Researchers should take several steps to make statistical results meaningful:
1. Perform a power analysis to determine adequate sample size and ensure power is above .50, ideally .80. Power is the probability of detecting real effects.
2. Never set the alpha level lower than .05 and try to set it higher to .10 if acceptable.
3. Report effect sizes and confidence intervals to provide context around statistical significance. Effect sizes indicate the magnitude of differences between groups.
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.
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.
when you can measure what you are speaking about and express it in numbers, you know something about it but when you cannot measure, when you cannot express it in numbers, your knowledge is of meagre and unsatisfactory kind.”
This presentation will address the issue of sample size determination for social sciences. A simple example is provided for every to understand and explain the sample size determination.
When you perform a hypothesis test in statistics, a p-value helps you determine the significance of your results. ... The p-value is a number between 0 and 1 and interpreted in the following way: A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.
This is a lecture that I gave to a Principles of Epidemiology MPH class. It takes a critical look at the use of p-values to judge the strength of evidence, and offers more holistic, informative approaches to interpreting statistical findings such as measures of effect size and confidence intervals.
In clinical trials and other scientific studies, an interim analysis is an analysis of data that is conducted before data collection has been completed. If a treatment is particularly beneficial or harmful compared to the concurrent placebo group while the study is on-going, the investigators are ethically obliged to assess that difference using the data at hand and to make a deliberate consideration of terminating the study earlier than planned.
In interim analysis, whenever a new drug shows adverse effect on human being while testing the effectiveness of several drugs, we immediately stop the trial by taking into account the fact that maximum number of patients receive most effective treatment at the earliest stage. Interim analysis is also used to possibly reduce the expected number of patients and to shorten the follow-up time needed to make a conclusion. One wouldn't have to spend extra money if he/she already have enough evidence about the outcome. In this presentation, the total sample size is divided into four equal parts to perform the analysis and decision is made based on each individual step.
when you can measure what you are speaking about and express it in numbers, you know something about it but when you cannot measure, when you cannot express it in numbers, your knowledge is of meagre and unsatisfactory kind.”
This presentation will address the issue of sample size determination for social sciences. A simple example is provided for every to understand and explain the sample size determination.
When you perform a hypothesis test in statistics, a p-value helps you determine the significance of your results. ... The p-value is a number between 0 and 1 and interpreted in the following way: A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.
This is a lecture that I gave to a Principles of Epidemiology MPH class. It takes a critical look at the use of p-values to judge the strength of evidence, and offers more holistic, informative approaches to interpreting statistical findings such as measures of effect size and confidence intervals.
In clinical trials and other scientific studies, an interim analysis is an analysis of data that is conducted before data collection has been completed. If a treatment is particularly beneficial or harmful compared to the concurrent placebo group while the study is on-going, the investigators are ethically obliged to assess that difference using the data at hand and to make a deliberate consideration of terminating the study earlier than planned.
In interim analysis, whenever a new drug shows adverse effect on human being while testing the effectiveness of several drugs, we immediately stop the trial by taking into account the fact that maximum number of patients receive most effective treatment at the earliest stage. Interim analysis is also used to possibly reduce the expected number of patients and to shorten the follow-up time needed to make a conclusion. One wouldn't have to spend extra money if he/she already have enough evidence about the outcome. In this presentation, the total sample size is divided into four equal parts to perform the analysis and decision is made based on each individual step.
Hypothesis is usually considered as the principal instrument in research and quality control. Its main function is to suggest new experiments and observations. In fact, many experiments are carried out with the deliberate object of testing hypothesis. Decision makers often face situations wherein they are interested in testing hypothesis on the basis of available information and then take decisions on the basis of such testing. In Six –Sigma methodology, hypothesis testing is a tool of substance and used in analysis phase of the six sigma project so that improvement can be done in right direction
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.
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.
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..
BUS 308 Week 3 Lecture 1 Examining Differences - Continued.docxcurwenmichaela
BUS 308 Week 3 Lecture 1
Examining Differences - Continued
Expected Outcomes
After reading this lecture, the student should be familiar with:
1. Issues around multiple testing
2. The basics of the Analysis of Variance test
3. Determining significant differences between group means
4. The basics of the Chi Square Distribution.
Overview
Last week, we found out ways to examine differences between a measure taken on two
groups (two-sample test situation) as well as comparing that measure to a standard (a one-sample
test situation). We looked at the F test which let us test for variance equality. We also looked at
the t-test which focused on testing for mean equality. We noted that the t-test had three distinct
versions, one for groups that had equal variances, one for groups that had unequal variances, and
one for data that was paired (two measures on the same subject, such as salary and midpoint for
each employee). We also looked at how the 2-sample unequal t-test could be used to use Excel
to perform a one-sample mean test against a standard or constant value. This week we expand
our tool kit to let us compare multiple groups for similar mean values.
A second tool will let us look at how data values are distributed – if graphed, would they
look the same? Different shapes or patterns often means the data sets differ in significant ways
that can help explain results.
Multiple Groups
As interesting as comparing two groups is, often it is a bit limiting as to what it tells us.
One obvious issue that we are missing in the comparisons made last week was equal work. This
idea is still somewhat hard to get a clear handle on. Typically, as we look at this issue, questions
arise about things such as performance appraisal ratings, education distribution, seniority impact,
etc.
Some of these can be tested with the tools introduced last week. We can see, for
example, if the performance rating average is the same for each gender. What we couldn’t do, at
this point however, is see if performance ratings differ by grade, do the more senior workers
perform relatively better? Is there a difference between ratings for each gender by grade level?
The same questions can be asked about seniority impact. This week will give us tools to expand
how we look at the clues hidden within the data set about equal pay for equal work.
ANOVA
So, let’s start taking a look at these questions. The first tool for this week is the Analysis
of Variance – ANOVA for short. ANOVA is often confusing for students; it says it analyzes
variance (which it does) but the purpose of an ANOVA test is to determine if the means of
different groups are the same! Now, so far, we have considered means and variance to be two
distinct characteristics of data sets; characteristics that are not related, yet here we are saying that
looking at one will give us insight into the other.
The reason is due to the way the variance is an.
BUS308 – Week 5 Lecture 1 A Different View Expected Ou.docxcurwenmichaela
BUS308 – Week 5 Lecture 1
A Different View
Expected Outcomes
After reading this lecture, the student should be familiar with:
1. What a confidence interval for a statistic is.
2. What a confidence interval for differences is.
3. The difference between statistical and practical significance.
4. The meaning of an Effect Size measure.
Overview
Years ago, a comedy show used to introduce new skits with the phrase “and now for
something completely different.” That seems appropriate for this week’s material.
This week we will look at evaluating our data results in somewhat different ways. One of
the criticisms of the hypothesis testing procedure is that it only shows one value, when it is
reasonably clear that a number of different values would also cause us to reject or not reject a
null hypothesis of no difference. Many managers and researchers would like to see what these
values could be; and, in particular, what are the extreme values as help in making decisions.
Confidence intervals will help us here.
The other criticism of the hypothesis testing procedure is that we can “manage” the
results, or ensure that we will reject the null, by manipulating the sample size. For example, if
we have a difference in a customer preference between two products of only 1%, is this a big
deal? Given the uncertainty contained in sample results, we might tend to think that we can
safely ignore this result. However, if we were to use a sample of, say, 10,000, we would find
that this difference is statistically significant. This, for many, seems to fly in the face of
reasonableness. We will look at a measure of “practical significance,” meaning the likelihood of
the difference being worth paying any attention to, called the effect size to help us here.
Confidence Intervals
A confidence interval is a range of values that, based upon the sample results, most likely
contains the actual population parameter. The “most likely” element is the level of confidence
attached to the interval, 95% confidence interval, 90% confidence interval, 99% confidence
interval, etc. They can be created at any time, with or without performing a statistical test, such
as the t-test.
A confidence interval may be expressed as a range (45 to 51% of the town’s population
support the proposal) or as a mean or proportion with a margin of error (48% of the town
supports the proposal, with a margin of error of 3%). This last format is frequently seen with
opinion poll results, and simply means that you should add and subtract this margin of error from
the reported proportion to obtain the range. With either format, the confidence percent should
also be provided.
Confidence intervals for a single mean (or proportion) are fairly straightforward to
understand, and relate to t-test outcomes simply. Details on how to construct the interval will be
given in this week’s second lecture. We want to understand how to interpret and understa.
Commonly used Statistics in Medical Research HandoutPat Barlow
We found this handout to be incredibly useful as a guide and resource for non-statistical professionals to make quick decisions about statistical methods. The handout accompanies the Commonly Used Statistics in Medical Research Part I Presentation
Chapter 12Choosing an Appropriate Statistical TestiStockph.docxmccormicknadine86
Chapter 12
Choosing an Appropriate Statistical Test
iStockphoto/ThinkstockLearning Objectives
After reading this chapter, you will be able to. . .
· understand the importance of using the proper statistical analysis.
· identify the type of analysis based on four critical questions.
· use the decision tree to identify the correct statistical test.
Here we are in the final chapter that will pull all prior chapters together. Chapters 1 to 3 discussed descriptive statistics while the latterchapters, 4 to 11, discussed inferential statistics. Each of the inferential chapters presented a statistical concept then conducted the appropriateanalysis to be able to test a hypothesis. The big question for students learning statistics is, "How do I know if I'm using the correct statisticaltest?" For experienced statisticians this question is easy to answer as it is based on a few criteria. However, to a student just learning statisticsor to the novice researcher, this question is a legitimate one. Many statistical reference texts include a guide that asks specific questionsregarding the type of research question, design, number and scales of measurement of variables, and statistical assumption of the data thatallows you to use an elegant chart known as a decision tree. Based on the answers to these questions, the decision tree is used to helpdetermine the type of analysis to be used for the research, thereby helping you answer this big question.
12.1 Considerations
To make the correct decisions based on the use of a decision tree, there are four specific questions that must be answered. These questions areas follows:
· What is your overarching research question?
· How many independent, dependent, and covariate variables are used in the study?
· What are the scales of measurement of each of your variables?
· Are there violations of statistical assumptions?
If you are able to answer these specific questions, then you will be able to determine the proper analysis for your study. These questions arecritically important, and if they cannot be answered, then not enough thought has gone into the research. That said, let us discuss each ofthese questions so that they can be considered and answered in the use of the decision tree.
What Is Your Overarching Research Question?Try It!
Derive your ownresearch question foryour Master's Thesisor DoctoralDissertation. Have a colleague orprofessor read it. What are theirthoughts or suggestions forimprovements?
Answering this question seems simple enough as all research has an overarching research questionthat drives the study, especially since this dictates the type of quantitative methodology. There arekey words in every research question that help determine the appropriate type of analysis. Forinstance, if the research question states, "What are the effects of job satisfaction on employeeproductivity?" the keyword is "effects" as in the cause and effect of job satisfaction (theindependent variable) on productivity (th ...
Inferential Analysis
Chapter 20
NUR 6812Nursing Research
Florida National University
Introduction - Inferential Analysis
We will discuss analysis of variance and regression, which are technically part of the same family of statistics known as the general linear method but are used to achieve different analytical goals
ANALYSIS OF VARIANCE
Analysis of variance (ANOVA) is used so often that Iversen and Norpoth (1987) said they once had a student who thought this was the name of an Italian statistician.
You can think of analysis of variance as a whole family of procedures beginning with the simple and frequently used t-test and becoming quite complicated with the use of multiple dependent variables (MANOVA, to be explained later in this chapter) and covariates.
Although the simpler varieties of these statistics can actually be calculated by hand, it is assumed that you will use a statistical software package for your calculations.
If you want to see how these calculations are done, you could try to compute a correlation, chi-square, t-test, or ANOVA yourself (see Yuker, 1958; Field, 2009), but in general it is too time consuming and too subject to human error to do these by hand.
IMPORTANT TERMINOLOGY
Several terms are used in these analyses that you need to be familiar with to understand the analyses themselves and the results. Many will already be familiar to you.
Statistical significance: This indicates the probability that the differences found are a result of error, not the treatment. Stated in terms of the P value, the convention is to accept either a 1% (P ≤ 0.01), or 1 out of 100, or 5% (P ≤ 0.05), or 5 out of 100, possibility that any differences seen could have been due to error (Cortina & Dunlap, 2007).
Research hypothesis: A research hypothesis is a declarative statement of the expected relationship between the dependent and independent variable(s).
Null hypothesis: The null hypothesis, based on the research hypothesis, states that the predicted relationships will not be found or that those found could have occurred by chance, meaning the difference will not be statistically significant.
Effect size: This is defined by Cortina and Dunlap as “the amount of variance in one variable accounted for by another in the sample at hand” (2007, p. 231). Effect size estimates are helpful adjuncts to significance testing. An important limitation, however, is that they are heavily influenced by the type of treatment or manipulation that occurred and the measures that are used.
Confidence intervals: Although sometimes suggested as an adjunct or replacement for the significance level, confidence intervals are determined in part by the alpha (significance level) (Cortina & Dunlap, 2007). Likened to a margin of error, the confidence intervals indicate the range within which the true difference between means may lie. A narrow confidence interval implies high precision; we can specify believable values within a narrow range ...
Inferential Analysis
Chapter 20
NUR 6812Nursing Research
Florida National University
Introduction - Inferential Analysis
We will discuss analysis of variance and regression, which are technically part of the same family of statistics known as the general linear method but are used to achieve different analytical goals
ANALYSIS OF VARIANCE
Analysis of variance (ANOVA) is used so often that Iversen and Norpoth (1987) said they once had a student who thought this was the name of an Italian statistician.
You can think of analysis of variance as a whole family of procedures beginning with the simple and frequently used t-test and becoming quite complicated with the use of multiple dependent variables (MANOVA, to be explained later in this chapter) and covariates.
Although the simpler varieties of these statistics can actually be calculated by hand, it is assumed that you will use a statistical software package for your calculations.
If you want to see how these calculations are done, you could try to compute a correlation, chi-square, t-test, or ANOVA yourself (see Yuker, 1958; Field, 2009), but in general it is too time consuming and too subject to human error to do these by hand.
IMPORTANT TERMINOLOGY
Several terms are used in these analyses that you need to be familiar with to understand the analyses themselves and the results. Many will already be familiar to you.
Statistical significance: This indicates the probability that the differences found are a result of error, not the treatment. Stated in terms of the P value, the convention is to accept either a 1% (P ≤ 0.01), or 1 out of 100, or 5% (P ≤ 0.05), or 5 out of 100, possibility that any differences seen could have been due to error (Cortina & Dunlap, 2007).
Research hypothesis: A research hypothesis is a declarative statement of the expected relationship between the dependent and independent variable(s).
Null hypothesis: The null hypothesis, based on the research hypothesis, states that the predicted relationships will not be found or that those found could have occurred by chance, meaning the difference will not be statistically significant.
Effect size: This is defined by Cortina and Dunlap as “the amount of variance in one variable accounted for by another in the sample at hand” (2007, p. 231). Effect size estimates are helpful adjuncts to significance testing. An important limitation, however, is that they are heavily influenced by the type of treatment or manipulation that occurred and the measures that are used.
Confidence intervals: Although sometimes suggested as an adjunct or replacement for the significance level, confidence intervals are determined in part by the alpha (significance level) (Cortina & Dunlap, 2007). Likened to a margin of error, the confidence intervals indicate the range within which the true difference between means may lie. A narrow confidence interval implies high precision; we can specify believable values within a narrow range ...
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 ...
Classic and Modern Philosophy: Rationalism and EmpicismMusfera Nara Vadia
Rationalism and the rationalists, such as Plato, Descartes, and so on.
Empiricism and empiricists, such as Aristotle, Locke, Hume, Kant, William James.
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What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
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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.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
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”.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
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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Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
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.
Overview on Edible Vaccine: Pros & Cons with Mechanism
STATISTICS : Changing the way we do: Hypothesis testing, effect size, power, and other misunderstood issues.
1. Chapter 4
Changing the Way We Do: Hypothesis
Testing, Power, Effect Size, and
Other Misunderstood Issues
Annisa Fitri Irwan
Della Oferischa
Musfera Nara Vadia
Rezky Jafri
2. There are a few important steps that researchers can take to make the
statistical results from their studies meaningful and useful. They are:
Perform a power analysis before undertaking a study in order to
determine the number of participants that should be included in a
study to ensure an adequate level of power (power should be higher
than .50 and ideally .80). Briefly put, power is the probability that you
will find differences between groups or relationships among variables if
they actually do exist.
Never set an alpha level lower than .05 and try to set it higher, to
.10 if at all acceptable to the research community one is working in.
Report effect sizes and their interpretation.
Report confidence intervals.
3. 1. Null Hypothesis Significant Tests
Null hypothesis (Ho) is there is no difference
between groups or that there is no relationship
between variables.
Once we reject null hypothesis we will be able
to accept alternative hypothesis (Ha).
4. Example:
HR: Will 15 minutes of practice of meaningful drills result in
more accurate grammar scores than 15 minutes of telling a story
where the grammar in question must be used?
H0 : There is no [statistical] difference between a group which
practices grammar using explicit meaningful drills for 15 minutes
each day and a group which uses grammar implicitly by telling
stories where the grammar is needed for 15 minutes each day.
Ha: There is a [statistical] difference between the explicit and
implicit group.
5. Since only two groups are being compared, a t-test can be used. The
t-test statistic is calculated based on three pieces of information.:
the mean scores of the groups, their variances, and the size of each
group (the sample size).
In NHST process, we should have already decided on a cut-off level
that we will use to consider the results of the statistic test extreme.
This is called alpha level or significant level.
Baayen (2008) “if the p-value is lower than alpha level we set, we
reject the null hypothesis and accept the alternative hypothesis that
there is a difference between the two groups (it does not necessarily
mean the alternative hypothesis is correct)”
P-value: the probability of finding a [insert statistic name here] this
large or larger if the null hypothesis were true is [insert p-value].
6. One-Tailed versus Two-Tailed Tests of
Hypothesis
if the only thing we care about is just one of the possibilities, then we can
use a one-tailed test. A one-tailed or directional test of a hypothesis looks
only at one end of the distribution. A one-tailed test will have more power to
find differences, because it can allocate the entire alpha level to one side of
the distribution and not have to split it up between both ends.
Two-tailed hypothesis is examining two possibilities of groups. The
hypothesis could go in either direction. For example: in our null hypothesis,
we would be examining both the possibility that the explicit group was better
than the implicit group and the possibility that the explicit group was worse
than the implicit group.
7. Outcomes of Statistical Testing
True situation in the populationOutcomeobservedinstudy
No effect exist
No effect exist Effect exist
Correct
situation
(probability= I-
α)
Type II error
(probability=ß)
Effect exist Type I error
(probability=α)
Correct
situation
(probability= I-
ß)
Power
8. Type I error (being
overeager): concluding there
is a relationship when there
is none.
Set type I error level by
setting alpha (α) level
o Commonly set at α = .05
o Possibility of a Type I error
is thus 5%
Type error II (being overly
cautious): concluding there is
no relationship when there is
one.
Set type II error level (ß) and then
calculate power (power = I – ß)
o Commonly set at ß = .20, resulting in
power =.80
o Possibility of Type II error is thus 20%
Avoid low power by:
o Having adequate sample sizes
o Using reliable dependent variable
o controlling for individual differences
o Including pre-test
o Using longer post-test
o Making sure not to violate statistical
assumptions.
9. Problems with NHST
There are problems with using NHST method of making
conclusions about experiments.
One is that some authors interpret a low p-value as
indicate of a very strong result. On the other hand,
probably a lower p-value does not make a study more
significant, in the generally accepted sense of being
important.
On the other hand, the p-value of a study is an index of
group size and the power of study, and this is why a p-
value of .049 and a p-value of .001 are not equivalent,
although both are lower than α=.05
10. Change the Way I Do Statistics
Reporting exact p-values (unless they are so small
it would take too much room to report them)
Talking about “statistical” results instead of
“significant” or “statistically significant” results
Providing confidence intervals and effect size
whenever possible.
11. 2. Power Analysis
Power is the probability of detecting a statistical result
when there are in fact differences between groups or
relationships between variables.
Power often translates into the probability that the test
will lead to a correct conclusion about the null
hypothesis.
12. What are the theoretical implications if
power is not high?
If the power of a test is .50, this means that there
is only a 50% chance that a true effect will be
detected. In other words, even though there is in
fact an effect for some treatment, the researcher
has only a 50/50 chance of finding that effect.
13. What is the optimal level of power?
Power should be above .50 and would be judged
adequate at .80. a power level of .80 would mean
that four out of five times a real effect in the
population will be found.
Power levels ought to be calculated before a
study is done, and not after.
14. Help with calculating power using R
How to use the arguments for the “pwr” library, how to
calculate effect sizes, and Cohen’s guidelines as to the
magnitude of effect sizes. Cohen meant for these guidelines
to be a help to those who may not know how to start doing
power analyses, but once you have a better idea of effect
sizes you may be able to make your own guidelines about
what constitutes a small, medium, or large effect size for the
particular question you are studying.
Remember that obtaining a small effect size means that you
think the difference between groups is going to be quite
small.
15. 3. Effect Size
Effect size is the magnitude of the impact of the independent variable on
the dependent variable.
An effect size gives the researcher insight into the size of the difference
between groups is important or negligible.
If the effect size is quite small, then it may make sense to simply discount
the findings as unimportant, even if they are statistical.
If the effect size is large, then the researcher has found something that it is
important to understand.
Effect sizes do not change no matter how many participants there are, that
makes effect sizes a valuable piece of information, much more valuable
than the question of whether a statistical test is “significant” or not.
16. Understanding Effect Size Measures
Huberty (2002) divided effect sizes into
two broad families: group difference
indexes and relationship indexes. Both the
group difference and relationship effect
sizes are ways to provide a standardized
measure of the strength of the effect that
is found.
17. A group difference index, or mean difference measure,
has been called the d family of effect sizes by Rosenthal
(1994). The prototypical effect size measure in this family
is Cohen’s d. Cohen’s d measures the difference between
two independent sample means, and expresses how large
the difference is in standard deviations.
Relationship indexes, also called the r family of effect
sizes, measure how much an independent and dependent
variable vary together or, in other words, the amount of
covariation in the two variables. The more closely the two
variables are related, the higher the effect size.
18. Calculating Effect Size for Power Analysis
How to determine the effect size to expect?
The best way to do this is to look at effect sizes from previous in this
area to see what the magnitude of effect sizes has been. If there is
none, the researcher must make an educated guess of the size of the
effect that they will find acceptable, or use Cohen’s effect size.
Cohen notes that effect size are likely to be small when one is
undertaking research in an area that has been little studied, as
researchers may not know yet what kinds of variables they need to
control for.
A small effect size is one that is not visible to the naked eye but exists
nevertheless.
Cohen notes that effect size magnitudes depend on the area.
19. Calculating Effect Size Summary
In general, statistical tests which include a categorical variable
that divides the sample into groups, such as the t-test or ANOVA,
use the d family of the effect sizes to measure effect size. The
basic idea of effect sizes in the d family is to look at the
difference between the means of two groups, as in µA-µB.
20. Table 4.6 Options for Computing Standardizers (the Denominator
for d Family Effect Sizes)
A The standard deviation of one of the groups, perhaps most
typically the control group
B The pooled standard deviation of [only the groups] being
compared
C The pooled standard deviation [of all the groups] in the
design
21. 4. Confidence Intervals
The confidence interval represents “a range of plausible
values for the corresponding parameter”, whether that
parameter be the true mean, the difference in scores or
whatever.
The width of the confidence interval indicates the
precision with which the difference can be calculated or,
more precisely, the amount of sampling error.
If there is a lot of sampling error in a study, then
confidence intervals will be wide, and the statistical
results may not be very good estimates.
22. Power through Replication and Belief in
the “Law of Small Numbers”
Tversky and Kahneman (1971) point out that replication studies will ideally
have a larger number of participants than the original study. With a sample
size that is larger than the original, the experimenter will have a better
chance of finding a significant result. Sample sizes play a direct role in the
amount of power that a study has, and also directly affect the p-value of the
test statistic.
Tversky and Kahneman’s proposed law of small numbers states that “the law of
large numbers applies to small numbers as well”
In other words, researchers believe that even a small sampling should
represent the whole population well, which leads to an unfounded confidence
in results found with small sample sizes.
23. Larson-Hall, Jenifer. 2010. A Guide to doing Statistic in Second Language Research
Using SPSS. New York: Routledge