This document discusses inferential statistics and hypothesis testing. It provides examples of researchers formulating hypotheses and collecting data to test them. Researchers take random samples from populations to test if there are meaningful differences between groups. Hypothesis testing involves comparing experimental and control groups after exposing them to different levels of an independent variable. The goal is to determine if the independent variable caused a detectable change in the dependent variable. Inferential statistics are used to test if sample means differ significantly, which would suggest the hypothesis is supported or not supported. Proper sampling and estimating sampling distributions, standard errors, and variability are important concepts for accurately testing hypotheses about populations based on sample data.
INFERENTIAL STATISTICS: AN INTRODUCTIONJohn Labrador
For instance, we use inferential statistics to try to infer from the sample data what the population might think. Or, we use inferential statistics to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study.
Parametric and non parametric test in biostatistics Mero Eye
This ppt will helpful for optometrist where and when to use biostatistic formula along with different examples
- it contains all test on parametric or non-parametric test
Basics of Educational Statistics (Inferential statistics)HennaAnsari
Inferential Statistics
6.1 Introduction to Inferential Statistics
6.1.1 Areas of Inferential Statistics
6.2.2 Logic of Inferential Statistics
6.2 Importance of Inferential Statistics in Research
Assessment 3 ContextYou will review the theory, logic, and a.docxgalerussel59292
Assessment 3 Context
You will review the theory, logic, and application of t-tests. The t-test is a basic inferential statistic often reported in psychological research. You will discover that t-tests, as well as analysis of variance (ANOVA), compare group means on some quantitative outcome variable.
Recall that null hypothesis tests are of two types: (1) differences between group means and (2) association between variables. In both cases there is a null hypothesis and an alternative hypothesis. In the group means test, the null hypothesis is that the two groups have equal means, and the alternative hypothesis is that the two groups do not have equal means. In the association between variables type of test, the null hypothesis is that the correlation coefficient between the two variables is zero, and the alternative hypothesis is that the correlation coefficient is not zero.
Notice in each case that the hypotheses are mutually exclusive. If the null is false, the alternative must be true. The purpose of null hypothesis statistical tests is generally to show that the null has a low probability of being true (the p value is less than .05) – low enough that the researcher can legitimately claim it is false. The reason this is done is to support the allegation that the alternative hypothesis is true.
In this context you will be studying the details of the first type of test. This is the test of difference between group means. In variations on this model, the two groups can actually be the same people under different conditions, or one of the groups may be assigned a fixed theoretical value. The main idea is that two mean values are being compared. The two groups each have an average score or mean on some variable. The null hypothesis is that the difference between the means is zero. The alternative hypothesis is that the difference between the means is not zero. Notice that if the null is false, the alternative must be true. It is first instructive to consider some of the details of groups. Means, and difference between them.
Null Hypothesis Significance Test
The most common forms of the Null Hypothesis Significance Test (NHST) are three types of t tests, and the test of significance of a correlation. The NHST also extends to more complex tests, such as ANOVA, which will be discussed separately. Below, the null hypothesis and the alternative hypothesis are given for each of the following tests. It would be a valuable use of your time to commit the information below to memory. Once this is done, then when we refer to the tests later, you will have some structure to make sense of the more detailed explanations.
1. One-sample t test: The question in this test is whether a single sample group mean is significantly different from some stated or fixed theoretical value - the fixed value is called a parameter.
· Null Hypothesis: The difference between the sample group mean and the fixed value is zero in the population.
· Alternative hypothesis: T.
INFERENTIAL STATISTICS: AN INTRODUCTIONJohn Labrador
For instance, we use inferential statistics to try to infer from the sample data what the population might think. Or, we use inferential statistics to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study.
Parametric and non parametric test in biostatistics Mero Eye
This ppt will helpful for optometrist where and when to use biostatistic formula along with different examples
- it contains all test on parametric or non-parametric test
Basics of Educational Statistics (Inferential statistics)HennaAnsari
Inferential Statistics
6.1 Introduction to Inferential Statistics
6.1.1 Areas of Inferential Statistics
6.2.2 Logic of Inferential Statistics
6.2 Importance of Inferential Statistics in Research
Assessment 3 ContextYou will review the theory, logic, and a.docxgalerussel59292
Assessment 3 Context
You will review the theory, logic, and application of t-tests. The t-test is a basic inferential statistic often reported in psychological research. You will discover that t-tests, as well as analysis of variance (ANOVA), compare group means on some quantitative outcome variable.
Recall that null hypothesis tests are of two types: (1) differences between group means and (2) association between variables. In both cases there is a null hypothesis and an alternative hypothesis. In the group means test, the null hypothesis is that the two groups have equal means, and the alternative hypothesis is that the two groups do not have equal means. In the association between variables type of test, the null hypothesis is that the correlation coefficient between the two variables is zero, and the alternative hypothesis is that the correlation coefficient is not zero.
Notice in each case that the hypotheses are mutually exclusive. If the null is false, the alternative must be true. The purpose of null hypothesis statistical tests is generally to show that the null has a low probability of being true (the p value is less than .05) – low enough that the researcher can legitimately claim it is false. The reason this is done is to support the allegation that the alternative hypothesis is true.
In this context you will be studying the details of the first type of test. This is the test of difference between group means. In variations on this model, the two groups can actually be the same people under different conditions, or one of the groups may be assigned a fixed theoretical value. The main idea is that two mean values are being compared. The two groups each have an average score or mean on some variable. The null hypothesis is that the difference between the means is zero. The alternative hypothesis is that the difference between the means is not zero. Notice that if the null is false, the alternative must be true. It is first instructive to consider some of the details of groups. Means, and difference between them.
Null Hypothesis Significance Test
The most common forms of the Null Hypothesis Significance Test (NHST) are three types of t tests, and the test of significance of a correlation. The NHST also extends to more complex tests, such as ANOVA, which will be discussed separately. Below, the null hypothesis and the alternative hypothesis are given for each of the following tests. It would be a valuable use of your time to commit the information below to memory. Once this is done, then when we refer to the tests later, you will have some structure to make sense of the more detailed explanations.
1. One-sample t test: The question in this test is whether a single sample group mean is significantly different from some stated or fixed theoretical value - the fixed value is called a parameter.
· Null Hypothesis: The difference between the sample group mean and the fixed value is zero in the population.
· Alternative hypothesis: T.
Biostatistics - the application of statistical methods in the life sciences including medicine, pharmacy, and agriculture.
An understanding is needed in practice issues requiring sound decisions.
Statistics is a decision science.
Biostatistics therefore deals with data.
Biostatistics is the science of obtaining, analyzing and interpreting data in order to understand and improve human health.
Applications of Biostatistics
Design and analysis of clinical trials
Quality control of pharmaceuticals
Pharmacy practice research
Public health, including epidemiology
Genomics and population genetics
Ecology
Biological sequence analysis
Bioinformatics etc.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
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.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
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.
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2. OVERVIEW
We will understand the logic underlying the testing
of hypothesis
Understanding of sampling, and probability will be
brought to bear in the exploration of hypothesis
Testable questions or focused predictions
3. Steps and
Motivation
1. A hypothesis is identified
2. Research is executed
3. Data are collected
4. Inferential statistics are used
5. To test the viability of the hypothesis
6. Was an anticipated relationship found
within the data?
4. EXAMPLE 1
Thisresearcherwantsto
knowifthetwo-prong
treatmentismore
beneficialthanbehavior
therapyalone
A clinical psychologist
believes that the link
between obsessive
thoughts and behavior can
be disrupted with a
combination of behavioral
and cognitive therapies.
Control group of (0bsessive
compulsive disorder) OC
patients receives standard
behavior therapy
Experimental group is
exposed to the same
therapy coupled with work
on reducing obsessive
thoughts.
5. EXAMPLE 2
Thisresearchwantsto
determineiffourth-years
studentsaremorelikelyto
voteforliberalcandidates,
whilefirst-yearstudentswill
tendtoendorseconservative
candidates.
A political psychologist
studies how higher
education affects college
students' voting behavior in
national elections.
He hypothesizes that
students generally become
more liberal and politically
aware across their four
college years.
He sets to compare the
voting behavior of first-year
students with that of
fourth-year students in a
mock national election.
Students from both classes
read a series of mock
candidate profiles and then
answer questions about
their beliefs concerning a
variety of public and social
policy issues.
6. EXAMPLE 3
A Health
Psychologist
Purpose
Hebelievesthatmiddle-aged
individualswho carefor
elderlyparentsareatgreater
riskforillnessthan similarly
agedpersonswith no
caregiverresponsibilities.
Study
The researcher interviews
the two sets of adults and
then gains permission to
examine their medical
records at the end of a 1-
year period.
Hypothesis
The care giver group will
show more frequent
illnesses, visits to the doctor,
hospitalizations, and
medicine prescriptions than
the noncaregiver group.
7. Important!
None of these researchers can ever hope to
measure the responses of every possible
respondent in their population of interest, so
such data are usually collected in the form of
some random sample.
11. PRACTICAL
MATTER
Did the independent
measure create an
observed and
systematic change in
the dependent
measure?
Did the experimental
group behave or
respond differently
than the control group
after both were
exposed to the
independent variable?
12. THEORETICAL
MATTER
Following exposure to
the independent
variable, is the 𝝁 of the
experimental group
verifiably different
from the 𝝁 of the
control group?
In other words,
Can we attribute the
differential and
measured between
group differences to the
fact that the control
group and experimental
group now effectively
represent different
populations with
different parameters?
13. We now turn
to:
1. How to draw samples from population?
2. How do we make estimation?
3. How do we conduct experiment?
15. Things we
must be
concerned
with:
Representative of the population from which it was
drawn
The average behavior witnessed in the sample
reflects what is usually true of the population
The sample statistics N (i.e., sample mean ˉχ and
standard deviation, s) are similar to those of
population's parameters (i.e., population mean
𝝁 and standard deviation σ)
16. Point
estimation
Point estimation is the process
of using a sample statistic (e.g.,
ˉχ, s) to estimate the value of
some population parameter
(e.g.,𝝁, σ)
17. ˉχ ≅ 𝝁
ˉχ ≅ 𝝁 sample mean is close or
equal in value to population
mean
18. Sampling
error
Any given sample statistic is
apt to contain some degree of
error (i.e., the difference
between estimated and actual
reality)—sampling error
19. Overcoming point
estimation's
limitations can be
achieved through
a somewhat more
laborious process
known as Interval
estimations
Interval estimation involves careful
examination and estimation of the
variability noted among sample
statistics based on the repeated
sampling of the same population.
21. MEAN
DIFFERENCES
Whether the sample data—now
divided into two groups—show
detectable differences due to the
influence of some independent
variable
22. This process of
detection centers
on the role
inferential
statistics play in
hypothesis
testing, which is
generally to
demonstrate
mean differences.
How does the average behavior in one
group of participants differ from the
average behavior found in other
groups? Did the manipulation of an
independent variable lead to a
different average level of behavior in
the dependent measure for the
experimental mental group than the
control group?
Control group and Experimental group (manipulated)
25. Importance of
Hypothesis
testing
Whether a sample statistic fits one or another
population
Independent variable impact on a dependent
variable
Researchers are able to make educated guesses
when limited information is available to guide
judgment.
Involving every person or animal is impossible,
impractical, and nonsensical.
Statistical inference enables researchers to evaluate
the veracity of a hypothesis as if a whole population
of participants were available instead of merely a
small representative sampling.
26. Random sample
drawn from
Population
Control
Group
Experime
ntal
Group
Ctr level
Indep Var
Exp level
Inde Var
Does a diff
exist between
sample
means?
Random Ass to
one of 2 Groups
Χc ,Sc Χe ,Se
Is the sample mean of the control Is the sample mean of the experim gr
Group ≅population μ? ≠to the original population μ?
Figure 9.1. The process of sampling and inferring whether a statistic is from one or another population.
Is the sample mean of the control
Is the sample mean of the experim gr
Group ≅population μ?
≠to the original population μ?
27. Distribution of
Sample
Means
A distribution of sample means is a group or
collection of sample means based on random
samples of a fixed size N from some
population (Several Samples chosen to
compare them. USA Voting as example, ˉχ1,
ˉχ2, ˉχ3… ˉχ N).
28. X
Y
X1
X2
X3
Xn
Unknown P 𝜇
Repeated Samples
Drawn
Sampling Distribution of X
A Sampling DistributionCreated by Repeated Sampling (Fixed Sample Size N)
of a Population
31. CENTRAL
LIMIT
THEOREM
The Central LimitTheorem proposes that as the size
of any sample, N, becomes infinitely large in size,
the shape of the sampling distribution of the mean
approaches normality—that is, it takes on the
appearance of the familiar bell-shaped curve – with a
mean equal to μ, the population's mean, and the
standard deviation equal to σ/ 𝑵, which is known as
the standard error of the mean. As N increases in
size, the standard error of the mean or 𝝈ˉχ will
decrease in magnitude, indicating that the sample
will be close in value to the actual population μ.
Thus, it will also be true that μ ˉχ ≅ 𝛍 and that 𝝈ˉχ ≅
𝛔/ 𝑵.
32. Y
X
40 55 70 85 100 115 130 145
160
𝝁
Figure 5.1. Hypothetical distribution of scores on an IQ test
Third Second First First Second Third
𝜎 𝜎 𝜎 𝜎 𝜎 𝜎
Below 𝜇 Below𝜇 Below 𝜇 Above 𝜇 Above 𝜇 Above 𝜇
Pop mean (𝜇) of 100
Standard deviation 𝜎15
110 1st 𝜎 around the mean
NORMAL DISTRIBUTION
33. The mean of
any sampling
distribution of a
sample statistic
is referred to as
the sampling
distribution's
expected value.
Symbolically μ ˉχ
Formula for calculating
μ ˉχ = ˉ𝜒/Nk
36. These must be known N is sample
size,
𝛔
2
is population variance, σ
population standard deviation.
37. LAWOF
LARGE
NUMBERS
The law of large numbers proposes that
the larger the size of a sample (N), the
greater the probability that the sample
mean (ˉχ) will be close to the value of
the population mean (μ).
38. STANDARD
ERRORAND
SAMPLING
ERROR
Sampling error is the difference between a
given sample mean and a population mean (ˉχ
- μ).
Theoretically, if we have a distribution of
sufficient size, we could readily show that the
(ˉχ - μ) = 0.
(That is, the sum of the sampling errors—the
positive as well as negative differences
between sample means and a population
mean—would be equal to 0. In theory, these
random deviations would cancel one another
out.)
39. ESTIMATING
THE
STANDARD
ERROROF
THE MEAN
The standard error of the mean provides a
researcher with a very important advantage:
The sample mean estimates the value of a
population mean.
A smaller standard error specifies a close
match between a sample mean and a
population mean. On the other hand, a larger
error points to considerable disparity
between the two indices.
40. To determine
standard
error:
1. Estimating population variance, and
2. Standard deviation from known values of
a. sample variance and
b. standard deviation.
Sample variance formula
S² = ⅀(χ -ˉχ)²
N
42. A biased estimate can be corrected,
that is, converted into an unbiased
estimate by reducing the value of the
denominator by one observation— in
formula terms, N becomes N – 1.
σ² = ŝ² = ⅀(χ -ˉχ)²
N- 1
The caret (ˆ) over ŝ indicates that the statistic is an unbiased
estimate.
44. By relying on the formula and logic behind these
unbiased estimators, we can now approximate the
variance of the population (σ²-χ)
To do so, of course, we need to rely on estimated
variance of the population (s²-χ) and the estimated
error of the mean (sˉχ).
Given that we do not know the true values of σ² and
σ, we must use estimates provided by ŝ² and ŝ,
respectively.
45. Estimated σ²-χ = s²-χ = ŝ²/N.
It follows that the standard error mean can be
estimated by using :
σˉχ = sˉχ = √ŝ²/N = ŝ/√N
when ŝ² and ŝ may be unavailable, the standard error
of the mean can be estimated using this formula:
Estimate σˉχ = sˉχ = s/√N-1 = √⅀ (x -ˉχ)²/N(N -1) =
√ss/N(N- 1)
