This document provides an overview of hypotheses for a presentation. It begins with learning outcomes which are to explain the meaning and significance of hypotheses, identify types of hypotheses, and illustrate why hypotheses are needed.
The presentation will cover the scientific method, meaning and types of variables, characteristics of good hypotheses, categories of hypotheses including null and alternative, and how to form and test hypotheses. Hypotheses are defined as educated guesses that relate variables and guide research. They must be testable, falsifiable, and contribute to theory. Hypotheses can be categorized by their formulation as null or alternative, by direction as directional or non-directional, and by their derivation as inductive or deductive.
This PPT slide presentation deals with the Meaning of hypothesis, Types of hypothesis, Parameters of a good hypothesis, Importance of hypothesis, Source of hypothesis, Format of hypotheis & Formulation of testable hypothesis.
For a detailed explanation Watch the Youtube video:
https://youtu.be/6g4tD162yhI
Hypothesis, Characteristics of a good hypothesis, contribution to research study, Types of hypothesis, Source, level of significance, two-tailed one-tailed test, types of errors
hypothesis and type of hypothesis is explained with appropriate examples
Hypotheses and type of hypotheses are explained with appropriate examples
Research hypothesis, null hypothesis, directional hypothesis, non-directional hypothesis, simple hypothesis, complex hypothesis etc
Research Design (Research Types, Quantitative Research Design and Qualitative...Alam Nuzhathalam
An overview of Research Design: Definition, Classification of Research Design, Experimental Research Design, Non Experimental Research Design, Qualitative Research Design, Quantitative Research Design..
Inductive and Deductive Approach to Research. Difference between Inductive an...Rohan Byanjankar
What is inductive and Deductive Approach to Research? The difference between Inductive and Deductive Reasoning to Research with clear example, figure and some major differences between them.
Types of Hypothesis-Advance Research MethodologyRehan Ehsan
This Presentation states the details of Hypothesis for students to get help in advance research methodology. Rearchers may also get help from this work.
This PPT slide presentation deals with the Meaning of hypothesis, Types of hypothesis, Parameters of a good hypothesis, Importance of hypothesis, Source of hypothesis, Format of hypotheis & Formulation of testable hypothesis.
For a detailed explanation Watch the Youtube video:
https://youtu.be/6g4tD162yhI
Hypothesis, Characteristics of a good hypothesis, contribution to research study, Types of hypothesis, Source, level of significance, two-tailed one-tailed test, types of errors
hypothesis and type of hypothesis is explained with appropriate examples
Hypotheses and type of hypotheses are explained with appropriate examples
Research hypothesis, null hypothesis, directional hypothesis, non-directional hypothesis, simple hypothesis, complex hypothesis etc
Research Design (Research Types, Quantitative Research Design and Qualitative...Alam Nuzhathalam
An overview of Research Design: Definition, Classification of Research Design, Experimental Research Design, Non Experimental Research Design, Qualitative Research Design, Quantitative Research Design..
Inductive and Deductive Approach to Research. Difference between Inductive an...Rohan Byanjankar
What is inductive and Deductive Approach to Research? The difference between Inductive and Deductive Reasoning to Research with clear example, figure and some major differences between them.
Types of Hypothesis-Advance Research MethodologyRehan Ehsan
This Presentation states the details of Hypothesis for students to get help in advance research methodology. Rearchers may also get help from this work.
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
"A die is a specialized tool used in manufacturing industries to cut or shape material mostly using a press. Like molds, dies are generally customized to the item they are used to create. Products made with dies range from simple paper clips to complex pieces used in advanced technology".
Writing introduction, hypothesis and objectives of a thesis and scientific pa...Md. Nazrul Islam
This is the guideline for writing a thesis or scientific paper for MS students.
- Introduction
- Background and Setting
- Identification of Problem
- Definitions of hypothesis
- Types of hypotheses
- Guidelines for writing objectives and research questions
- Purpose Statement
- Objectives or Research Questions
- Assumptions
- Limitations
- Significance of The Study
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8
More Components: Knowledge, Literature, Intellectual Projects
Keywords
action; critical evaluation; instrumentalism; intellectual projects; knowledge; literature; policy; practice; reflexive action; research; theory; understanding; value stances
In the last two chapters, we first introduced the idea of a mental map for navigating the literature plus the tools for thinking that represent the key to this map. We then looked at the first map component: the two dimensions of variation amongst knowledge claims. Here we complete our introduction to the mental map by describing its other three components:
three
kinds of knowledge
that are generated by reflecting on, investigating and taking action in the social world;
four
types of literature
that inform understanding and practice;
five
sorts of intellectual project
that generate literature about the social world.
Figure 8.1 Tools for thinking and the creation of three kinds of knowledge about the social world
Three kinds of knowledge
The three kinds of knowledge that we distinguish are
theoretical
,
research
and
practice
. We describe each below and show how they relate to the set of tools for thinking summarized in
Chapter 6
.
Figure 8.1
represents that relationship, showing that the tools for thinking play a central role. They are employed both to generate and to question the three kinds of knowledge.
What is theoretical knowledge?
The tools for thinking are most obviously reflected in
theoretical knowledge
– you cannot have a theory without a set of connected concepts. We define theoretical knowledge as deriving from the creation or use of theory, in the following way. On the basis of a theory about the social world, we make claims to knowledge about what the social world is like. The theory itself may or may not be our own and will have been developed on the basis of patterns discerned in that social world, whether through general observation (armchair theorizing), through specific investigations (empirically based theorizing) or a mixture of the two.
For example, in order to provide warranting for the claim that all children should be given the chance to learn a foreign language before the age of eight, an author might offer as evidence the theoretical knowledge that there is a ‘critical period’ for language acquisition. The theory upon which the author is drawing for this knowledge has been built up over the years by various theorists (beginning with Eric Lenneberg). The theorists have used both general observation about what happens when people of different ages learn a language and a range of empirical studies that have sought to establish what the critical age and determining factors are. Bundled up in the theory are potential claims about roles for biology, environment and motivation. The author would need to unpack these roles if the fundamental claim were to be developed into an empirical research study (to see how well it worked to offer foreign langua ...
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.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
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”.
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.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
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.
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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!
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
2. Hypothesis Prepared By:- Group 1 WagariRefu TeklewoinKassaye ZewduHakimu MeseretYohannes HunbelewGebreTsadik Michael Gezae
3. Learning Outcomes Upon completion of this program, we will be able to Explain the meaning and significance of hypothesis in scientific research Identify the types of hypotheses Illustrate why we need a hypothesis Identify and categorize research variables Create Operational Definitions Formulate a valid hypothesis Identify Characteristics of a good hypothesis Test the hypothesis
4. Presentation Content Brief summary on the Scientific Method Meaning of Hypothesis Meaning and Types of variables Characteristics of Hypothesis Categories of Hypothesis Forming a Hypothesis Testing a Hypothesis
5. The scientific Method Is an overarching perspective On how scientific investigations should proceed Consists of a set of research principles and methods that help researchers obtain valid results from their research studies
6. The scientific Method (Cont…) Researchers generally agree that the scientific method is composed of the following key elements An empirical approach, Observations, Questions, Hypotheses, Experiments, Analyses, Conclusions, and Replication
7. Research Questions & Hypothesis Hypothesis is the fourth element of the scientific method However, we may not use hypothesis for all types of research. In a qualitative study, inquirers state research questions, not objectives (i.e., specific goals for the research) or hypotheses (i.e., predictions that involve variables and statistical tests).
8. In qualitative research, the research questions assume two forms: a central question and associated sub questions The central question is a statement of the question being examined in the study in its most general form. so as to not limit the inquiry Research Questions & Hypothesis
9. Guidelines for writing broad, qualitative research questions: Ask one or two central questions followed by no more than five to seven sub-questions Relate the central question to the specific qualitative strategy of inquiry (like ethnography , phenomenology, etc) Begin the research questions with the words “what” or “how” to convey an open and emerging design Examples: How do women in a psychology doctoral program describe their decision to return to school? “What is it like for a mother to live with a teenage child who is dying of cancer?” Focus on a single phenomenon or concept
10. Guidelines (Cont…) Use exploratory verbs that convey the language of emerging design of research. These verbs tell the reader that the study will Discover (e.g., grounded theory) Seek to understand (e.g., ethnography) Explore a process (e.g., case study) Describe the experiences (e.g., phenomenology) Report the stories (e.g., narrative research) Use non-directional language Expect the research questions to evolve and to change during the study Use open-ended questions without reference to the literature or theory If the information is not redundant with the purpose statement, specify the participants and the research site for the study
11. Hypothesis Defined An educated guess A tentative point of view A proposition not yet tested A preliminary explanation A preliminary Postulate
12. Various Authors “A hypothesis is a conjectural statement of the relation between two or more variables”. (Kerlinger, 1956) “Hypotheses are single tentative guesses, good hunches – assumed for use in devising theory or planning experiments intended to be given a direct experimental test when possible”. (Eric Rogers, 1966) “Hypothesis is a formal statement that presents the expected relationship between an independent and dependent variable.”(Creswell, 1994) A hypothesis is a logical supposition, a reasonable guess, an educated conjecture. It provides a tentative explanation for a phenomenon under investigation." (Leedy and Ormrod, 2001).
13. Hypothesis vs Theory vs Fact A theory is a well-established principle that has been developed to explain some aspect of the natural world. A theory arises from repeated observation and testing and incorporates facts, laws, predictions, and tested hypotheses that are widely accepted. A hypothesis is a specific, testable prediction about what you expect to happen in your study. For example, a study designed to look at the relationship between study habits and test anxiety might have a hypothesis that states, “This study is designed to assess the hypothesis that students with better study habits will suffer less test anxiety.” Unless your study is exploratory in nature, your hypothesis should always explain what you expect to happen during the course of your experiment or research. While the terms are sometimes used interchangeably in general practice, the difference between a theory and a hypothesis is important when studying experimental design. Some important distinctions to note include: A theory predicts events in general terms, while a hypothesis makes a specific prediction about a specified set of circumstances. A theory has been extensively tested and is generally accepted, while a hypothesis is a speculative guess that has yet to be tested.
14. One common feature for facts, theories, and hypotheses in science is that they are all treated as fallible — the likelihood of error might vary greatly, but they are still regarded as something less than absolute truth.
15. Purpose Guides/gives direction to the study/investigation Defines Facts that are relevant and not relevant Suggests which form of research design is likely to be the most appropriate Provides a framework for organizing the conclusions of the findings Limits the research to specific area Offers explanations for the relationships between those variables that can be empirically tested Furnishes proof that the researcher has sufficient background knowledge to enable her/him to make suggestions in order to extend existing knowledge Structures the next phase in the investigation and therefore furnishes continuity to the examination of the problem
17. Forms of Hypothesis Hypotheses can take various forms, depending on the question being asked and the type of study being conducted Some hypotheses may simply describe how two things may be related. For example, correlational research In others the researcher might hypothesize that one variable causes a change in the other variable (causal relationship In their simplest forms, hypotheses are typically phrased as “if-then” statements
18. A Hypothesis must make a prediction must identify at least two variables should have an elucidating power should strive to furnish an acceptable explanation or accounting of a fact must be falsifiable meaning hypotheses must be capable of being refuted based on the results of the study must be formulated in simple, understandable terms should correspond with existing knowledge In general, a hypothesis needs to be unambiguous, specific, quantifiable, testable and generalizable.
19. Characteristics of a Testable Hypothesis 1. A Hypothesis must be conceptually clear - concepts should be clearly defined - the definitions should be commonly accepted - the definitions should be easily communicable 2. The hypothesis should have empirical reference - Variables in the hypothesis should be empirical realities - If they are not it would not be possible to make the observation and ultimately the test 3. The Hypothesis must be specific - Place, situation and operation
20.
21.
22. Categorizing Hypotheses (Cont…) 1. Null Hypotheses and Alternate Hypotheses Null hypothesis always predicts that no differences between the groups being studied (e.g., experimental vs. control group) or no relationship between the variables being studied By contrast, the alternate hypothesis always predicts that there will be a difference between the groups being studied (or a relationship between the variables being studied)
23. Categorizing Hypotheses (Cont…) Alternate Hypothesis can further be classified as 2. Directional Hypothesis and Non-directional Hypothesis
24. Categorizing Hypotheses (Cont…) 2. Directional Hypothesis and Non-directional Hypothesis Simply based on the wording of the hypotheses we can tell the difference between directional and non-directional If the hypothesis simply predicts that there will be a difference between the two groups, then it is a non-directional hypothesis. It is non-directional because it predicts that there will be a difference but does not specify how the groups will differ. If, however, the hypothesis uses so-called comparison terms, such as “greater,”“less,”“better,” or “worse,” then it is a directional hypothesis. It is directional because it predicts that there will be a difference between the two groups and it specifies how the two groups will differ
25. Categorizing Hypotheses (Cont…) 3. Inductive and Deductive Hypotheses(Theory Building and Theory Testing) classified in terms of how they were derived: - Inductive hypothesis - a generalization based on observation - Deductive hypothesis - derived from theory
26. Forming/Developing a Hypothesis Articulating the hypotheses that will be tested is one of the steps in the planning phase of a research study A hypothesis is formulated after the problem has been stated and the literature study has been conducted It is formulated when the researcher is totally aware of the theoretical and empirical background to the problem
27. The Initial Idea The initial idea is the starting point Often vague or general, it requires refining before research hypotheses can be generated Refinement of the initial idea is based on (1) a search of relevant research literature (2) initial observations of the phenomenon Narrow and formalize the initial idea into a statement of the problem
28. Statement of the Problem In the form of a question that clearly indicates an expected relationship The nature of the question will dictate the required level of constraint of a study Causal questions will require experimental research Questions about relationships can be answered with lower constraint research Convert into research hypothesis by operationally defining the variables
29. In General Ideas lead to observations library research Then Statement of problem and Then Problem statements become research hypotheses when constructs are operationalized
30. Operational Definitions The procedures used to measure and/or manipulate a variable Most variables can be operationally defined in many different ways, Thus creating many different research hypotheses from a single statement of a problem
31. Hypotheses States clearly the expected relationship between the variables The form is a declarative statement, but it is a tentative statement to be tested in research Implicitly or explicitly, the variables in the research hypothesis are stated in operational definition terms
32. The Role of Theory In research planning, theory guides the process Theory is often the primary source of research hypotheses Theory guides the selection of variables as well as their operational definitions Most research is based on multiple, overlapping and interacting theories
33. Variables Any factor that can take on different values is a scientific variable and influences the outcome of a research. Examples include Gender, Colour, Country Weight, Time, Height, etc..
34. Types of Variables There are many categories of variables Independent vs. Dependent vs. Controlled Variables Categorical vs. Continuous Variables Quantitative vs. Qualitative Variables
35. Independent vs. Dependent vs. Controlled Variables The independent variable is called “independent” because it is independent of the outcome being measured. It is what causes or influences the outcome. The dependent variable is influenced by the independent variable. Controlled variables are variables that the scientist does not want to change during the course of the experiment Hence the research includes finding ways to vary the independent variable Finding ways to keep the controlled variables from changing and measure the dependent variable
36. Categorical vs. Continuous Variables Categorical variables are variables that can take on specific values only within a defined range of values like gender, marital status consisting of discrete, mutually exclusive categories, such as “male/female,” “White/Black,” etc Continuous variables are variables that can theoretically take on any value along a continuum like age, income weight, height etc.. When compared with categorical variables, continuous variables can be measured with a greater degree of precision. The choice of which statistical tests will be used to analyze the data is partially dependent on whether the researcher uses categorical or continuous variables. Certain statistical tests are appropriate for categorical variables, while other statistical tests are appropriate for continuous variables. As with many decisions in the research-planning process, the choice of which type of variable to use is partially dependent on the question that the researcher is attempting to answer.
37. Quantitative vs. Qualitative Variables Qualitative variables are variables that vary in kind, like “attractive” or “not attractive,” “helpful” or “not helpful,” or “consistent” or “not consistent” Quantitative variables are those that vary in amount like height, weight, salary etc
38. Summary - Hypothesis Formation First identify a general area of interest to be researched; Example: effects of smoking on health Then identify a research question – the research question should be more narrowly defined (more specific) than the general research topic. Example: “Does smoking cause lung cancer?” Then operationally define the variables. The researcher is in control of the independent variable in the experiment. The dependant variable, however, is merely observed in the context of the experiment. For an experiment to be valid, it must contain at least two variables. Now it is time to formulate the hypothesis in an attempt to answer the question by making it a conditional statement like "Smoking may cause lung cancer.” Refine it by writing a formalized hypothesis like "If smoking causes lung cancer, then individuals who smoke have a higher frequency of developing the disease." This type of "if-then" hypothesis is considered the most useful. Verify that the hypothesis includes a subject group. A subject group defines who or what the researcher is studying. In the example above, the subject group is the smokers.
39. Summary (Cont…) Verify that a treatment or exposure is included in the experiment. A treatment is literally what is being done to the subject group. In our example, the exposure is smoke or smoking. Prepare for an outcome measure, which is a measurement concerned with how the treatment is going to be assessed. The outcome measure in our smoking scenario is the frequency of smokers developing cancer in subject population. Understand your control group. The control group or placebo is a group similar to the subject group, but this group does not receive the treatment. It is a population that the subject group is compared to. In the smoking example, the control group is non-smokers. Remember: - Hypothesis can be adjusted/refined/changed as more information is gathered but before the actual examination/experiment is carried out.
40. Hypothesis Testing All hypothesis tests are conducted the same way. The researcher states a hypothesis to be tested, formulates an analysis plan, analyzes sample data according to the plan, and accepts or rejects the null hypothesis, based on results of the analysis.
41. Hypothesis Testing (Cont..) 1. State the hypotheses. Every hypothesis test requires the analyst to state a null and an alternative hypothesis. The hypotheses are stated in such a way that they are mutually exclusive. That is, if one is true, the other must be false; and vice versa. 2. Formulate an analysis plan. The analysis plan describes how to use sample data to accept or reject the null hypothesis. It should specify the following elements. Significance level. Often, researchers choose significance levels equal to 0.01, 0.05, or 0.10; but any value between 0 and 1 can be used. Test method. Typically, the test method involves a test statistic and a sampling distribution. Computed from sample data, the test statistic might be a mean score, proportion, difference between means, difference between proportions, z-score, t-score, chi-square, etc. Given a test statistic and its sampling distribution, a researcher can assess probabilities associated with the test statistic. If the test statistic probability is less than the significance level, the null hypothesis is rejected.
42. Analyze sample data. Using sample data perform computations called for in the analysis plan.Test statistic. When the null hypothesis involves a mean or proportion, use either of the following equations to compute the test statistic. Test statistic = (Statistic - Parameter) / (Standard deviation of statistic) Test statistic = (Statistic - Parameter) / (Standard error of statistic) where Parameter is the value appearing in the null hypothesis, and Statistic is the point estimate of Parameter. As part of the analysis, you may need to compute the standard deviation or standard error of the statistic. Previously, we presented common formulas for the standard deviation and standard error.When the parameter in the null hypothesis involves categorical data, you may use a chi-square statistic as the test statistic. Instructions for computing a chi-square test statistic are presented in the lesson on the chi-square goodness of fit test. P-value. The P-value is the probability of observing a sample statistic as extreme as the test statistic, assuming the null hypothesis is true. Hypothesis Testing (Cont..)
43. Hypothesis Testing When you want to make statements about a population, you usually draw samples How generalizable is the sample-based finding? Evidence has to be evaluated statistically before arriving at a conclusion regarding the hypothesis Depends on whether information is generated from the sample with fewer or larger observations
44. Steps in Hypothesis Testing Problem Definition Clearly state the null and alternate hypotheses. Choose the relevant test and the appropriate probability distribution Determine the degrees of freedom Determine the significance level Choose the critical value Compare test statistic and critical value Compute relevant test statistic Decide if one-or two-tailed test Does the test statistic fall in the critical region? No Do not reject null Yes Reject null
45. Basic Concepts of Hypothesis Testing The Null and Alternate hypothesis Choosing the relevant statistical test and appropriate probability distribution. Depends on - Size of the sample - Whether the population standard deviation is known or not Choosing the Critical Value. The three criteria used are - Significance Level - Degrees of Freedom - One or Two Tailed Test
46. Significance Level Indicates the percentage of sample means that is outside the cut-off limits (critical value) The higher the significance level () used for testing a hypothesis, the higher the probability of rejecting a null hypothesis when it is true (Type I error) Accepting a null hypothesis when it is false is called a Type II error and its probability is ()
47. Significance Level (Contd.) When choosing a level of significance, there is an inherent tradeoff between these two types of errors Power of hypothesis test (1 - ) A good test of hypothesis ought to reject a null hypothesis when it is false 1 - should be as high a value as possible
48. Degree of Freedom The number or bits of "free" or unconstrained data used in calculating a sample statistic or test statistic A sample mean (X) has `n' degree of freedom A sample variance (s2) has (n-1) degrees of freedom
49. One or Two-tail Test One-tailed Hypothesis Test Determines whether a particular population parameter is larger or smaller than some predefined value Uses one critical value of test statistic Two-tailed Hypothesis Test Determines the likelihood that a population parameter is within certain upper and lower bounds May use one or two critical values
51. Hypothesis Testing About a Single Mean Step-by-Step 1) Formulate Hypotheses 2) Select appropriate formula 3) Select significance level 4) Calculate z or t statistic 5) Calculate degrees of freedom (for t-test) 6) Obtain critical value from table 7) Make decision regarding the Null-hypothesis
52. Hypothesis Testing About a Single Mean - Example 1(2 tailed) Ho: = 5000 (hypothesized value of population) Ha: 5000 (alternative hypothesis) n = 100 = 4960 = 250 = 0.05 Rejection rule: if |zcalc| > z/2 then reject Ho.
53. Hypothesis Testing About a Single Mean - Example 2 Ho: = 1000 (hypothesized value of population) Ha: 1000 (alternative hypothesis) n = 12 = 1087.1 s = 191.6 = 0.01 Rejection rule: if |tcalc| > tdf, /2 then reject Ho.
54. Hypothesis Testing About a Single Mean - Example 3(1 tailed) Ho: 5000 (hypothesized value of population) Ha: < 5000 (alternative hypothesis) n = 50 = 4970 = 250 = 0.01 Rejection rule: if then reject Ho.
55. Hypothesis Test of Difference between Means Mayor of a city wants to see if males and females earn the same A random sample of 400 males and 576 females was taken and following was found
56. Hypothesis Test of Difference between Means The appropriate test depends on - whether samples are from related or unrelated samples - whether population standard deviations are known or not - if not, whether they can be assumed to be equal or not
57. Hypothesis Test of Difference between Means In salary example, the null hypothesis is Ho: 1- 2 =c (=0) Ha: 1- 2 c Since we have unrelated samples with known (for large samples, we can use sample SD as pop SD) but unequal ’s the standard error of difference in means is
58. Hypothesis Test of Difference between Means The calculated value of z is For =.01 and a two-tailed test, the Z-table value is 2.58 Since is greater than , the null hypothesis is rejected
59. Hypothesis Testing of Proportion Quality control dept of a light bulb company claims 95% of its products are defect free The CEO checks 225 bulbs and finds only 87% to be defect free Is the claim of 95% true at .05 level of significance ? So we have hypothesized values and sample values
60. Hypothesis Testing of Proportion The null hypothesis is Ho:p=0.95 The alternate hypothesis is Ha: p 0.95 First, calculate the standard error of the proportion using hypothesized values as Since np and nq are large, we can use the Z table. The appropriate z value is 1.96
61. Hypothesis Testing of Proportion The limits of the acceptance region are Since the sample proportion of 0.87 does not fall within the acceptance region, the CEO should reject the quality control department’s claim
62. Hypothesis Testing of Difference between Proportions Manager wants to see if John and Linda, two salespeople, have the same conversion He picks samples and finds that
63. Hypothesis Testing of Difference between Proportions Are their conversion rates different at 0.05 significance level? The null hypothesis is Ho: The alternate hypothesis is Ha: The best estimate of p (proportion of success) is also,
64. Hypothesis Testing of Difference between Proportions An estimate of the standard error of the difference of proportions is The z value can be calculated as The z value obtained from the table is 1.96 (for ). Thus, we fail to reject the null hypothesis
65. The Probability Values (P-value) Approach to Hypothesis Testing P-value provides researcher with alternative method of testing hypothesis without pre-specifying Largest level of significance at which we would not reject Ho
66. The Probability Values (P-value) Approach to Hypothesis Testing Difference Between Using and p-value Hypothesis testing with a pre-specified Researcher is trying to determine, "is the probability of what has been observed less than ?“ Reject or fail to reject Ho accordingly
67. The Probability Values (P-value) Approach to Hypothesis Testing Using the p-Value Researcher can determine "how unlikely is the result that has been observed?“ Decide whether to reject or fail to reject Ho without being bound by a pre-specified significance level In general, the smaller the p-value, the greater is the researcher's confidence in sample findings
68. The Probability Values (P-value) Approach to Hypothesis Testing: Example Ho: = 25 (hypothesized value of population) Ha: 25 (alternative hypothesis) n = 50 = 25.2 = 0.7 SE( )= = 0.1; Z= =2 From Z-table, prob Z >2 is 0.0228. As this is a 2-tailed test, the p-value is 2 0.228=.0456
69. The Probability Values (P-value) Approach to Hypothesis Testing Using the p-Value P-value is generally sensitive to sample size A large sample should yield a low p-value P-value can report the impact of the sample size on the reliability of the results
70. Relationship between C.I and Hypothesis Testing (Example 1) A direct mktr knows that average no of purchases per month in entire database is 5.6 By sampling ‘loyals’ he finds that their average is 6.1(i.e, =6.1) Is it merely a sampling accident? Ho: = 5.6 (hypothesized value of population) Ha: 5.6 (alternative hypothesis) n = 35 = 2.5
71. Relationship between C.I and Hypothesis Testing (Example 1) Std err =0.42 The appropriate Z for =.05 is 1.96 The Confidence Interval is = (4.78, 6.42) Since 6.1 falls in the interval, we cannot reject the null hypothesis
72. Confidence Intervals and Hypothesis Testing Hypothesis testing and Confidence Intervals are two sides of the same coin. t = = Interval estimate for
73. Relationship between C.I and Hypothesis Testing (Example 2) Revisit the first example we started with Test the performance of two lists in terms of response rates Sample (1,000) from the first list provides a response rate of 3.5% Sample (1,200) from the second list provides a response rate of 4.5% Do the two lists (population) really have a difference or is it an artifact of the sample?
74. Relationship between C.I and Hypothesis Testing (Example 2) C.I. of list 1: (0.035)+/- 1.96*(SE1) SE1 = Sqrt[(0.035*0.965)/1000]=0.006 C.I.1=(0.0232,0.0467) C.I. of list 2: (0.045)+/-1.96*(SE2) SE2=Sqrt[(0.045*0.955)/1200]=0.006 C.I.2 =(0.033,0.0568) What can we infer based on these confidence Intervals? Lack of sufficient evidence to infer that there is any difference between the response rates in the two samples.