic and Non Narcotic Analgesic..pdfNarcotic and Non Narcotic Analgesic..pdf
Narcotic and Non Narcotic Analgesic..pdf
 
Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...
Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...
Beauty Amidst the Bytes_ Unearthing Unexpected Advantages of the Digital Wast...
 
prashanth updated resume 2024 for Teaching Profession
prashanth updated resume 2024 for Teaching Professionprashanth updated resume 2024 for Teaching Profession
prashanth updated resume 2024 for Teaching Profession
 
Decoding the Tweet _ Practical Criticism in the Age of Hashtag.pptx
Decoding the Tweet _ Practical Criticism in the Age of Hashtag.pptxDecoding the Tweet _ Practical Criticism in the Age of Hashtag.pptx
Decoding the Tweet _ Practical Criticism in the Age of Hashtag.pptx
 
How to Manage Buy 3 Get 1 Free in Odoo 17
How to Manage Buy 3 Get 1 Free in Odoo 17How to Manage Buy 3 Get 1 Free in Odoo 17
How to Manage Buy 3 Get 1 Free in Odoo 17
 
Q-Factor General Quiz-7th April 2024, Quiz Club NITW
Q-Factor General Quiz-7th April 2024, Quiz Club NITWQ-Factor General Quiz-7th April 2024, Quiz Club NITW
Q-Factor General Quiz-7th April 2024, Quiz Club NITW
 
ARTERIAL BLOOD GAS ANALYSIS........pptx
ARTERIAL BLOOD  GAS ANALYSIS........pptxARTERIAL BLOOD  GAS ANALYSIS........pptx
ARTERIAL BLOOD GAS ANALYSIS........pptx
 

Hypothesis testing

  • 2. What is a Hypothesis Test? • A hypothesis test is a statistical method that uses sample data to evaluate a hypothesis about a population • A standardized methodology we use to answer a research question of interest • The most commonly utilized inferential procedure • Incorporates the concepts of z-scores, probability, and the distribution of sample means • The general goal of the hypothesis test: • To rule out chance (sampling error) as a plausible explanation for the results from a research study
  • 3. The Logic of Hypothesis Testing 1. We have a hypothesis about a population • Typically about a population parameter: μ = 50 2. Based on our hypothesis, we predict the characteristics our sample should have • M should be around 50 3. Obtain a random sample from the population • Sample n = 20 from the population and compute their M 4. Compare the sample statistic with our hypothesis about the population • If the values are consistent, the hypothesis is reasonable • If there is a large discrepancy, we decide the hypothesis is unreasonable
  • 4. The Unknown Population • Typically, research involves an unknown population • After we administer “tutoring treatment” to our sample of students, what is the new μ? • Remember, σ should remain the same • The focus of our hypothesis is the unknown population
  • 5. The Research Study Sample • Theoretically: • We would treat the entire population, randomly sample from the treated population, and evaluate the M • Realistically: • We sample from the original population, treat the sample only, and evaluate the M
  • 6. The Purpose of the Hypothesis Test 1. There does not appear to be a treatment effect The difference between the sample and the population can be explained by sampling error 2. There does appear to be a treatment effect The difference between the sample and the population is too large to be explained by sampling error To decide between two explanations:
  • 7. The Hypothesis Test: Step 1 State the hypothesis about the unknown population • The null hypothesis (H0) • States that there is no change in the general population before and after an intervention. • In the context of an experiment, H0 predicts that the independent variable (IV) will have no effect on the dependent variable • The scientific/alternative hypothesis (H1) • States that there is a change in the general population following an intervention • In the context of an experiment, H1 predicts that the independent variable (IV) will have an effect on the dependent variable
  • 8. SAT Example • Population parameters of a normally distributed variable are μ = 500 and σ = 50 • I believe my prep course will have some effect on this mean value • My hypotheses: • Null (H0): Even with treatment, the mean SAT score will remain at 500 • Alternative (H1): With treatment, the mean SAT score will be different from* 500 *Note: Here we do not specify a direction (increase/decrease); just some difference 500: 500: 1 0   SAT SAT H H  
  • 9. The Hypothesis Test: Step 2 Set the criteria for a decision • Determine before the experiment what sample means are inconsistent with the null hypothesis • The sampling distribution of the mean for the population is divided into two parts: 1. Sample means likely to be obtained if H0 is true (sample means close to the null value) 2. Sample means that are very unlikely to be obtained if H0 is true (sample means that are very different from the null value)
  • 10. The Alpha (α) Level a.k.a. the Level of Significance The α level establishes the criterion, or “cut-off”, for making a decision about the null hypothesis. The alpha level also determines the risk of a Type I error (TBD in next section) • How we define which sample means have “high” or “low” probabilities • Typically set at: • α = 0.05, • α = 0.01 • α = 0.001 • Separates the typical values from the extreme, unlikely-to- occur values (in the critical region)
  • 11. The Hypothesis Test: Step 3 Collect data and compute sample statistics • After we state they hypotheses and establish our critical regions: • Randomly sample from the population • Give the sample the treatment/intervention • Summarize the sample with the appropriate statistic (e.g.: the M) • Compute the test statistic M M z    The z-score (the test statistic) 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)
  • 12. The Hypothesis Test: Step 4 Make a decision •Use the z-score obtained for the sample statistic and make a decision about the null hypothesis (H0) based on the critical region. Either: • Reject the null hypothesis • The sample data fall in the critical region • This event is unlikely if the null hypothesis is true, so we conclude to reject the null • This does NOT mean that we have proven the alternative • Fail to reject the null hypothesis (retain the null) • The sample data do not fall in the critical region • We do not have enough evidence to show that the null hypothesis is incorrect (NOT that the null hypothesis is “true”)
  • 13. Making your decision: One mo’ time! • Use the z-score obtained for the sample statistic and make a decision about the null hypothesis (H0) based on the critical region IF: My sample mean has a corresponding z = 0.87 • My treatment effect is not convincing. I do not have enough evidence and fail to reject the null. IF: My sample mean has a corresponding z = -2.50 • This is an unlikely event if the null is true, so I reject the null. I have convincing evidence my treatment works and has an effect. Fail to reject H0 Reject H0 Reject H0
  • 14. An Analogy for Hypothesis Testing Research Study 1. H0: There is no treatment effect 2. Researchers gather evidence to show that the treatment actually does have an effect 3. If there is enough evidence, the researchers reject H0 and conclude that there is a treatment effect 4. If there is not enough evidence, the researcher fails to reject H0 Jury Trial 1. H0: Defendant did not commit a crime 2. Police gathers evidence to show that the defendant really did commit a crime 3. If there is enough evidence, the jury rejects H0 and concludes that the defendant is guilty of the crime 4. If there is not enough evidence, the jury fails to find the defendant guilty Both are trying to refute the null hypothesis (H0) They are not concluding that there is no treatment effect; simply that there is not enough evidence to conclude there is an effect They are not concluding that the defendant is innocent; simply that there is not enough evidence for a guilty verdict
  • 15. Statistical Significance A result is statistically significant if it is unlikely to occur when the null hypothesis (H0) is true (Sufficient to reject the null hypothesis [H0]) • An effect is significant if we decide to reject the null hypothesis after conducting a hypothesis test • Z = 0.87, p > 0.05 does not fall in the critical region, fail to reject the null • Z = -2.50, p < 0.05 falls in the critical region, reject the null
  • 16. The z-Score as a Test Statistic • A Test Statistic = A single, specific statistic (converted from sample data) that is used to test the hypothesis • The z-score formula as a recipe • Make a hypothesis about the value of µ. This is H0. • Plug the hypothesized value in the formula along with the other values • If the results is a z-score near zero (where z-scores are supposed to be), fail to reject H0. M M z   
  • 17. The z-Score Formula as a Ratio If z is large, the obtained difference is larger than expected by chance • For example: z = 3 indicates the obtained difference is three times larger than what would be expected by chance    M M z   Sample mean – hypothesized population mean Standard error between M and µ Obtained difference Difference due to chance OR 3 1 3 
  • 18. Uncertainty and Errors in Hypothesis Testing
  • 19. Type I Errors (α) • A Type I error occurs when the sample data appear to show a treatment effect when, in fact, there is none • We reject a null hypothesis (H0) that is actually true • We falsely conclude that the treatment has an effect • Caused by unusual, unrepresentative samples that fall into the critical region despite a null effect of treatment • Type I errors are very unlikely
  • 20. Type II Errors (β) • A Type II error occurs when the sample does not appear to have been affected by the treatment when, in fact, it has (the treatment does have an effect) • We fail to reject the null hypothesis (H0) that is actually false • We falsely conclude that the treatment had no effect • 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 our data
  • 21. The Relationship Between α & Errors • The alpha (α) level is the probability that the test will lead to a Type I error • If α = .05: The probability that the test will lead to a Type I error is 5% • If α = .01: The probability that the test will lead to a Type I error is 1% • How does changing α influence Type II errors? • As we make α smaller, we decrease the chance of making a Type I error. • However, we also make it harder to reject the null; thus increasing the risk of a Type II error
  • 22. Critical Region Boundaries If α = .05, z = +/-1.96 If α = .01, z = +/-2.58 If α = .001, z = +/-3.30
  • 24. The Study: Prenatal alcohol exposure on birth weights A random sample of n = 16 pregnant rats is obtained. The mother rats are given a daily dose of alcohol. At birth, one pup is selected from each litter to produce a sample of n = 16 newborn rats. The average weight for the sample is M = 15 grams. It is known that regular newborn rats have an average weight of μ = 18 grams, with σ = 4
  • 25. Step 1 State the hypotheses and select the alpha (α) level • For this test, we will use an alpha level of α = .05 • We are taking a 5% risk of committing a Type I error H0 :malcoholexp =18 H1 :malcoholexp ¹18 Even with alcohol exposure, the rats still average 18 grams at birth or Alcohol exposure does not have an effect on birth weight Alcohol exposure will change birth weight
  • 26. Step 2 Set the decision criteria by locating the critical region • The 3-step process: If we obtain a sample mean that is in the critical region, we conclude that the sample is not compatible with the null hypothesis and we reject H0
  • 27. Step 3 • Collect the data, and compute the test statistic • In this case, the z-score: z = M -m sM = 15-18 4 16 æ è ç ö ø ÷ = -3 4 4 æ è ç ö ø ÷ = -3 1 = -3.00
  • 28. Step 4 Make a decision • Our z-score (-3.00) exceeds the critical value of +/-1.96 • It is in the critical region • Our interpretation: • This event is unlikely if the null is true Reject the null hypothesis. Alcohol does have a significant effect on the birth weight of rats.
  • 29. Things to Keep In Mind • State the hypotheses: • Your hypotheses lays out the whole point of the test • Phrased in terms of the population parameters • When setting critical values: • What are they? • Are they positive? Negative? Both? • Results • What do we conclude about the null? • State your results in scientific language: The treatment with alcohol had a significant effect on the birth weight of newborn rats, z = -3.00, p < .05. • Conclusions • What do we conclude about the point of the study?
  • 30. Factors Influencing a Hypothesis Test 1. The size of difference between M and μ • Numerator of z-score • Bigger difference, more likely to reject 2. The variability of the scores (σ) • Denominator of z-score (standard error) • More variability, less accurate, less likely to reject 1. The number of scores in the sample (n) • Denominator of z-score (standard error) • Bigger sample, more accurate, more likely to reject
  • 31. Assumptions of Hypothesis Testing with z-Scores 1. Random sampling • Ensures a representative sample 2. Independent observations • No consistent relationship between observations • The occurrence of the first has no bearing on the second 3. The value of σ is unchanged by the treatment • In effect, the treatment adds/subtracts a constant from every value in the distribution • Remember, when this occurs, the mean will change but not the SD 4. Normal sampling distribution (n > 30 or normal population) • To justify using the Unit Normal Table
  • 33. • Two-tailed test • Critical region involves means that are either higher or lower than expected by chance • There are two “tails” to this distribution • One-tailed test • Critical region involves only the area you specify • Specifies an increase or decrease • There is one “tail” to this distribution
  • 34. • One-tailed test: • Two-tailed test: H0 :m £100 H1 :m >100 100: 100: 1 0     H H
  • 36. Effect Size Intended to provide a measurement of the absolute magnitude of a treatment effect, independent of the size of the sample(s) being used. • Statistical significance does not necessarily mean the difference is substantial or meaningful • It allows us to conclude the null hypothesis is unlikely and offers support for the alternative hypothesis • BUT cannot make any real claims about the treatment effect found • If the standard error is very small, even a very small treatment effect may result in rejecting the null hypothesis • With a large enough sample, you will find a significant effect for almost any sized difference
  • 37. Measuring Effect Size • (0.0 < d < 0.2) = Small effect size • (0.2 < d < 0.8) = Medium effect size • (d > 0.8) = Large effect size Cohen's d = mean difference standard deviation = mtreatment -mno.treatment s We don’t know this estimated Cohen's d = mean difference standard deviation = Mtreatment -mno.treatment s so we use this
  • 38. Cohen’s d uses σ to measure effect size estimated Cohen's d = mean difference standard deviation = Mtreatment -mno.treatment s (let's just call this) Cohen's d = 15 100 = 0.15
  • 39. Cohen’s d uses σ to measure effect size estimated Cohen's d = mean difference standard deviation = Mtreatment -mno.treatment s (let's just call this) Cohen's d = 15 15 =1.00
  • 41. Power The probability that the test will correctly reject a false null hypothesis. •Will identify a treatment effect if one truly exists •Factors that affect power: • Effect size • A larger effect size  more likely to reject H0  power increases • Sample size • Larger sample size  more likely to reject H0  increased power • Alpha level • Lower α  less likely to reject H0  less power • One- versus two-tailed test • One-tailed  more likely to reject H0  more power