16 hypothesis testing

563 views
480 views

Published on

Published in: Technology
0 Comments
1 Like
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total views
563
On SlideShare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
Downloads
24
Comments
0
Likes
1
Embeds 0
No embeds

No notes for slide

16 hypothesis testing

  1. 1. 14-04-2012 1 Research Methodology Dr. NimitChowdhary,Professor Saturday, April 14, 2012 1© Dr. Nimit Chowdhary © Dr. Nimit Chowdhary Research Methodology Workshop p. 2 Saturda y, April 14, 2012 ‘X’ is innocent ‘X ‘ is Guilty
  2. 2. 14-04-2012 2 © Dr. Nimit Chowdhary Research Methodology Workshop p. 3 Saturday, April 14, 2012  We all operate on basis of theories we hold  A theory is a set of systematically interrelated concepts, definitions, propositions that are advanced to explain and predict phenomena (fact)  Theories tend to be abstract and involve multiple variables  Hypothesis is simple, two-variable propositions involving concrete instances © Dr. Nimit Chowdhary Research Methodology Workshop p. 4 Saturday, April 14, 2012 Research  Test theory  Theorize Theory  Suggest a system to researcher to impose on data
  3. 3. 14-04-2012 3 Theory  Concepts  Constructs Research  Variables A concept is a bundle of meanings or characteristics associated with certain events, objects, conditions, situations, etc. Variables accept numerical values for empirical testing and measurement Variable is used synonymously for construct A construct is an image or idea specifically invented or created for a given research and/ or- theory building purpose © Dr. Nimit Chowdhary Resear ch Method ology Worksh op p. 6Saturday, April 14, 2012 Theory The abstract statements that make claims about the world and how it work. Research problems are usually stated at a theoretical level Example “poverty leads to poor health”
  4. 4. 14-04-2012 4 © Dr. Nimit Chowdhary Resear ch Method ology Worksh op p. 7Saturday, April 14, 2012 Concepts The building blocks of theory which are usually abstract and cannot be directly measured  Descriptive/ nominal/ conceptual definition  Operational definition Example “poverty” Concept Descriptive definition Operational definition Customer A patron of firm ‘x’ or one who buys products and services from firm ‘x’ One who has purchased at least one third of his family’s need from firm ‘x’ during the last 3 months Year A twelve month period Financial year, April 1 through March 31 Boy A male youth A male of 12-16 years of age Small-scaleunit An industrial undertaking which manufactures some product/s on a small scale An industrial unit with investment in plant and machinery less than 3 crores
  5. 5. 14-04-2012 5  What is ‘rural’ as in rural tourism? © Dr. Nimit Chowdhary Research Methodology Workshop p. 9 Saturday, April 14, 2012 © Dr. Nimit ChowdharySaturday, April 14, 2012 Constructs The phenomenon which point to the existence of the concept Example “poor living conditions” Remember that ‘poverty’ was the concept. ‘Poverty’ is explained as ‘poor living conditions’
  6. 6. 14-04-2012 6 © Dr. Nimit ChowdharySaturday, April 14, 2012 Variables The components of the constructs which can be measured Example “provision of sanitary facilities” Construct ‘poor living conditions’ can be construed from a number of ‘measurable’ variables like ‘provision on sanitary facilities’ © Dr. Nimit ChowdharySaturday, April 14, 2012 Value The actual units or methods of measurement of the variables. These are data in their most concrete form Example “number of people per toilet”
  7. 7. 14-04-2012 7 © Dr. Nimit Chowdhary Research Methodology Workshop p. 13 Saturday, April 14, 2012  Identify variables  Relate variables  Nature of relationship  Degree of relationship  Create a system of variables (Model)  Predict variables © Dr. Nimit Chowdhary Research Methodology Workshop p. 14 Saturday, April 14, 2012  Dichotomousvariables  Discrete variables  Continuous variable
  8. 8. 14-04-2012 8 © Dr. Nimit Chowdhary Research Methodology Workshop p. 15 Saturday, April 14, 2012  Independent variables  Dependent variables © Dr. Nimit Chowdhary Research Methodology Workshop p. 16 Saturday, April 14, 2012  A moderating variable is a second independent variable that is included because it is believed to have a significant contributory or contingent effect on the originallystated IV-DV relationship. The introduction of a 4-day week (IV) will lead to higher productivity (DV) especially among younger workers (MV)
  9. 9. 14-04-2012 9 © Dr. Nimit Chowdhary Research Methodology Workshop p. 17 Saturday, April 14, 2012  An almost infinite number of extraneous variables (EV) exist that might conceivably effect a given relationship.Some can be treated as IV or MV, but most must either be assumed or excluded from the study. In routine office work (EV) the introduction of a 4-day week (IV) will lead to higher productivity (DV) especially among younger workers (MV) © Dr. Nimit Chowdhary Research Methodology Workshop p. 18 Saturday, April 14, 2012  The intervening variables (IVV) are factors that may theoretically affect the observed phenomenonbut cannot be seen, measured, or manipulated; its affects must be inferred from the effects of the independent and the moderator variables on observed phenomenon. The introduction of a 4-day week will lead to higher productivity by increasing job satisfaction (IVV).
  10. 10. 14-04-2012 10 © Dr. Nimit Chowdhary Research Methodology Workshop p. 19 Saturday, April 14, 2012 Proposition (Problem) is a statement about concepts that may be judged as true or false if it refers to observable phenomenon. When a propositionis formulated for empirical testing, we call it a hypothesis. As a declarativestatement, a hypothesis is of a tentative and conjectural nature.  Is an assumptionabout relations between variables  Is a predictive statement that relates an independent variable to a dependent variable.  Are tentative, intelligent guesses as to the solutionof the problem © Dr. Nimit Chowdhary Research Methodology Workshop p. 20 Saturday, April 14, 2012
  11. 11. 14-04-2012 11  Is a specific statement of prediction. It describes in concrete terms what you expect to happen in the study  Is an assumptionabout the populationof study  Delimitsthe area of research and keeps the researcher on right track © Dr. Nimit Chowdhary Research Methodology Workshop p. 21 Saturday, April 14, 2012 © Dr. Nimit Chowdhary Research Methodology Workshop p. 22 Saturday, April 14, 2012  Descriptive Hypothesis- state existence, size, form, or distribution of some variable People in equatorial regions (cases) have less than average heights (variables)  Relational Hypothesis- that describe relationship between two variables with respect to some case  Correlational Hypothesis Foreign cars are perceived by American consumers to be of better quality than domestic quality  Explanatory hypothesis An increase in family income leads to an increase in the percentage of income spent on junk food
  12. 12. 14-04-2012 12 © Dr. Nimit Chowdhary Research Methodology Workshop p. 23 Saturday, April 14, 2012  Null Hypothesis- is an hypothesis of ‘no difference’. It states that no difference exists between the parameter and the statistic being compared to or no relationship exits between the variables being compared. Ho: There is no relationship between a family’s income and its expenditure on junk food  Alternative (Research) Hypothesis- describes the researcher’s prediction that, there exists a relationship between two variables. H1: Family’s expenditure on junk food increases with rise in family income. Consider mean demand for computers during assemblylead time. Rather than estimate the mean demand, our operations manager wants to know whether the mean is different from 350 units. In other words, someone is claiming that the mean time is 350 units and we want to check this claim out to see if it appears reasonable © Dr. Nimit Chowdhary Research Methodology Workshop p. 24 Saturday, April 14, 2012
  13. 13. 14-04-2012 13 That the standard deviation [σ]was assumed to be 75, the sample size [n] was 25, and the samplemean [ ] was calculated to be 370.16 © Dr. Nimit Chowdhary Research Methodology Workshop p. 25 Saturday, April 14, 2012 X We can rephrase this request into a test of the hypothesis: H0:  = 350 Thus, our research hypothesis becomes: H1:  ≠ 350 © Dr. Nimit Chowdhary Research Methodology Workshop p. 26 Saturday, April 14, 2012
  14. 14. 14-04-2012 14 For example, if we’re trying to decide whether the mean is not equal to 350, a large value of (say, 600) would provide enough evidence. If is close to 350 (say, 355) we could not say that this provides a great deal of evidence to infer that the populationmean is different than 350. © Dr. Nimit Chowdhary Research Methodology Workshop p. 27 Saturday, April 14, 2012 X X The two possible decisions that can be made: Conclude that there is enough evidence to support the alternative hypothesis (also stated as: reject the null hypothesis in favor of the alternative) Conclude that there is not enough evidence to support the alternative hypothesis (also stated as: failing to reject the null hypothesis in favor of the alternative) NOTE: we do not say that we accept the null hypothesis if a statistician is around…
  15. 15. 14-04-2012 15  Nullhypothesis: ‘X’ is innocent  Alternate:‘X’ has committed theft  Eitherthere is enough evidence to concludethat ‘X’ has committed theft (Accept alternative hypothesis..policemay generate evidence)  Or there is not enough evidence to concludethat ‘X’ has committed theft (Which does not mean that ‘X’ has not committedtheft…onlysufficient evidence is not there) The testing procedure begins with the assumption that the null hypothesis is true. Thus, until we have further statistical evidence, we will assume: H0: = 350 (assumed to beTRUE) The next step will be to determine the sampling distribution of the sample mean assuming the true mean is 350. is normal with 350 75/SQRT(25) = 15
  16. 16. 14-04-2012 16 1. Un-standardized test statistic: Is in the guts of the sampling distribution? Depends on what you define as the “guts” of the sampling distribution. If we define the guts as the center 95% of the distribution [this means  = 0.05], then the critical values that define the guts will be 1.96 standard deviations of X-Bar on either side of the mean of the sampling distribution [350], or UCV = 350 + 1.96*15 = 350 + 29.4 = 379.4 LCV = 350 – 1.96*15 = 350 – 29.4 = 320.6
  17. 17. 14-04-2012 17 2. Standardized test statistic: Since we defined the “guts” of the sampling distribution to be the center 95% [ = 0.05], If the Z-Score for the sample mean is greater than 1.96, we know that will be in the reject region on the right side or If the Z-Score for the sample mean is less than -1.97, we know that will be in the reject region on the left side. Z = ( - )/ = (370.16 – 350)/15 = 1.344 Is this Z-Score in the guts of the sampling distribution???
  18. 18. 14-04-2012 18 3.The p-value approach (which is generally used with a computer and statisticalsoftware):Increase the “Rejection Region” until it “captures” the sample mean. For this example, since is to the right of the mean, calculate P( > 370.16) = P(Z > 1.344) = 0.0901 Since this is a two tailed test, you must double this area for the p- value. p-value = 2*(0.0901)= 0.1802 Since we defined the guts as the center 95% [ = 0.05],the reject region is the other 5%. Since our sample mean, , is in the 18.02% region, it cannot be in our 5% rejection region [ = 0.05].
  19. 19. 14-04-2012 19 Un-standardized Test Statistic: Since LCV (320.6) < (370.16) < UCV (379.4), we reject the null hypothesis at a 5% level of significance. Standardized Test Statistic: Since -Z/2(-1.96) < Z(1.344) < Z/2 (1.96), we fail to reject the null hypothesis at a 5% level of significance. P-value: Since p-value (0.1802) > 0.05 [], we fail to reject the hull hypothesis at a 5% level of significance.
  20. 20. 14-04-2012 20  Discussions with colleagues and experts about a problem, its origin and objectives in seeking a solution  Examinationof data and record for possible trends, peculiarities  Review of similar studies © Dr. Nimit Chowdhary Research Methodology Workshop p. 39 Saturday, April 14, 2012  Exploratory personal investigation/ observation  Logicaldeduction from the existing theory  Continuity of research  Intuition and personal experince © Dr. Nimit Chowdhary Research Methodology Workshop p. 40 Saturday, April 14, 2012
  21. 21. 14-04-2012 21 Conceptual clarity Should be clear and precise Specific Should be specific and limited in scope Consistent Should be consistent with the objectives of research Testable Should be capable of being tested Expectancy Should state the expected relationship between the variables © Dr. Nimit Chowdhary Research Methodology Workshop p. 41 Saturday, April 14, 2012 Simplicity Should be stated as far as possible in simple terms Objectivity Should not include value judgments, relative terms or any moral preaching Theoretical relevance Should be consistent with a substantial body of established or known facts or existing theory Availability of techniques Statistical methods should be available for testing the proposed hypothesis © Dr. Nimit Chowdhary Research Methodology Workshop p. 42 Saturday, April 14, 2012
  22. 22. 14-04-2012 22

×