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  1. 1. Welcome <br />Presentation on<br />Hypothesis<br />
  2. 2. Hypothesis<br />Prepared By:- Group 1<br />WagariRefu<br />TeklewoinKassaye<br />ZewduHakimu<br />MeseretYohannes<br />HunbelewGebreTsadik<br /> Michael Gezae<br />
  3. 3. Learning Outcomes<br />Upon completion of this program, we will be able to<br />Explain the meaning and significance of hypothesis in scientific research<br />Identify the types of hypotheses<br />Illustrate why we need a hypothesis<br />Identify and categorize research variables<br />Create Operational Definitions<br />Formulate a valid hypothesis<br />Identify Characteristics of a good hypothesis<br />Test the hypothesis<br />
  4. 4. Presentation Content<br />Brief summary on the Scientific Method<br />Meaning of Hypothesis<br />Meaning and Types of variables <br />Characteristics of Hypothesis<br />Categories of Hypothesis<br />Forming a Hypothesis<br />Testing a Hypothesis<br />
  5. 5. The scientific Method<br />Is an overarching perspective<br />On how scientific investigations should proceed <br />Consists of a set of research principles and methods<br />that help researchers obtain valid results<br />from their research studies<br />
  6. 6. The scientific Method (Cont…)<br />Researchers generally agree that the scientific method is composed of the following key elements <br />An empirical approach,<br />Observations, <br />Questions, <br />Hypotheses, <br />Experiments, <br />Analyses, <br />Conclusions, and <br />Replication<br />
  7. 7. Research Questions & Hypothesis<br />Hypothesis is the fourth element of the scientific method<br />However, we may not use hypothesis for all types of research.<br />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). <br />
  8. 8. In qualitative research, the research questions assume two forms: <br />a central question and <br />associated sub questions<br />The central question is a statement of the question being examined in the study in its most general form.<br />so as to not limit the inquiry<br />Research Questions & Hypothesis<br />
  9. 9. Guidelines for writing broad, qualitative research questions:   <br />Ask one or two central questions followed by no more than five to seven sub-questions<br />Relate the central question to the specific qualitative strategy of inquiry (like ethnography , phenomenology, etc)<br />Begin the research questions with the words “what” or “how” to convey an open and emerging design<br />Examples: <br />How do women in a psychology doctoral program describe their decision to return to school?<br />“What is it like for a mother to live with a teenage child who is dying of cancer?”<br />Focus on a single phenomenon or concept<br />
  10. 10. Guidelines (Cont…)<br />Use exploratory verbs that convey the language of emerging design of research. These verbs tell the reader that the study will <br />Discover (e.g., grounded theory) <br />Seek to understand (e.g., ethnography) <br />Explore a process (e.g., case study)   <br />Describe the experiences (e.g., phenomenology) <br />Report the stories (e.g., narrative research) <br />Use non-directional language<br />Expect the research questions to evolve and to change during the study<br />Use open-ended questions without reference to the literature or theory<br />If the information is not redundant with the purpose statement, specify the participants and the research site for the study<br />
  11. 11. Hypothesis Defined<br />An educated guess<br />A tentative point of view<br />A proposition not yet tested<br />A preliminary explanation<br />A preliminary Postulate<br />
  12. 12. Various Authors<br />“A hypothesis is a conjectural statement of the relation between two or more variables”. (Kerlinger, 1956)<br />“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)<br />“Hypothesis is a formal statement that presents the expected relationship between an independent and dependent variable.”(Creswell, 1994)<br />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).<br />
  13. 13. Hypothesis vs Theory vs Fact<br />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.<br />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.<br />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:<br />A theory predicts events in general terms, while a hypothesis makes a specific prediction about a specified set of circumstances.<br />A theory has been extensively tested and is generally accepted, while a hypothesis is a speculative guess that has yet to be tested.<br />
  14. 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. <br />
  15. 15. Purpose<br />Guides/gives direction to the study/investigation<br />Defines Facts that are relevant and not relevant<br />Suggests which form of research design is likely to be the most appropriate<br />Provides a framework for organizing the conclusions of the findings<br />Limits the research to specific area<br />Offers explanations for the relationships between those variables that can be empirically tested<br />Furnishes proof that the researcher has sufficient background knowledge to enable her/him to make suggestions in order to extend existing knowledge<br />Structures the next phase in the investigation and therefore furnishes continuity to the examination of the problem<br />
  16. 16. Basis<br />Individual experience, <br />Socio-Culture background,<br />Business Ethic,<br />Economic events<br />Etc..<br />
  17. 17. Forms of Hypothesis<br />Hypotheses can take various forms, depending on the question being asked and the type of study being conducted<br />Some hypotheses may simply describe how two things may be related. For example, correlational research<br />In others the researcher might hypothesize that one variable causes a change in the other variable (causal relationship<br />In their simplest forms, hypotheses are typically phrased as “if-then” statements<br />
  18. 18. A Hypothesis<br />must make a prediction<br />must identify at least two variables<br />should have an elucidating power<br />should strive to furnish an acceptable explanation or accounting of a fact<br />must be falsifiable meaning hypotheses must be capable of being refuted based on the results of the study<br />must be formulated in simple, understandable terms<br />should correspond with existing knowledge<br />In general, a hypothesis needs to be unambiguous, specific, quantifiable, testable and generalizable. <br />
  19. 19. Characteristics of a Testable Hypothesis<br />1. A Hypothesis must be conceptually clear<br /> - concepts should be clearly defined<br /> - the definitions should be commonly accepted<br /> - the definitions should be easily communicable<br />2. The hypothesis should have empirical reference<br /> - Variables in the hypothesis should be empirical realities<br /> - If they are not it would not be possible to make the observation and ultimately the test<br />3. The Hypothesis must be specific<br /> - Place, situation and operation<br />
  20. 20. Characteristics of a Testable Hypothesis<br />4. A hypothesis should be related to available techniques of research<br /> - Either the techniques are already available or<br /> - The researcher should be in a position to develop suitable <br /> techniques<br />5. The hypothesis should be related to a body of theory<br /> - Hypothesis has to be supported by theoretical argumentation<br /> - It should depend on the existing body of knowledge<br />In this way <br /><ul><li>the study could benefit from the existing knowledge and
  21. 21. later on through testing the hypothesis could contribute to the reservoir of knowledge</li></li></ul><li>Categorizing Hypotheses<br />Can be categorized in different ways<br />1. Based on their formulation <br />Null Hypotheses and Alternate Hypotheses<br />2. Based on direction<br />Directional and Non-directional Hypothesis<br />3. Based on their derivation<br />Inductive and Deductive Hypotheses<br />
  22. 22. Categorizing Hypotheses (Cont…)<br />1. Null Hypotheses and Alternate Hypotheses<br />Null hypothesis always predicts that <br />no differences between the groups being studied (e.g., experimental vs. control group) or <br />no relationship between the variables being studied<br />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)<br />
  23. 23. Categorizing Hypotheses (Cont…)<br />Alternate Hypothesis can further be classified as<br />2. Directional Hypothesis and Non-directional Hypothesis<br />
  24. 24. Categorizing Hypotheses (Cont…)<br />2. Directional Hypothesis and Non-directional Hypothesis<br />Simply based on the wording of the hypotheses we can tell the difference between directional and non-directional<br />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. <br />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<br />
  25. 25. Categorizing Hypotheses (Cont…)<br />3. Inductive and Deductive Hypotheses(Theory Building and Theory Testing)<br />classified in terms of how they were derived:<br />- Inductive hypothesis - a generalization based on observation<br />- Deductive hypothesis - derived from theory <br />
  26. 26. Forming/Developing a Hypothesis<br />Articulating the hypotheses that will be tested is one of the steps in the planning phase of a research study<br />A hypothesis is formulated after <br />the problem has been stated and <br />the literature study has been conducted <br />It is formulated when the researcher is totally aware of the theoretical and empirical background to the problem<br />
  27. 27. The Initial Idea<br />The initial idea is the starting point<br />Often vague or general, it requires refining before research hypotheses can be generated<br />Refinement of the initial idea is based on<br /> (1) a search of relevant research literature (2) initial observations of the phenomenon<br />Narrow and formalize the initial idea into a statement of the problem<br />
  28. 28. Statement of the Problem<br />In the form of a question that clearly indicates an expected relationship<br />The nature of the question will dictate the required level of constraint of a study<br />Causal questions will require experimental research<br />Questions about relationships can be answered with lower constraint research<br />Convert into research hypothesis by operationally defining the variables<br />
  29. 29. In General<br />Ideas lead to<br />observations<br />library research<br />Then Statement of problem and<br />Then Problem statements become research hypotheses when constructs are operationalized<br />
  30. 30. Operational Definitions<br />The procedures used to measure and/or manipulate a variable<br />Most variables can be operationally defined in many different ways, <br />Thus creating many different research hypotheses from a single statement of a problem<br />
  31. 31. Hypotheses<br />States clearly the expected relationship between the variables<br />The form is a declarative statement, but it is a tentative statement to be tested in research<br />Implicitly or explicitly, the variables in the research hypothesis are stated in operational definition terms<br />
  32. 32. The Role of Theory<br />In research planning, theory guides the process<br />Theory is often the primary source of research hypotheses<br />Theory guides the selection of variables as well as their operational definitions<br />Most research is based on multiple, overlapping and interacting theories<br />
  33. 33. Variables<br />Any factor that can take on different values is a scientific variable and influences the outcome of a research.<br />Examples include<br />Gender, <br />Colour,<br />Country <br />Weight, <br />Time, <br />Height, etc..<br />
  34. 34. Types of Variables<br />There are many categories of variables<br />Independent vs. Dependent vs. Controlled Variables<br />Categorical vs. Continuous Variables<br />Quantitative vs. Qualitative Variables<br />
  35. 35. Independent vs. Dependent vs. Controlled Variables<br />The independent variable is called “independent” because it is independent of the outcome being measured. <br />It is what causes or influences the outcome. <br />The dependent variable is influenced by the independent variable.<br /> Controlled variables are variables that the scientist does not want to change during the course of the experiment<br />Hence the research includes <br />finding ways to vary the independent variable<br />Finding ways to keep the controlled variables from changing and<br />measure the dependent variable<br />
  36. 36. Categorical vs. Continuous Variables<br />Categorical variables are variables that can take on specific values only within a defined range of values like gender, marital status<br />consisting of discrete, mutually exclusive categories, such as “male/female,” “White/Black,” etc<br />Continuous variables are variables that can theoretically take on any value along a continuum like age, income weight, height etc..<br />When compared with categorical variables, continuous variables can be measured with a greater degree of precision. <br />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. <br />Certain statistical tests are appropriate for categorical variables, while other statistical tests are appropriate for continuous variables. <br />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.<br />
  37. 37. Quantitative vs. Qualitative Variables<br />Qualitative variables are variables that vary in kind, like “attractive” or “not attractive,” “helpful” or “not helpful,” or “consistent” or “not consistent”<br />Quantitative variables are those that vary in amount like height, weight, salary etc<br />
  38. 38. Summary - Hypothesis Formation<br />First identify a general area of interest to be researched; <br /> Example: effects of smoking on health<br />Then identify a research question – the research question should be more narrowly defined (more specific) than the general research topic. <br /> Example: “Does smoking cause lung cancer?”<br />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.<br />Now it is time to formulate the hypothesis in an attempt to answer the question by making it a conditional statement like <br />"Smoking may cause lung cancer.”<br />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.<br />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.<br />
  39. 39. Summary (Cont…)<br />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.<br />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.<br />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.<br />Remember: - Hypothesis can be adjusted/refined/changed as more information is gathered but before the actual examination/experiment is carried out.<br />
  40. 40. Hypothesis Testing<br />All hypothesis tests are conducted the same way. <br />The researcher <br />states a hypothesis to be tested, <br />formulates an analysis plan, <br />analyzes sample data according to the plan, and<br />accepts or rejects the null hypothesis, based on results of the analysis.<br />
  41. 41. Hypothesis Testing (Cont..)<br />1. State the hypotheses. <br /> 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. <br />2. Formulate an analysis plan. <br /> The analysis plan describes how to use sample data to accept or reject the null hypothesis. It should specify the following elements. <br />Significance level. <br /> Often, researchers choose significance levels equal to 0.01, 0.05, or 0.10; but any value between 0 and 1 can be used.<br />Test method. <br /> 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.<br />
  42. 42. Analyze sample data. <br /> Using sample data perform computations called for in the analysis plan.Test statistic. <br /> When the null hypothesis involves a mean or proportion, use either of the following equations to compute the test statistic.<br />Test statistic = (Statistic - Parameter) / (Standard deviation of statistic) Test statistic = (Statistic - Parameter) / (Standard error of statistic)<br />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.<br />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.<br />Hypothesis Testing (Cont..)<br />
  43. 43. Hypothesis Testing<br />When you want to make statements about a population, you usually draw samples<br />How generalizable is the sample-based finding?<br />Evidence has to be evaluated statistically before arriving at a conclusion regarding the hypothesis<br />Depends on whether information is generated from the sample with fewer or larger observations<br />
  44. 44. Steps in Hypothesis Testing<br />Problem Definition<br />Clearly state the null and alternate hypotheses.<br />Choose the relevant test and the appropriate probability distribution<br />Determine the degrees of freedom<br />Determine the significance level<br />Choose the critical value<br />Compare test statistic and critical value<br />Compute relevant test statistic<br />Decide if one-or two-tailed test<br />Does the test statistic fall in the critical region?<br />No<br />Do not reject null<br />Yes<br />Reject null<br />
  45. 45. Basic Concepts of Hypothesis Testing<br />The Null and Alternate hypothesis<br />Choosing the relevant statistical test and appropriate probability distribution. Depends on<br /> - Size of the sample<br /> - Whether the population standard deviation is known or not<br />Choosing the Critical Value. The three criteria used are<br /> - Significance Level<br /> - Degrees of Freedom<br /> - One or Two Tailed Test<br />
  46. 46. Significance Level<br />Indicates the percentage of sample means that is outside the cut-off limits (critical value)<br />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)<br />Accepting a null hypothesis when it is false is called a Type II error and its probability is ()<br />
  47. 47. Significance Level (Contd.)<br />When choosing a level of significance, there is an inherent tradeoff between these two types of errors<br />Power of hypothesis test (1 - )<br />A good test of hypothesis ought to reject a null hypothesis when it is false<br />1 -  should be as high a value as possible<br />
  48. 48. Degree of Freedom<br />The number or bits of "free" or unconstrained data used in calculating a sample statistic or test statistic<br />A sample mean (X) has `n' degree of freedom<br />A sample variance (s2) has (n-1) degrees of freedom<br />
  49. 49. One or Two-tail Test<br />One-tailed Hypothesis Test <br />Determines whether a particular population parameter is larger or smaller than some predefined value<br />Uses one critical value of test statistic<br />Two-tailed Hypothesis Test <br />Determines the likelihood that a population parameter is within certain upper and lower bounds<br />May use one or two critical values<br />
  50. 50. Hypothesis Testing<br />
  51. 51. Hypothesis Testing About a Single Mean<br />Step-by-Step<br />1) Formulate Hypotheses<br />2) Select appropriate formula<br />3) Select significance level<br />4) Calculate z or t statistic<br />5) Calculate degrees of freedom (for t-test)<br />6) Obtain critical value from table<br />7) Make decision regarding the Null-hypothesis<br />
  52. 52. Hypothesis Testing About a Single Mean - Example 1(2 tailed)<br />Ho:  = 5000 (hypothesized value of population)<br />Ha:   5000 (alternative hypothesis)<br />n = 100<br /> = 4960 <br /> = 250<br /> = 0.05<br />Rejection rule: if |zcalc| > z/2 then reject Ho.<br />
  53. 53. Hypothesis Testing About a Single Mean - Example 2<br />Ho:  = 1000 (hypothesized value of population)<br />Ha:   1000 (alternative hypothesis)<br />n = 12<br /> = 1087.1<br />s = 191.6<br /> = 0.01<br />Rejection rule: if |tcalc| > tdf, /2 then reject Ho.<br />
  54. 54. Hypothesis Testing About a Single Mean - Example 3(1 tailed)<br />Ho:  5000 (hypothesized value of population)<br />Ha:  < 5000 (alternative hypothesis)<br />n = 50<br /> = 4970<br />  = 250<br /> = 0.01<br />Rejection rule: if then reject Ho.<br />
  55. 55. Hypothesis Test of Difference between Means<br />Mayor of a city wants to see if males and females earn the same<br />A random sample of 400 males and 576 females was taken and following was found<br />
  56. 56. Hypothesis Test of Difference between Means<br />The appropriate test depends on<br /> - whether samples are from related or unrelated samples<br /> - whether population standard deviations are known or not<br /> - if not, whether they can be assumed to be equal or not<br />
  57. 57. Hypothesis Test of Difference between Means<br />In salary example, the null hypothesis is<br /> Ho: 1- 2 =c (=0) <br /> Ha: 1- 2 c <br />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<br />
  58. 58. Hypothesis Test of Difference between Means<br />The calculated value of z is<br />For =.01 and a two-tailed test, the Z-table value is 2.58<br />Since is greater than , the null hypothesis is rejected<br />
  59. 59. Hypothesis Testing of Proportion<br />Quality control dept of a light bulb company claims 95% of its products are defect free<br />The CEO checks 225 bulbs and finds only 87% to be defect free<br />Is the claim of 95% true at .05 level of significance ?<br />So we have hypothesized values and sample values <br />
  60. 60. Hypothesis Testing of Proportion<br />The null hypothesis is Ho:p=0.95<br />The alternate hypothesis is Ha: p 0.95<br />First, calculate the standard error of the proportion using hypothesized values as<br />Since np and nq are large, we can use the Z table. The appropriate z value is 1.96<br />
  61. 61. Hypothesis Testing of Proportion<br />The limits of the acceptance region are<br />Since the sample proportion of 0.87 does not fall within the acceptance region, the CEO should reject the quality control department’s claim<br />
  62. 62. Hypothesis Testing of Difference between Proportions<br />Manager wants to see if John and Linda, two salespeople, have the same conversion<br />He picks samples and finds that <br />
  63. 63. Hypothesis Testing of Difference between Proportions<br />Are their conversion rates different at 0.05 significance level?<br />The null hypothesis is Ho:<br />The alternate hypothesis is Ha:<br />The best estimate of p (proportion of success)<br /> is<br />also, <br />
  64. 64. Hypothesis Testing of Difference between Proportions<br />An estimate of the standard error of the difference of proportions is<br />The z value can be calculated as<br />The z value obtained from the table is 1.96 (for ). Thus, we fail to reject the null hypothesis <br />
  65. 65. The Probability Values (P-value) Approach to Hypothesis Testing<br />P-value provides researcher with alternative method of testing hypothesis without pre-specifying <br />Largest level of significance at which we would not reject Ho<br />
  66. 66. The Probability Values (P-value) Approach to Hypothesis Testing<br />Difference Between Using  and p-value<br />Hypothesis testing with a pre-specified <br />Researcher is trying to determine, "is the probability of what has been observed less than ?“<br />Reject or fail to reject Ho accordingly<br />
  67. 67. The Probability Values (P-value) Approach to Hypothesis Testing<br />Using the p-Value<br />Researcher can determine "how unlikely is the result that has been observed?“<br />Decide whether to reject or fail to reject Ho without being bound by a pre-specified significance level<br />In general, the smaller the p-value, the greater is the researcher's confidence in sample findings<br />
  68. 68. The Probability Values (P-value) Approach to Hypothesis Testing: Example<br />Ho:  = 25 (hypothesized value of population)<br />Ha:   25 (alternative hypothesis)<br />n = 50<br /> = 25.2<br /> = 0.7<br />SE( )= = 0.1; Z= =2<br />From Z-table, prob Z >2 is 0.0228. As this is a 2-tailed test, the p-value is 2 0.228=.0456<br />
  69. 69. The Probability Values (P-value) Approach to Hypothesis Testing<br />Using the p-Value<br />P-value is generally sensitive to sample size<br />A large sample should yield a low p-value<br />P-value can report the impact of the sample size on the reliability of the results<br />
  70. 70. Relationship between C.I and Hypothesis Testing (Example 1)<br />A direct mktr knows that average no of purchases per month in entire database is 5.6<br />By sampling ‘loyals’ he finds that their average is 6.1(i.e, =6.1)<br />Is it merely a sampling accident?<br />Ho:  = 5.6 (hypothesized value of population)<br />Ha:   5.6 (alternative hypothesis)<br />n = 35<br /> = 2.5<br />
  71. 71. Relationship between C.I and Hypothesis Testing (Example 1)<br />Std err =0.42<br />The appropriate Z for =.05 is 1.96 <br />The Confidence Interval is<br /> = (4.78, 6.42)<br />Since 6.1 falls in the interval, we cannot reject the null hypothesis<br />
  72. 72. Confidence Intervals and Hypothesis Testing<br />Hypothesis testing and Confidence Intervals are two sides of the same coin.<br />t = = Interval estimate for <br />
  73. 73. Relationship between C.I and Hypothesis Testing (Example 2)<br />Revisit the first example we started with<br />Test the performance of two lists in terms of response rates<br />Sample (1,000) from the first list provides a response rate of 3.5%<br />Sample (1,200) from the second list provides a response rate of 4.5%<br />Do the two lists (population) really have a difference or is it an artifact of the sample?<br />
  74. 74. Relationship between C.I and Hypothesis Testing (Example 2)<br />C.I. of list 1:<br />(0.035)+/- 1.96*(SE1)<br />SE1 = Sqrt[(0.035*0.965)/1000]=0.006<br />C.I.1=(0.0232,0.0467)<br />C.I. of list 2:<br />(0.045)+/-1.96*(SE2)<br />SE2=Sqrt[(0.045*0.955)/1200]=0.006<br />C.I.2 =(0.033,0.0568)<br />What can we infer based on these confidence Intervals?<br />Lack of sufficient evidence to infer that there is any difference between the response rates in the two samples.<br />
  75. 75. References<br />http://www.experiment-resources.com<br />http://www.ehow.com<br />http://stattrek.com<br />http://www.methodspace.com<br />http://www.aqr.org.uk – Association of Qualitative Research<br />The books supplied by our instructor<br />
  76. 76. Thank<br />YOU<br />
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