This document discusses hypothesis testing and related statistical concepts. It begins with an outline of the key topics to be covered, including the concept of hypothesis testing, motivation for its use, null and alternative hypotheses, types of errors, and examples. It then provides more detailed explanations and examples of these topics:
- Hypothesis testing involves using sample data to determine if there is evidence to reject or fail to reject claims about a population.
- Examples show how hypothesis testing can help decision makers determine if new suppliers or products meet claimed standards.
- The null hypothesis states there is no difference or effect, while the alternative hypothesis specifies an expected difference.
- Type I errors incorrectly reject the null hypothesis, while type
inferential statistics, statistical inference, language technology, interval estimation, confidence interval, standard error, confidence level, z critical value, confidence interval for proportion, confidence interval for the mean, multiplier,
According to Wikipedia point estimation involves the use of sample data to calculate a single value (known as a point estimate since it identifies a point in some parameter space) which is to serve as a "best guess" or "best estimate" of an unknown population parameter (for example, the population means).
Simple Linear Regression: Step-By-StepDan Wellisch
This presentation was made to our meetup group found here.: https://www.meetup.com/Chicago-Technology-For-Value-Based-Healthcare-Meetup/ on 9/26/2017. Our group is focused on technology applied to healthcare in order to create better healthcare.
inferential statistics, statistical inference, language technology, interval estimation, confidence interval, standard error, confidence level, z critical value, confidence interval for proportion, confidence interval for the mean, multiplier,
According to Wikipedia point estimation involves the use of sample data to calculate a single value (known as a point estimate since it identifies a point in some parameter space) which is to serve as a "best guess" or "best estimate" of an unknown population parameter (for example, the population means).
Simple Linear Regression: Step-By-StepDan Wellisch
This presentation was made to our meetup group found here.: https://www.meetup.com/Chicago-Technology-For-Value-Based-Healthcare-Meetup/ on 9/26/2017. Our group is focused on technology applied to healthcare in order to create better healthcare.
The Cramer-Rao Inequality provides us with a lower bound on the variance of an unbiased estimator for a parameter.
The Cramer-Rao Inequality Let X = (X1,X2,. . ., Xn) be a random sample from a distribution with d.f. f(x|θ), where θ is a scalar parameter. Under certain regularity conditions on f(x|θ), for any unbiased estimator φˆ (X) of φ (θ)
Multiple Linear Regression II and ANOVA IJames Neill
Explains advanced use of multiple linear regression, including residuals, interactions and analysis of change, then introduces the principles of ANOVA starting with explanation of t-tests.
The Cramer-Rao Inequality provides us with a lower bound on the variance of an unbiased estimator for a parameter.
The Cramer-Rao Inequality Let X = (X1,X2,. . ., Xn) be a random sample from a distribution with d.f. f(x|θ), where θ is a scalar parameter. Under certain regularity conditions on f(x|θ), for any unbiased estimator φˆ (X) of φ (θ)
Multiple Linear Regression II and ANOVA IJames Neill
Explains advanced use of multiple linear regression, including residuals, interactions and analysis of change, then introduces the principles of ANOVA starting with explanation of t-tests.
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..
-Hypotheses
-What is Hypothesis testing
-Basic Concepts in Hypotheses Testing (in detail)
~Alternate Hypothesis
~Level of Significance
~Critical Region
~Decision Rule(Test of Hypothesis)
~Type I Error & Type II Error
~Power of Test
~One Tailed & Two Tailed Test
~One Sample & Two Sample Tests
` Types of Hypotheses
` Steps in Hypotheses Testing
~Parametric & Non Parametric Tests
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Chapter 8: Hypothesis Testing
8.1: Basics of Hypothesis Testing
Hypothesis TestingThe Right HypothesisIn business, or an.docxadampcarr67227
Hypothesis Testing
The Right Hypothesis
In business, or any other discipline, once the question has been asked there must be a statement as to what will or will not occur through testing, measurement, and investigation. This process is known as formulating the right hypothesis. Broadly defined a hypothesis is a statement that the conditions under which something is being measured or evaluated holds true or does not hold true. Further, a business hypothesis is an assumption that is to be tested through market research, data mining, experimental designs, quantitative, and qualitative research endeavors. A hypothesis gives the businessperson a path to follow and specific things to look for along the road.
If the research and statistical data analysis supports and proves the hypothesis that becomes a project well done. If, however, the research data proved a modified version of the hypothesis then re-evaluation for continuation must take place. However, if the research data disproves the hypothesis then the project is usually abandoned.
Hypotheses come in two forms: the null hypothesis and the alternate hypothesis. As a student of applied business statistics you can pick up any number of business statistics textbooks and find a number of opinions on which type of hypothesis should be used in the business world. For the most part, however, and the safest, the better hypothesis to formulate on the basis of the research question asked is what is called the null hypothesis. A null hypothesis states that the research measurement data gathered will not support a difference, relationship, or effect between or amongst those variables being investigated. To the seasoned research investigator having to accept a statement that no differences, relationships, and/or effects will occur based on a statistical data analysis is because when nothing takes place or no differences, effects, or relationship are found there is no possible reason that can be given as to why. This is where most business managers get into trouble when attempting to offer an explanation as to why something has not happened. Attempting to provide an answer to why something has not taken place is akin to discussing how many angels can be placed on the head of a pin—everyone’s answer is plausible and possible. As such business managers need to accept that which has happened and not that which has not happened.
Many business people will skirt the null hypothesis issue by attempting to set analternative hypothesis that states differences, effects and relationships will occur between and amongst that which is being investigated if certain conditions apply.Unfortunately, however, this reverse position is as bad. The research investigator might well be safe if the data analysis detects differences, effect or relationships, but what if it does not? In that case the business manager is back to square one in attempting to explain what has not happened. Although the hypothesis situation may seem c.
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Data Science Project Life Cycle
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Install packages in R/ R Studio
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Shortcuts & Tips
Resources & reference
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SlideShare Description for "Chatty Kathy - UNC Bootcamp Final Project Presentation"
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Discover how Chatty Kathy, an innovative project developed at the UNC Bootcamp, aims to tackle the challenge of low physical activity among older adults. Our AI-driven solution uses peer interaction to boost and sustain exercise levels, significantly improving health outcomes. This presentation covers our problem statement, the rationale behind Chatty Kathy, synthetic data and persona creation, model performance metrics, a visual demonstration of the project, and potential future developments. Join us for an insightful Q&A session to explore the potential of this groundbreaking project.
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MCG reports that the more favorable market conditions expected over the next few years, helped by the winding down of pandemic restrictions and a hybrid working environment will be driving market momentum forward. The continuous injection of capital by alternative investment firms, as well as the growing infrastructural investment from cloud service providers and social media companies, whose revenues are expected to grow over 3.6x larger by value in 2026, will likely help propel center provision and innovation. These factors paint a promising picture for the industry players that offset rising input costs and adapt to new technologies.
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8. Statistics for Data Analysis
What are the four main things we should know before
studying data analysis?
Descriptive statistics
Distributions (normal distribution / sampling distribution)
Inferential statistics/ Hypothesis testing
8
9. Outline
Concept
Motivation
Example: Quality Control Problem
Null & Alternative Hypothesis
One & Two – tailed tests
Type I & Type II errors
Courtroom Analogy
Fallacies in Statistical Hypothesis Testing
Example: Testing of Mean (σ known) One Tailed Test
Example: Testing of Mean (σ known) Two Tailed Test
9
10. Concept
10
It is the procedure to test truth of a statement/claim about the
population parameter on the basis of sample selected from the
population.
The purpose of hypothesis testing is to determine whether there is
enough statistical evidence against a certain belief, or hypothesis,
about a parameter.
Is the sample statistic a function of chance or luck rather than an
accurate representation of the population parameter?
11. Motivation
CASE – I
The purchase manager of a machine tool making company has to decide
whether to buy castings from a new supplier or not.
The new supplier claims that his castings have higher hardness than those
of the competitors.
If the claim is true, then it would be in the interest of the company to
switch from the existing suppliers to the new supplier because of the
higher hardness, all other conditions being similar.
However, if the claim is not true, the purchase manager should continue
to buy from the existing suppliers.
He needs a tool which allows him to test such a claim. Testing of
hypothesis provides such a tool to the decision maker.
11
12. Motivation
If the purchase manager were to use this tool, he would ask the
new supplier to deliver a small number of castings.
This sample of castings will be evaluated and based on the
strength of the evidence produced by the sample, the purchase
manager will accept or reject the claim of the new supplier and
accordingly make his decision.
The claim made by the new supplier is a hypothesis that needs to
be tested and a statistical procedure which allows us to perform
such a test is called testing of hypothesis.
12
13. Motivation
CASE - II
The CEO of a light bulbs manufacturer needs to test that if the bulbs can
last on average 1000 burning hours. If the plan manager randomly sampled
100 bulbs and finds that the sample average is 980 hours with a standard
deviation of 80 hours. At 5 % level of significance do light bulbs lasts an
average of 1000 hours?
CASE - III
A bolt manufacturer claims that on an average 3% bolts manufactured by his
factory are defective. A sample of 200 bolts is selected and is found to have
5 % defective bolts.
The dilemma is to accept the claim or reject ?
If again a sample of 200 bolts is selected and is found to have 3.2 %
defective bolts.
To accept the claim or reject ?
14
18. Motivation
More cases
Is there statistical evidence, from a random sample of potential
customers, to support the hypothesis that more than 10% of the
potential customers will purchase a new product?
Is a new drug effective in curing a certain disease? A sample of patients is
randomly selected and given the drug. Then the conditions of the
patients are then measured.
The CEO of a large electric utility claims that 80 percent of his
1,000,000 customers are very satisfied with the service they receive. To
test this claim, the local newspaper surveyed 100 customers, using
simple random sampling. Among the sampled customers, 73 percent say
they are very satisfied. Based on these findings, can we reject the CEO's
hypothesis that 80% of the customers are very satisfied? Use a 0.05 level
of significance.
19
31. Quality Control Problem: Bolt Manufacturer
To test the claim we set up a cut-off value/critical value (let 4 %).
If the average number of defective bolts in the sample exceeds
this cut – off value, we decide to reject his claim and accept
otherwise.
Important thing to notice that we can change this cut – off value
as per accuracy desired.
E.g., if we want to be more sure that the claim is false
before we reject it, we can set a higher cut – off value, 5.5
%. In this case we need more evidence to reject the claim.
32
32. Quality Control Problem: Bolt Manufacturer
Here, we are less likely to reject the hypothesis/claim when it is
true as the rejection region is reduced.
Hence, the size of rejection region and the cut – off value is
determined by the researcher.
Significance level shows how sure we want to be when rejecting
H0.
33
33. Hypothesis Testing: Basic Concepts
Hypothesis
An assumption made about a population parameter
E.g. At most 3% bolts manufactured by his factory are defective
Purpose of HypothesisTesting
To make a judgment about the difference between the sample statistic and
the population parameter
The sample contains 5 % defectives. Is this an accurate representation of
the bolt’s population?
The mechanism adopted to make this objective judgment is the core
of hypothesis testing
34. Null & Alternative Hypothesis
Null hypothesis H0
It is a statement of the no difference
and any observed difference are by
chance.
The null hypothesis refers to a
specified value of the population
parameter, not a sample statistic.
Begin with the assumption that the
null hypothesis is TRUE
Always contains the ‘=’ sign
Alternative hypothesis H1 or HA
It is one in which some difference is
expected.
It says that any observed difference in
the data can be generalized to the
population.
It is the complementary/opposite
statement to Null hypothesis
Never contains the ‘=’ sign
These two hypotheses are mutually exclusive and exhaustive so
that one is true to the exclusion of the other
35. Null & Alternative Hypothesis
Null hypothesis H0
It is a statement of the no
difference and any observed
difference are by chance.
The null hypothesis refers to a
specified value of the population
parameter, not a sample statistic.
Begin with the assumption that the
null hypothesis isTRUE
Always contains the ‘=’ sign
Alternative hypothesis H1 or HA
It is one in which some difference
is expected.
It says that any observed
difference in the data can be
generalized to the population.
It is the complementary/opposite
statement to Null hypothesis
Never contains the ‘=’ sign
These two hypotheses are mutually exclusive and exhaustive so
that one is true to the exclusion of the other
36. Null & Alternative Hypothesis
Null hypothesis H0
It is a statement of the no
difference and any observed
difference are by chance.
The null hypothesis refers to a
specified value of the population
parameter, not a sample statistic.
Begin with the assumption that the
null hypothesis isTRUE
Always contains the ‘=’ sign
Alternative hypothesis H1 or HA
It is one in which some difference
is expected.
It says that any observed
difference in the data can be
generalized to the population.
It is the complementary/opposite
statement to Null hypothesis
Never contains the ‘=’ sign
These two hypotheses are mutually exclusive and exhaustive so
that one is true to the exclusion of the other
If null hypothesis is true, no action is
required.That’s why the name
38. Quiz time
39
Can any one of the two be called the null hypothesis?
No, because the roles of Ho and H1 are not
symmetrical.
39. Quiz time
40
True or False?
Null hypothesis assume that any observed difference
between the true value and estimated value are due to
chance.
40. Quiz time
41
True or False?
Null hypothesis assume that any observed difference
between the true value and estimated value are due to
chance.
True
41. Null & Alternative Hypothesis
A consumer analyst reports that the mean life of a certain type of
automobile battery is not (claim) 74 months.
A radio station publicizes that its proportion of the local listing
audience is greater than or equal to (claim) 39 %
1 : 74
H Mean
0 : 74
H Mean =
1 : 39
H P
0 : 39
H P
42. Null & Alternative Hypothesis
A consumer analyst reports that the mean life of a certain type of
automobile battery is not (claim) 74 months.
A radio station publicizes that its proportion of the local listing
audience is greater than or equal to (claim) 39 %
1 : 74
H Mean
0 : 74
H Mean =
1 : 39
H P
0 : 39
H P
43. Null & Alternative Hypothesis: More Examples
Suppose we wanted to test the hypothesis that the mean familiarity
rating exceeds 4.0, the neutral value on a 7 point scale.
A new Internet Shopping Service will be introduced if more than 40%
people use it.
44. Null & Alternative Hypothesis: More Examples
Suppose we wanted to test the hypothesis that the mean familiarity
rating exceeds 4.0, the neutral value on a 7 point scale.
A new Internet Shopping Service will be introduced if more than 40%
people use it.
1 : 4.0
H Mean
0 : 4.0
H Mean
1 : 0.40
H P
0 : 0.40
H P
45. Null & Alternative Hypothesis
A consumer analyst reports that the mean life of a certain type of
automobile battery is not (claim) 74 months.
A radio station publicizes that its proportion of the local listing
audience is greater than or equal to (claim) 39 %
1 : 74
H Mean
0 : 74
H Mean =
1 : 39
H P
0 : 39
H P
46. Null & Alternative Hypothesis: More Examples
Suppose we wanted to test the hypothesis that the mean familiarity
rating exceeds 4.0, the neutral value on a 7 point scale.
A new Internet Shopping Service will be introduced if more than 40%
people use it.
47. Null & Alternative Hypothesis: More Examples
Suppose we wanted to test the hypothesis that the mean familiarity
rating exceeds 4.0, the neutral value on a 7 point scale.
A new Internet Shopping Service will be introduced if more than 40%
people use it.
1 : 4.0
H Mean
0 : 4.0
H Mean
1 : 0.40
H P
0 : 0.40
H P
49. One Tailed/ Two Tailed Tests
One - tailed tests
Determines whether a particular population parameter is larger or
smaller than some predefined value
If the claim/ hypothesis is expressed in one direction (increasing or
decreasing), then we choose one tailed test.
Ho: Population mean attitudes are greater than or equal to 3.0
Ha: Population mean attitudes are less than 3.0
Two – tailed tests
Determines the likelihood that a population parameter is within certain
upper and lower bounds
If the Research Hypothesis is expressed without direction
Ho: Population mean attitudes = 4.5
Ha: Population mean attitudes are not equal to 4.5
52
62. Courtroom Analogy…
The basic concepts in hypothesis testing are actually quite analogous
to those in a criminal trial.
If on a jury, must presume defendant is innocent unless enough
evidence to conclude is guilty.
Trial held because prosecution believes status quo of innocence is
incorrect.
Prosecution collects evidence, like researchers collect data, in hope
that jurors will be convinced that such evidence is extremely unlikely
if the assumption of innocence were true.
• Defendant is
innocent.
Null
Hypothesis
• Defendant is guilty.
Alternate
Hypothesis
63. Courtroom Analogy…
Potential choices and errors
Choice - 1
• We cannot rule out that defendant is
innocent, so he or she is set free without
penalty.
• Potential error: A criminal has been
erroneously freed.
Choice - 2
• We believe enough evidence to conclude the
defendant is guilty.
• Potential error: An innocent person falsely
convicted.
Choice 2 is usually seen as more serious.
64. Related Terminology
Type I error
The error of rejecting the null hypothesis, when it is true (incorrect
decision)
Is similar to convicting an innocent person
Known as False alarm
Also known as False positive error
Type II error
The error of accepting the null hypothesis, when it is false
(incorrect decision)
Is similar to letting a guilty person go free
Known as Failure to sound the alarm
Also known as False negative error
65. Related Terminology
Level of significance
The probability of type I error
The conditional probability of rejecting the null hypothesis, when it
is true (incorrect decision)
Its good to have low value of
Generally taken as 0.01, 0.05 or 0.1
Also known as Producer’s Risk
Confidence level
The probability of accepting the null hypothesis, when it is true (i. e.
correct decision)
Most common values are 99 %, 95 % or 90 %
1
−
66. Related Terminology
Weakness of the test
The probability of type II error
The probability of accepting the null hypothesis, when it is
false (i. e. incorrect decision)
Also known as Consumer’s Risk
Its good to have low value of
Power of the test
1 - The probability of type II error
The conditional probability of rejecting the null hypothesis, when it
is false (i. e. correct decision)
1
−
67. Important Fact
Alpha and Beta have an inverse
relationship.
We can not reduce both types
of errors simultaneously
We fix one of the errors,
generally producer’s risk and
then try to minimize other
68. How can we decrease type I error?
To decrease type I error / to increase confidence interval:
Set low level of significance/ reduce rejection region
69. How can we decrease type II error?
To decrease type I error / to increase power of test:
Increase sample size
Large enough sample ensures to detect a practical difference when one truly
exists.
Set high level of significance/ increase rejection region
70. Type I Vs Type II Error
Which one is worse?
Both types of errors are problems for individuals, corporations,
and data analysis.
A false positive (with null hypothesis of health) in medicine
causes unnecessary worry or treatment, while a false negative
gives the patient the dangerous illusion of good health and the
patient might not get an available treatment.
A false positive in manufacturing quality control (with a null
hypothesis of a product being well made) discards a product that
is actually well made, while a false negative stamps a broken
product as operational.
A false positive (with null hypothesis of no effect) in scientific
research suggest an effect that is not actually there, while a false
negative fails to detect an effect that is there.
71. Type I Vs Type II Error
Which one is worse?
Based on the real-life consequences of an error, one type may be more
serious than the other.
For example, NASA engineers would prefer to throw out an electronic
circuit that is really fine (type I, false positive) than to use one on a
spacecraft that is actually broken (type II, false negative). In that
situation a type I error raises the budget, but a type II error would
risk the entire mission.
On the other hand, criminal courts set a high bar for proof and
procedure and sometimes acquit someone who is guilty (type II, false
negative) rather than convict someone who is innocent (type I, false
positive).
For any given sample size the effort to reduce one type of error generally
results in increasing the other type of error.
The only way to minimize both types of error, without just improving
the test, is to increase the sample size, and this may not be feasible.
74. Critical Value
Critical values for any test is the boundary of acceptance region or in other
words, it’s the cut point between the acceptance and rejection region.
For one tailed test
It is positive for right tailed test & negative for left tailed test
It is calculated by using the tables of area under standard normal
curve
E.g., at 5 % level of significance critical values for right/ left tailed tests
are 1.645/-1.645
For two tailed test
It gives the upper and lower bounds for the sample statistic
It may be positive or negative
E.g., at 1 % level of significance critical values for two tailed tests are
+/- 2.58
75. Critical Values for z - Test
For left tailed test
• - 2.326
At 1 % level of
significance
• - 1.645
At 5 % level of
significance
• - 1.282
At 10 % level of
significance
76. Critical Values for z - Test
For right tailed test
• 2.326
At 1 % level of
significance
• 1.645
At 5 % level of
significance
• 1.282
At 10 % level of
significance
77. Critical Values for z - Test
For two tailed test
• ± 2.576
At 1 % level of
significance
• ± 1.960
At 5 % level of
significance
• ± 1.645
At 10 % level of
significance
78.
79.
80.
81.
82.
83.
84. P-value
The p-value is computed by assuming that the null hypothesis is true, and
then asking how likely we would be to observe such extreme results (or
even more extreme results) under that assumption.
85.
86.
87. P Value
The P value, or calculated probability, is the probability of finding the observed, or
more extreme, results when the null hypothesis (H 0) of a study question is true —
the definition of ‘extreme’ depends on how the hypothesis is being tested.
96
99. Various Tests of Significance
Parametric
test
Non-
parametric test
100. Selecting the appropriate tool
111
Parametric & Non-Parametric Tests
Make sure to check all assumptions before applying any statistical
technique.
Parametric Tests
T-test
Anova
Non-parametric
test
U-test
H-test
101. Selecting the Appropriate Technique
112
ResponseVariable(s) (DVs)
One DV More
than one
DV
Explanato
ry
Variable(s
) (IDVs)
One
IDV
Metric Non-
metric
Metric
Metric Simple
Regression
LDA/Logit
Reg
Path
Analysis
Non-metric t test/Anova Chi Square
Test
Manova
More
than
one IDV
All Metric Multiple Reg MDA/Multipl
e Logit Reg
Path
Analysis
All Non-
metric
n – way Anova Complex
Crosstab/
Log-linear
analysis
n – way
Manova
'n' is the number of non-metric IDV's
102. Selecting the appropriate tool
113
ResponseVariable(s) (DVs)
One DV More
than one
DV
Explanator
y
Variable(s)
(IDVs)
One IDV
Metric Non-
metric
Metric
Metric Simple
Regression
LDA/Logit Reg Path Analysis
Non-metric t test/Anova Chi Square
Test
Manova
More
than one
IDV
All Metric Multiple Reg MDA/Multiple
Logit Reg
Path Analysis
All Non-
metric
n – way Anova Complex
Crosstab/
Log-linear
analysis
n – way
Manova
Mixed n – way
Ancova/Dummy
var Regression
Multi-Nominal
Reg
n– way
Mancova
'n' is the number of non-metric IDV's
103. Response Variable(s) (DVs)
One DV
One IDV
Metric Non-metric
Metric Simple Regression LDA/Logit Reg
Non-metric t test/Anova Chi Square Test
Bivariate Analysis
112. One Sample z – test/ testing of mean (σ known)
A sample of 40 sales receipts from a grocery store has a mean of $137
and population s. d. is $30.2. Use these values to test whether or not the
mean is sales at the grocery store are different from $150.
Step 1: Set the null and alternative hypotheses
Null Hypothesis
Alternative Hypothesis
0 : 150
H Mean =
1 : 150
H Mean
113. One Sample z – test/ testing of mean (σ known)
An insurance company is reviewing its current policy rates. When
originally setting the rates they believed that the average claim amount
was $1,800. They are concerned that the true mean is actually higher
than this, because they could potentially lose a lot of money. They
randomly select 40 claims, and calculate a sample mean of $1,950.
Assuming that the standard deviation of claims is $500, and set α = 0.05,
test to see if the insurance company should be concerned.
Step 1: Set the null and alternative hypotheses
Null Hypothesis
Alternative Hypothesis
0 : 1800
H Mean
1 : 1800
H Mean
114. Quiz time
129
True or False?
In Type 1 error we declare an effect which does not exist.
True
115. Quiz time
130
True or False?
if we reduce the confidence level from 95% to 90% the chances of
us declaring that the effect observed in the sample actually prevails
in the population, are higher.
True
116. Quiz time
131
True or False?
In Type-2 error, we may miss an effect which actually exists.
True
117. Quiz time
132
True or False?
if we increase the confidence level from 95% to 99%, the chances of
us missing that the effect which actually prevails in the population,
are higher.
True
118. 143
My Interesting answers/posts
Want to excel in Statistics?
https://www.quora.com/How-can-I-get-better-at-statistics-within-a-
month/answer/Nisha-Arora-9
Effect of change of origin & Scale in variance?
https://www.quora.com/If-I-multiply-the-result-of-my-observations-by-3-
how-variance-and-mean-will-vary/answer/Nisha-Arora-9
Do you need to brsuh-up your probability concepts?
https://www.quora.com/How-do-I-know-when-to-add-and-when-to-
multiply-in-questions-based-on-probability/answer/Nisha-Arora-9
119. 144
My Interesting answers/posts
Role of Null & Alternative hypothesis?
https://www.quora.com/Can-I-switch-around-the-null-and-alternative-
hypothesis-in-hypothesis-testing/answer/Nisha-Arora-9
Type I error or Type II error?
https://www.quora.com/Why-dont-people-care-much-about-power-1-
Type-II-error-of-a-hypothesis-test/answer/Nisha-Arora-9
Hypothesis testing in layman’s terms?
https://learnerworld.tumblr.com/post/147285942960/how-do-you-explain-
hypothesis-testing-to-a-layman
120. 145
My Expertise
❖Statistics
❖Data Analysis
❖Machine Learning, Data Science, Analytics
❖R Programming, Shiny R
❖Python
❖SPSS, Excel, PowerBI
❖Mathematics, Operation Research
❖Data Visualization & Storytelling
❖Reporting & Dashboarding
121. 146
Reach Out to Me
http://stats.stackexchange.com/users/79100/learner
https://www.researchgate.net/profile/Nisha_Arora2/contributions
https://www.quora.com/profile/Nisha-Arora-9
http://learnerworld.tumblr.com/
Dr.aroranisha@gmail.com