Types of "T-Test" - Research Methodology, Hypothesis Testing
Hypothesis (अनुमानम्) is a predictive statement, capable of being tested by scientific methods, that relates an independent variable to some dependent variable.
The t-test compares the actual difference between two means in relation to the variation in the data (expressed as the standard deviation of the difference between the means).
General Linear Model is an ANOVA procedure in which the calculations are performed using the least square regression approach to describe the statistical relationship between one or more prediction in continuous response variable. Predictors can be factors and covariates. Copy the link given below and paste it in new browser window to get more information on General Linear Model:- http://www.transtutors.com/homework-help/statistics/general-linear-model.aspx
Designing studies with recurrent events | Model choices, pitfalls and group s...nQuery
In this free webinar, we will examine the important design considerations for analyzing recurring events and counts.
Watch the webinar at: https://www.statsols.com/en/webinar/designing-studies-with-recurrent-events
Designing studies with recurrent events (Model choices, pitfalls and group sequential design)
Standard error is used in the place of deviation. it shows the variations among sample is correlate to sampling error. list of formula used for standard error for different statistics and applications of tests of significance in biological sciences
PAGE
O&M Statistics – Inferential Statistics: Hypothesis Testing
Inferential Statistics
Hypothesis testing
Introduction
In this week, we transition from confidence intervals and interval estimates to hypothesis testing, the basis for inferential statistics. Inferential statistics means using a sample to draw a conclusion about an entire population. A test of hypothesis is a procedure to determine whether sample data provide sufficient evidence to support a position about a population. This position or claim is called the alternative or research hypothesis.
“It is a procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement” (Mason & Lind, pg. 336).
This Week in Relation to the Course
Hypothesis testing is at the heart of research. In this week, we examine and practice a procedure to perform tests of hypotheses comparing a sample mean to a population mean and a test of hypotheses comparing two sample means.
The Five-Step Procedure for Hypothesis Testing (you need to show all 5 steps – these contain the same information you would find in a research paper – allows others to see how you arrived at your conclusion and provides a basis for subsequent research).
Step 1
State the null hypothesis – equating the population parameter to a specification. The null hypothesis is always one of status quo or no difference. We call the null hypothesis H0 (H sub zero). It is the hypothesis that contains an equality.
State the alternate hypothesis – The alternate is represented as H1 or HA (H sub one or H sub A). The alternate hypothesis is the exact opposite of the null hypothesis and represents the conclusion supported if the null is rejected. The alternate will not contain an equal sign of the population parameter.
Most of the time, researchers construct tests of hypothesis with the anticipation that the null hypothesis will be rejected.
Step 2
Select a level of significance (α) which will be used when finding critical value(s).
The level you choose (alpha) indicates how confident we wish to be when making the decision.
For example, a .05 alpha level means that we are 95% sure of the reliability of our findings, but there is still a 5% chance of being wrong (what is called the likelihood of committing a Type 1 error).
The level of significance is set by the individual performing the test. Common significance levels are .01, .05, and .10. It is important to always state what the chosen level of significance is.
Step 3
Identify the test statistic – this is the formula you use given the data in the scenario. Simply put, the test statistic may be a Z statistic, a t statistic, or some other distribution. Selection of the correct test statistic will depend on the nature of the data being tested (sample size, whether the population standard deviation is known, whether the data is known to be normally distributed).
The sampling distribution of the test statistic is divided into t.
General Linear Model is an ANOVA procedure in which the calculations are performed using the least square regression approach to describe the statistical relationship between one or more prediction in continuous response variable. Predictors can be factors and covariates. Copy the link given below and paste it in new browser window to get more information on General Linear Model:- http://www.transtutors.com/homework-help/statistics/general-linear-model.aspx
Designing studies with recurrent events | Model choices, pitfalls and group s...nQuery
In this free webinar, we will examine the important design considerations for analyzing recurring events and counts.
Watch the webinar at: https://www.statsols.com/en/webinar/designing-studies-with-recurrent-events
Designing studies with recurrent events (Model choices, pitfalls and group sequential design)
Standard error is used in the place of deviation. it shows the variations among sample is correlate to sampling error. list of formula used for standard error for different statistics and applications of tests of significance in biological sciences
PAGE
O&M Statistics – Inferential Statistics: Hypothesis Testing
Inferential Statistics
Hypothesis testing
Introduction
In this week, we transition from confidence intervals and interval estimates to hypothesis testing, the basis for inferential statistics. Inferential statistics means using a sample to draw a conclusion about an entire population. A test of hypothesis is a procedure to determine whether sample data provide sufficient evidence to support a position about a population. This position or claim is called the alternative or research hypothesis.
“It is a procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement” (Mason & Lind, pg. 336).
This Week in Relation to the Course
Hypothesis testing is at the heart of research. In this week, we examine and practice a procedure to perform tests of hypotheses comparing a sample mean to a population mean and a test of hypotheses comparing two sample means.
The Five-Step Procedure for Hypothesis Testing (you need to show all 5 steps – these contain the same information you would find in a research paper – allows others to see how you arrived at your conclusion and provides a basis for subsequent research).
Step 1
State the null hypothesis – equating the population parameter to a specification. The null hypothesis is always one of status quo or no difference. We call the null hypothesis H0 (H sub zero). It is the hypothesis that contains an equality.
State the alternate hypothesis – The alternate is represented as H1 or HA (H sub one or H sub A). The alternate hypothesis is the exact opposite of the null hypothesis and represents the conclusion supported if the null is rejected. The alternate will not contain an equal sign of the population parameter.
Most of the time, researchers construct tests of hypothesis with the anticipation that the null hypothesis will be rejected.
Step 2
Select a level of significance (α) which will be used when finding critical value(s).
The level you choose (alpha) indicates how confident we wish to be when making the decision.
For example, a .05 alpha level means that we are 95% sure of the reliability of our findings, but there is still a 5% chance of being wrong (what is called the likelihood of committing a Type 1 error).
The level of significance is set by the individual performing the test. Common significance levels are .01, .05, and .10. It is important to always state what the chosen level of significance is.
Step 3
Identify the test statistic – this is the formula you use given the data in the scenario. Simply put, the test statistic may be a Z statistic, a t statistic, or some other distribution. Selection of the correct test statistic will depend on the nature of the data being tested (sample size, whether the population standard deviation is known, whether the data is known to be normally distributed).
The sampling distribution of the test statistic is divided into t.
Statistical inference: Statistical Power, ANOVA, and Post Hoc testsEugene Yan Ziyou
This deck was used in the IDA facilitation of the John Hopkins' Data Science Specialization course for Statistical Inference. It covers the topics in week 4 (statistical power, ANOVA, and post hoc tests).
The data and R script for the lab session can be found here: https://github.com/eugeneyan/Statistical-Inference
This document contain all topics of research methodology of module-3 according to the syllabus of BPUT odisha. The document is done for the PG and PHD students who are doing research.
Happiness Data SetAuthor Jackson, S.L. (2017) Statistics plain ShainaBoling829
Happiness Data Set
Author: Jackson, S.L. (2017) Statistics plain and simple. (4th ed.). Boston, MA: Cengage Learning.
I attach the previous essay so you have idea on how to do this assignment. It is similar to the assignment last week.
Assignment Content
1.
Top of Form
As you get closer to the final project in Week 6, you should have a better idea of the role of statistics in research. This week, you will calculate a one-way ANOVA for the independent groups. Reading and interpreting the output correctly is highly important. Most people who read research articles never see the actual output or data; they read the results statements by the researcher, which is why your summary must be accurate.
Consider your hypothesis statements you created in Part 2.
Calculate a one-way ANOVA, including a Tukey's HSD for the data from the Happiness and Engagement Dataset.
Write a 125- to 175-word summary of your interpretation of the results of the ANOVA, and describe how using an ANOVA was more advantageous than using multiple t tests to compare your independent variable on the outcome. Copy and paste your Microsoft® Excel® output below the summary.
Format your summary according to APA format.
Submit your summary, including the Microsoft® Excel® output to the assignment.
Reference/Module:
Module 13: Comparing More Than Two Groups
Using Designs with Three or More Levels of an Independent Variable
Comparing More than Two Kinds of Treatment in One Study
Comparing Two or More Kinds of Treatment with a Control Group
Comparing a Placebo Group to the Control and Experimental Groups
Analyzing the Multiple-Group Design
One-Way Between-Subjects ANOVA: What It Is and What It Does
Review of Key Terms
Module Exercises
Critical Thinking Check AnswersModule 14: One-Way Between-Subjects Analysis of Variance (ANOVA)
Calculations for the One-Way Between-Subjects ANOVA
Interpreting the One-Way Between-Subjects ANOVA
Graphing the Means and Effect Size
Assumptions of the One-Way Between-Subjects ANOVA
Tukey's Post Hoc Test
Review of Key Terms
Module Exercises
Critical Thinking Check AnswersChapter 7 Summary and ReviewChapter 7 Statistical Software Resources
In this chapter, we discuss the common types of statistical analyses used with designs involving more than two groups. The inferential statistics discussed in this chapter differ from those presented in the previous two chapters. In Chapter 5, single samples were being compared to populations (z test and t test), and in Chapter 6, two independent or correlated samples were being compared. In this chapter, the statistics are designed to test differences between more than two equivalent groups of subjects.
Several factors influence which statistic should be used to analyze the data collected. For example, the type of data collected and the number of groups being compared must be considered. Moreover, the statistic used to analyze the data will vary depending on whether the study involves a between-subjects design (designs in ...
STATISTICS : Changing the way we do: Hypothesis testing, effect size, power, ...Musfera Nara Vadia
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This is for Architectural students...
These are the symbols to represent their drawings. Please remember that these symbols are really very important. So use them on your sheet wisely.
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This paper has discussed main problems of transportation and also the solutions for tomorrow’s transportation; focusing on the
Governance challenges of our transportation.
One of the oldest fort of Rajputana History.
Jaisalmer Fort - History, Planning, Architecture, Construction and other details.
By: Adarsh Kumar ( B.Arch 5th sem)
reference is taken from google.
JAISALMER “The Golden City” - RajasthanAr. Avitesh
Detailed study of Jaisalmer - Climate, Culture, Planning, construction techniques etc.
presented by Adarsh Kumar- B.Arch 5th sem ( elective - history of Rajasthan)
references are taken from google.
What Exactly Is Contouring in Survey & Levelling?
It will be helpful for Architectural and Civil engineering students.
A presentation by Harshit Gupta (B.Arch 1st year).
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
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Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
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Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
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2. 2
Hypothesis (अनुमानम्) is a predictive
statement, capable of being tested by
scientific methods, that relates an
independent variables to some
dependent variable.
A hypothesis states what we are looking
for and it is a proportion which can be
put to a test to determine its validity.
Example - Students who receive counseling will
show a greater increase in creativity than students
not receiving counseling.
Clear and precise.
Capable of being tested.
Stated relationship between variables.
limited in scope and must be specific.
Stated as far as possible in most simple terms so
that the same is easily understand by all concerned.
But one must remember that simplicity of hypothesis
has nothing to do with its significance.
Consistent with most known facts.
Responsive to testing with in a reasonable time. One
can’t spend a life time collecting data to test it.
Explain what it claims to explain; it should have
empirical reference.
3. 3
The Alternative hypothesis is negation of
null hypothesis and is denoted by 𝐻𝑎
If Null is given as
𝐻0: 𝜇 = 𝜇0
Then alternative Hypothesis can be written
as
𝐻𝑎: 𝜇 ≠ 𝜇0
𝐻𝑎: 𝜇 > 𝜇0
𝐻𝑎: 𝜇 < 𝜇0
It is an assertion that we hold as true unless
we have sufficient statistical evidence to
conclude otherwise.
Null Hypothesis is denoted by 𝐻0.
If a population mean is equal to
hypothesized mean then Null Hypothesis can
be written as
𝐻0: 𝜇 = 𝜇0
4. State the null (Ho)
and alternate (Ha)
Hypothesis
State a
confidence
level; 99%, 95%.
Decide a test
statistics; z-test,
T-test, F-test.
Calculate the
value of test
statistics
Calculate the
p-value at given
significance level
from the table
Compare
the p-value with
calculated
value
Accept Ho
± 0.05 >
Calculated
value
Reject Ho
± 0.05 <
Calculated
value
t value > ±1.96,
P value < ± 0.05,
Null hypothesis will reject.
5. Z - test
Population - finite
Population variance is
known
Theoretical
Sample Size – large
T- Test ANOVA Test
Population - infinite Population - infinite
Not Known Not Known
Practical Practical
Normal Distribution Normal Distribution
Sample Size – Small Sample Size – Small
If groups are two. If groups are more than two.
A t-test can only be used when comparing the means of two groups (a.k.a. pairwise
comparison). If you want to compare more than two groups, or if you want to do multiple
pairwise comparisons, use an anova test or a post-hoc test.
Sources: Research Shiksha -https://www.youtube.com/watch?v=3loeng2zmMM,
https://www.scribbr.com/statistics/t-test/
6. T-Test
One Sample
T-Test
Independent Sample
T-Test
Related Sample
T-Test
Paired Sample
T-Test Repeated Sample
T-Test
Source: Research Shiksha -https://www.youtube.com/watch?v=3loeng2zmMM
The t-test compares the actual
difference between two means in
relation to the variation in the data
(expressed as the standard deviation of
the difference between the means).
7. Source: Research Shiksha -https://www.youtube.com/watch?v=3loeng2zmMM
Mostly we have heard these types of claims around us -
1. You are conducting an experiment to see if a given therapy works to reduce test anxiety in a sample
of college students.
2. Any green tea company claims that if you will take their products regularly for detoxing, you can
loose 5 Kg weight in a month.
3. One physics coaching center claims that all students will get marks above 80 in one month
coaching.
4. Any height booster powder company claims that child’s height will increase 2 inches in just 6
months.
In one sample T Test, Population means µ compares with sample mean x̄
So null hypothesis H0 : µ = x̄
One sample T test 𝒕 =
𝝁−ഥ
𝒙
𝝈
𝒏−𝟏
Where 𝝈 = std. deviation
n = sample of the population
µ = Population mean
𝒙 = sample mean
8. Source: Research Shiksha -https://www.youtube.com/watch?v=3loeng2zmMM
Step 1 – open SPSS
Step 2 – Data
Step 3 – Analysis
9. Sourse: Research Shiksha -https://www.youtube.com/watch?v=3loeng2zmMM
Where µ = Population mean = 5 Kg
𝒙 = sample mean = 4.02
T = -6.212
which is greater than ± 1.96
P = 0.000
Which is smaller than ± 0.05
Conclusion:
Null hypothesis has been rejected.
Company’s statement (claim) is wrong.
10. In Independent sample T Test,
Comparing two different groups which are independent.
So null hypothesis H0 : x̄1 = x̄2
Where: x̄1 is sample mean of group 1 and
x̄2 is sample mean of group 2.
For Example -
1. In a library, males and females are spending equal time.
2. Girls and boys are spending same money on hair care products.
3. In two buildings, daily water consumption is same.
4. Job retention is same for males in females in a company.
Two steps
Assumption
(Levene) test
T Test
(to know if samples are
comparable or not)
Independent
Sample T-Test
Assumption
Fulfilled (if F value of
Levene’s testing > ± 0.05)
Not Fulfilled (if F value of
Levene’s testing < ± 0.05)
Large sample
Small sample
11. Source: Research Shiksha -https://www.youtube.com/watch?v=3loeng2zmMM
Step 1 – open SPSS
Step 2 – Data
Step 3 – Analysis
12. Sourse: Research Shiksha -https://www.youtube.com/watch?v=3loeng2zmMM
Where 𝒙𝟏 = sample mean Group 1 = 154.60
𝒙𝟐 = sample mean Group 2 = 119.78
sin. value = 0.120 (Levene’s testing value Which is greater than ± 0.05 )
i.e. assumption is fulfilled.
(if assumption is fulfilled check upper value of “t”
if assumption is not fulfilled check lower value of t.)
T = 5.070
which is greater than ± 1.96
P = 0.000
Which is smaller than ± 0.05
Conclusion:
Null hypothesis has been rejected.
Travel expenses of audit department
and sales department are not same.
13. Sourse: Research Shiksha -https://www.youtube.com/watch?v=3loeng2zmMM
(Post- sample)
* Sample will be same for pre-sample and post- sample.
For exam -
Skill test is same for a class before the workshop and after the workshop.
Salary is same for employes of a company before 1 year tranning programme and after
programme.
Sale is same of a fashion store before online adviretesment and after advirtesment.
In Paired sample T Test,
Comparing of one group before and after experiment.
So null hypothesis H0 : x̄1 = x̄2
Where: x̄1 is sample mean of group before experiment.
x̄2 is sample mean of group after experiment.
Sample
Experiment
Sample
(Pre- sample)
14. Sourse: Research Shiksha -https://www.youtube.com/watch?v=3loeng2zmMM
Step 1 – open SPSS
Step 2 – Data
Step 3 – Analysis
15. Sourse: Research Shiksha -https://www.youtube.com/watch?v=3loeng2zmMM
Where 𝒙𝟏 = sample mean Pre Tanning = 51.4333
𝒙𝟐 = sample mean Post Training = 68.8000
T = - 9.945
which is greater than ± 1.96
P = 0.000
Which is smaller than ± 0.05
Conclusion:
Null hypothesis has been rejected.
Creativity level was not same as before
Training. Training is highly useful.
16. Sourse: Research Shiksha -https://www.youtube.com/watch?v=3loeng2zmMM
* Sample will be same for both analysis.
For exam -
Time of using computer and mobile is same for a month of a student .
Feedback is same for design & construction of one faculty.
Spending hours for Yoga and gym are equal in three months of a model.
In Repeated sample T Test,
Comparing two tests for one sample.
So null hypothesis H0 : x̄1 = x̄2
Where: x̄1 is sample mean for test 1.
x̄2 is sample mean for test 2.
Sample
Test 1
Test 2
17. Sourse: Research Shiksha -https://www.youtube.com/watch?v=3loeng2zmMM
Step 1 – open SPSS
Step 2 – Data
Step 3 – Analysis
18. Sourse: Research Shiksha -https://www.youtube.com/watch?v=3loeng2zmMM
Where 𝒙𝟏 = sample mean feedback 1 = 2323.3333
𝒙𝟐 = sample mean feedback 2 = 1246.6667
T = 3.925
which is greater than ± 1.96
P = 0.000
Which is smaller than ± 0.05
Conclusion:
Null hypothesis has been rejected.
Feedback for two subjects are not same.
One who is good in mathematics not in
science.
19. References
1. https://www.scribbr.com/
2. Research Shiksha - https://www.youtube.com/watch?v=pDmxhreZZcc&t=626s
3. https://www.youtube.com/watch?v=qyCUl8rsl-A&t=463s
4. https://www.youtube.com/watch?v=3loeng2zmMM&t=553s
5. Hypothesis testing; z test, t-test. f-test - BY NARENDER SHARMA
(https://www.slideshare.net/shakehandwithlife/hypothesis-testing-z-test-ttest-ftest?qid=6f69d0df-08b3-42a7-afff-
08534e2bc866&v=&b=&from_search=11)
6. https://www.investopedia.com/terms/t/t-test.asp
19