Free Essay

# Non Parametric Tests

In: Other Topics

Submitted By raja9899
Words 1170
Pages 5
6 - NONPARAMETRIC TESTS FOR COMPARING TWO POPULATIONS

In situations where the normality of the population(s) is suspect or the sample sizes are so small that checking normality is not really feasible, it is sometimes preferable to use nonparametric tests to make inferences about “average” value.

Wilcoxon Rank Sum Test (a.k.a. Mann-Whitney U Test)
This test is an alternative to the two-sample t-test for comparing the “average” value of two populations where the samples from each population are taken independently.

The hypotheses tested can be stated as follows:

[pic] The distribution of population 1 and population 2 are identical. If the populations are symmetric (but not necessarily normal) the null hypothesis can be expressed in terms of the population medians as: [pic]

[pic] The distribution of population 1 and population 2 are different. (two-tailed) [pic]

or

[pic] The distribution of population 1 is shifted to the right of the distribution for population 2, i.e. the population 1 values are generally larger than the population 2 values. (right-tailed) [pic]

or

[pic] The distribution of population 1 is shifted to the left of the distribution for population 2, i.e. the population 1 values are generally smaller than the population 2 values. (left-tailed) [pic]

The tests statistic is based on the sum of the ranks assigned to the observed data from each population when the combined sample is ranked from smallest to largest. We will always assume that the sample size (m) for population 1 is less than or equal to the sample size (n) from population 2.

Example: Anticipated Length of Office Visit and Weight Status of Patients
Researchers wanted to compare the anticipated office visit time for patients whose BMI indicates normal weight vs. those whose BMI indicates the patient is overweight. It is hypothesized that doctors will report a shorter anticipated office visit time for patients who are classified as overweight. Stating this hypothesis in terms of medians the research hypothesis would be that median office visit time for normal weight patients is greater than that for overweight patients.

[pic] vs. [pic]

The data below are the anticipated office visit time (min) for these two groups of patients.

Normal: 20 25 30 35 40 45 50

Overweight: 5 10 15 15 20 30

The sum of the ranked appointment lengths for normal weight patients is: _________.

The sum of the ranked appointment length for overweight patients is: ____________.

The sum of the ranks for the overweight patients is smaller than the rank sum for the normal weight patients but this would be expected even if the null hypothesis were true. Why?

The test statistic,[pic], is the sum of the ranks for population O, the overweight patients. We can use the table on the following page to determine whether to reject the null or not. Intuitively we will reject the null hypothesis if the sum of the ranked appointment lengths for the overweight patients is “small”. The table tells what “small” is for a given significance level ([pic]).

For m = 6 and n = 7 we find the following from the table:

From Wilcoxon Rank Sum Table: 1-tail α ’ .025 α ’ .050 2-tail α ’ .050 α ’ .100 m n W d P W d P
6 7 27 57 7 .0175 29 55 9 .0367

The table says we will reject the null at the [pic]level if:
[pic] for [pic] (
[pic] > 55 for [pic]
[pic]< 27 or [pic] for [pic]

We have evidence to conclude that the anticipated office visit times are generally smaller than the anticipated office times for patients with BMI’s considered normal (p < .05).

WILCOXON RANK SUM TEST IN JMP
[pic]

Wilcoxon Signed Rank Test
This test is an alternative to the paired t-test which is used when we do not wish to assume that the population of paired differences is normally distributed. As with the Mann-Whitney U test, the Wilcoxon Signed-Rank Test use ranks based on the paired differences rather than the actual values.

Example: Effect of Togetherness on the Heart Rate of Rats

|Rat |Alone Rate |Together Rate |di = Ti – Ai |Sign || di | |Rank |di| |Signed Rank |
|1 |463 |523 |60 | | | | |
|2 |462 |494 |32 | | | | |
|3 |462 |461 |-1 | | | | |
|4 |456 |535 |79 | | | | |
|5 |450 |476 |26 | | | | |
|6 |426 |454 |28 | | | | |
|7 |418 |448 |30 | | | | |
|8 |415 |408 |-7 | | | | |
|9 |409 |470 |61 | | | | |
|10 |402 |437 |35 | | | | |

We then calculate [pic] = the sum of the positive signed ranks = _______________

and [pic] = the sum of the negative signed ranks = _______________

Are hypotheses can be stated in terms of the median of the paired differences. Listed below are the hypotheses along with the test statistic based on the signed rank sums used to test it.

Intuitively we will conclude there has been a heart rate increase if….

Details of the Wilcoxon Signed Rank Test

Let [pic]

[pic] vs. [pic] (two-tailed) Test statistic [pic] In practical terms the null says there is no change in the rats heart rate after the change in environment, the alternative says there is a shift up or down in their heart rate.

[pic] vs. [pic] (right-tailed) Test statistic [pic]
In practical terms the alternative says that there is an increase or shift up in their heart rate as the difference is defined to be Together – Alone.

[pic] vs. [pic] (left-tailed) Test statistic [pic]
In practical terms the alternative says that there is a decrease or shift down in their heart rate as the difference is defined to be Together – Alone.

For this example, if had originally hypothesized that the heart rate of a rat will increase when it is placed in a social environment then we have the right-tailed alternative and our test statistic W = _______.

The Wilcoxon Signed Rank Test Table (handed out) give p-values associated with an observed test statistic value w for a given sample size, i.e. number of pairs, n.
[pic]

Here our p-value = ____________, thus we reject the null hypothesis and conclude that the heart rate of a rat will generally increase when it is taken from a solitary confinement and placed in a social environment with other rats.

WILCOXON SIGNED RANK TEST IN JMP

We first use JMP to form the paired differences as we did for the paired t-test.
[pic]

Select Distribution > Test Mean > Enter 0 for the hypothesized value and check the nonparametric test box. [pic]

The results of the test are shown below.
[pic]
Conclusion:
TABLE FOR WILCOXON RANK SUM TEST (Page 1)
[pic]

TABLE FOR WILCOXON RANK SUM TEST (Page 2)
[pic]

TABLE FOR WILCOXON SIGNED RANK TEST (Page 1)
[pic]

TABLE FOR WILCOXON SIGNED RANK TEST (Page 2)
[pic]

-----------------------
Data Table
[pic]

Select Nonparametric > Wilcoxon Test
[pic]

The p-values for the upper-tailed t-Test and the Wilcoxon signed-rank test have been highlighted. The test statistic reported by JMP for Wilcoxon test =[pic]
Why? I don’t know, but we only need the p-value anyway.

### Similar Documents

#### Test

...Test Data   Elvis Presley ± ISSUnit 1 ± Match Risks/ThreatsDr. Grubb12-13-2011 Risks or Threats: 1. Violation of a security policy by a user.C. Place employee on probation, review acceptable use policy (AUP) and employeeManual, and discuss status during performance reviews.2. Disgruntled employee sabotage.I. Track and monitor abnormal employee behavior, erratic job performance, and use of ITinfrastructure during off-hours. Begin IT access control lockout procedures based onAUP monitoring and compliance.3. Download of non-business videos using the internet to an employee-owned computer.A. Enable content filtering and antivirus scanning at the entry and exit points of theinternet. Enable workstation auto-scans and auto-quarantine for unknown file types.4. Malware infection of a user¶s laptop.L. Use workstation antivirus and malicious code policies, standards, procedures, andguidelines. Enable an automated antivirus protection solution that scans and updatesindividual workstations with proper protection.5. Unauthorized physical access to the LAN. N. Make sure wiring closets, data centers, and computer rooms are secure.Provide no access without proper credentials.6. LAN server operating system vulnerabilities.F. Define vulnerability window policies, standards, procedures, and guidelines.Conduct LAN domain vulnerability assessments.7. Download of unknown file types from unknown sources by local users.B. Apply file transfer monitoring, scanning, and alarming for unknown......

Words: 372 - Pages: 2

Free Essay

#### Non-Destructive Tests

...Non Destructive Test (NDT) X-Ray Advantages of X-Ray X-rays are invisible electromagnetic energy, which is used as a way to get or make images of internal tissues, bones and organs of our body. It is by this process that an expert determines bones of a patient are intact or broken after an accident. Likewise, you can find internal injuries to organs. In addition, X-rays are used to find out whether or not a person has a cancerous tumour. With the increasing technological advances, the dose of the radiation exposure to patients has decreased (www.chem.ucla.edu). X-rays are a form of ionizing radiation which can pass through materials. The X-ray technology is an invaluable tool for medicine, industry, science and security. For example, it can be used to observe the fractured bones and swallowed objects, to monitor the blood flow of patients and to check for cavities. In addition, X-rays can be used to diagnose cancer, kill bacteria in food, detect flaws in machinery or products, analyze the structure of crystals or distant stars and inspect baggage at airports (www.chem.ucla.edu). Now there were more modern medical devices, which process image digitally. This technique automatically selects the parameters of the human organs to be examined (www.chem.ucla.edu). Disadvantages of X-Ray The discovery and immediate use of X-rays and radioactive elements, in the late 19th century and early 20th century brought benefits to science and medicine, but......

Words: 1356 - Pages: 6

#### Test

...Maximize | 25X1 | + | 15X2 | | | (maximize profit) | Subject to: | 3X1 | + | 2X2 | ≤ | 240 | (wiring capacity constraint) | | 2X1 | + | X2 | ≤ | 140 | (drilling capacity constraint) | | | | X1, X2 | ≥ | 0 | (non-negativity constraints) | Optimal Solution: X1 = 40 X2 = 60 Profit = \$1,900 7-15 Electrocomp’s management realizes that it forgot to include two critical constraints (see Problem 7-14). In particular, management decides that to ensure an adequate supply of air conditioners for a contract, at least 20 air conditioners should be manufactured. Because Electrocomp incurred an oversupply of fans in the preceding period, management also insists that no more than 80 fans be produced during this production period. Resolve this product mix problem to find the new optimal solution. Let X1 = the number of air conditioners scheduled to be produced X2 = the number of fans scheduled to be produced Maximize | 25X1 | + | 15X2 | | | (maximize profit) | Subject to: | 3X1 | + | 2X2 | ≤ | 240 | (wiring capacity constraint) | | 2X1 | + | X2 | ≤ | 140 | (drilling capacity constraint) | | X1 | | | ≥ | 20 | (a/c contract constraint) | | | | X2 | ≤ | 80 | (maximum # of fans constraint) | | | | X1, X2 | ≥ | 0 | (non-negativity constraints) | Optimal Solution: X1 = 40 X2 = 60 Profit = \$1,900 7-16 A candidate for mayor in a small town has allocated \$40,000 for last-minute advertising in the days preceding the election.......

Words: 4454 - Pages: 18

#### Parametric and Non-Parametric Statistics Use in Research Methods

... Lilian Otieno, Resident Lecturer I am tasked to distinguish between parametric and non-parametric statistics and explain when to use each method in analysis of data. I shall first seek to define what parametric and non-parametric statistics mean and then compare and contrast them in the analysis of data. Parametric statistics is a branch of statistics that assumes that the data has come from a type of probability distribution and makes inferences about the parameters of the distribution. Most well-known elementary statistical methods are parametric. (According to Wikipedia, the online dictionary). In statistical analysis, parametric significance tests are only valid if certain assumptions are met. If they are not, nonparametric tests can be used. A parameter is a measure of an entire population, such as the mean height of every man in London. In statistical analysis, one practically never has measurements from a whole population and has to infer the characteristics of the population from a sample. Generally speaking parametric methods make more assumptions than non-parametric methods. If those extra assumptions are correct, parametric methods can produce more accurate and precise estimates. They are said to have more statistical power. However, if assumptions are incorrect, parametric methods can be very misleading. For that reason they are often not considered robust. On the other hand, parametric formulae are often simpler to write down and faster to compute. In some,...

Words: 3625 - Pages: 15

#### Test

...Tests of Hypotheses: z-test and t-test 0801-HypothesisTests.doc Page 1 of 4 NOTES TESTS OF HYPOTHESES As was mentioned earlier, sometimes we cannot survey or test all persons or objects; therefore, we have to take a sample. From the results of analysis from the sample data, we can predict the results from the population. Some questions that one may want to answer are 1. Are unmarried workers more likely to be absent from work than married workers? 2. Are the sixth graders in a certain school significantly less skilled in their mathematical abilities than the average student in the district? 3. In Fall 1996, did students in Math 163-01 score the same on the exam as students in Math 163-02? 4. Is there any difference between the strengths of steel wire produced by the XY Company and Bob’s Wire Company? 5. A hospital spokesperson claims that the average daily room charge for a specific procedure is \$622. Can we reject this claim? WHAT IS A HYPOTHESIS? Hypothesis: A statement about the value of a population parameter developed for the purpose of testing. Examples of hypotheses, or statements, made about a population parameter are: The mean monthly income from all sources for systems analysts is \$3,625. Twenty percent of all juvenile offenders ultimately are caught and sentenced to prison. Hypothesis testing: A procedure, based on sample evidence and probability theory, used to determine whether the hypothesis is a reasonable statement and should not be rejected, or......

Words: 1347 - Pages: 6

#### Four Test of Competitive Resources Power – Vrin (Valuable, Rare, Inimitiatable, Non-Substitutable)

...operates more than 17,000 stores in more than 50 countries. How many of the four tests of the competitive power of a resource does the store network pass? Explain your answer. INTRODUCTION Starbucks Corporation, an American company founded in 1971 in Seattle, WA. It is start just as a single store in Seattle’s historic Pike Place Market. Starbucks has about182, 000employees across 19,767 company operated and licensed stores in 62 countries. Their product mix includes roasted and handcrafted high-quality/ premium priced coffees, tea, a variety of fresh food items and other beverages. They also sell a variety of coffee and tea products and license their trademarks through other channels such as licensed stores, grocery and national foodservice accounts. Starbucks also markets its products mix with other brand names within its portfolio of companies, which include Teavana, Tazo, Seattle’s Best Coffee, Starbucks VIA, Starbucks Refreshers, Evolution Fresh, LaBoulange and Verismo. Starbucks had total revenue of \$14.89 billion as of September 29th, 2013. FOUR TEST OF COMPETITIVE RESOURCES POWER – VRIN (VALUABLE, RARE, INIMITIATABLE, NON-SUBSTITUTABLE) The four test of the competitive power of a resources does the Starbucks pass is depend on the resources itself where resources is divided into tangible and intangible resources. Below is the explanation regarding to the Starbuck’s resources and which test is true for each resource. 1. Specialty Coffees , foods and......

Words: 1107 - Pages: 5

#### Causes of Non-Performance of Grade 7 and 8 Students on Mathematics Summative Test

...measurement. Thus tests may be used in the process of evaluation. Tests, along with inventories, scales, questionnaires, and the like, are measurement devices used to obtain data or information needed for evaluation. Evaluation describes something in terms of specific numbers or percentages. Judgment is the essential characteristic of evaluation, it is made by attaching a value or a qualitative description to a measurement derived from a test. In Canossa Academy, particularly in Mathematics area the student was rated with the following components; seatwork, homework, recitation, attitude, quizzes, and exams. Seatwork is administered right after the discussion, while the quizzes will be given if the students meet the mastery level. Meanwhile, exams will be administered at the end of a large chunk of learning. After the computation was made, the teacher will then assess and interpret the data, but based on the outcome of the formative and summative assessment, there are unparalleled results. There is a high outcome in terms of seatwork but low when it comes to summative assessment. The formative assessment that is done during the instruction must be a preparation for their summative test, it must be the determinants if the teacher can move already to the next topic or need to add more learning experiences, but with the case of grade 7 and 8 students, they perform well during seatwork and quizzes but not in quarterly test. This study intends to know the causes of......

Words: 1995 - Pages: 8

#### Test

...students. The outputs with greatest impact were two student tests conducted at the national level. Analysis of variance showed that location and type of school had a significant impact on school efficiencies. Regression results show that both cost per students and cost per teacher are significant determinants of school efficiency.The paper provides insightsinto the understanding of schools’ performance management for schools, evaluators, and policy decision makers. INTRODUCTION Education is a priority area for Abu Dhabi government. It is important in the performance assessment process to know to what extent schools are achieving their stated missions and expectations. Abu Dhabi schools system has never had a comprehensive performance plan that compares schools relative to each other in an objective and scientific manner. Every year, the results of national exams at the end of secondary school, which are used as entry requirements for higher education, have been made publicly available. These results are usually used to rank the secondary schools by several newspapers, and usually a highly debated issue when it comes to school performance, school choice, and the perverse effects of such simplistic ranking system. Analysis of performance in Abu Dhabi has to be contextualized with the relative maturity of the concept for the country and level of implicit understanding bythe stakeholders. Public schools in Abu Dhabi are non-profit organizations (government funded units).......

Words: 13109 - Pages: 53

#### Test

...section presents results and implication of the analysis. The last section presents conclusions of the analysis. 1. Literature review Previous studies have used structural and nonstructural approaches to investigate behavior of the banking market. Structural approaches are mainly based on the traditional industrial organization theory which focuses on the structure-conductperformance (SCP) paradigm and on the efficient structure paradigm. Literature based on structural approaches has investigated how the market concentration weakens the market competition by fostering collusive behavior among firms. Conversely, non-structural approaches assume that factors other than market structure and concentration may affect competitive behavior, such as entry/exit barriers and the general contestability of the market (Panzar, J.C. and J. N. Rosse, 1987; Rosse, J.N. and J.C Panzar, 1977). Non-structural approaches have been developed in the context of the new empirical industrial organization (NEIO) literature. This study is based on structural approaches expecting to uncover the advantage of enhancing banks operational efficiency against bank concentration. The next section presents basic arguments of structure conduct performance hypothesis (SCH) and efficient structure hypothesis (ESH), application in banking industry and their findings. SCP was first introduced by Mason in 1939 as a method of analyzing markets and firms (Worthington, Ian, Chris Briton, and Andy Rees, 2001). As......

Words: 8694 - Pages: 35

#### Parametric Bootstrapping

...0.015707963 0.001570796 sample_mean_vars #0.132826885 0.015370697 0.001603544 *from Part 2 #The two types of variances seem to yield very similar values with very slight discrepancies. #variance of sample mean n_values=c(10,100,1000) var_sample.mean=1/n_values #0.100 0.010 0.001 #Compared to the variance of sample means, the variance of sample medians are greater in value on average. #Part 4 n=1000 sample_mean = mean(rnorm(n,1, 1)) pboot_vars=numeric() n_values = c(10,100,1000) for (i in 1:3) { pboot_vars[i] = var(replicate(B, median((rnorm(n_values[i],sample_mean, 1))))) } pboot_vars #0.131888264 0.016435213 0.001627244 sample_med_vars #0.132826885 0.015370697 0.001603544 *from Part 2 #Comparing the 2 results, we observe that #the parametric boostrap variances arevery similar to the sample median variances obtained from part 2. #Part 5 pivotalCIs = numeric() n_values = c(10,100,1000) for (i in 1:3) { pboot.meds=replicate(B, median(rnorm(n_values[i],sample_mean, 1))) pboot.percentile=quantile(pboot.meds, prob = c(.025, .975)) pboot.hat = median(rnorm(n_values[i],sample_mean,1)) pboot.CI = paste(2*pboot.hat -pboot.percentile[2], 2*pboot.hat pboot.percentile[1] ) pivotalCIs[i]=pboot.CI } pivotalCIs #("0.316571394209908, 1.74238781441729") #n=10 ("0.587680704469166, 1.07943416747069") #n=100 ("0.892268791169873, 1.04776628329487") #n=1000 CIs ("0.265111943430679 1.69377252141066") #n=10 ("0.757126210069845 1.24312238725003") #n=100 ("0.922210181934582 1.07918375732663")......

Words: 471 - Pages: 2

Free Essay

#### Non Parametric Statistics

...article was published October 1958 in The Ecological Society of America 2. Find five terms that you do not know the meaning of in the paper. DEFINE these terms Non parametric statistics: is defined to be a function on a sample that has no dependency on a parameter, and whose interpretation does not depend on the population fitting any parametrized distributions. Statistics based on the ranks of observations are one example of such statistics and these play a central role in many non-parametric approaches. Stippled Area: is the creation of a pattern simulating varying degrees of solidity or shading by using small dots. Such a pattern may occur in nature and these effects are frequently emulated by artists. The term stipple can also apply to a random pattern of small depressions applied to a surface to increase the friction and make the surface easier to grip. Hawking: is a feeding strategy in birds which involves catching flying insects in the air. The term usually refers to a technique of sallying out from a perch to snatch an insect and then returning to the same or a different perch. This technique is called “fly catching” and some birds known for it are several families of “flycatchers”, for example Old World flycatchers, Monarch flycatchers, and Tyrant flycatchers. Allopatric: Occurring in separate, non-overlapping geographic areas. Allopatric populations of related organisms are unable to interbreed because of geographic separation. The development......

Words: 306 - Pages: 2

#### Friedman Test

...safiek@umt.edu.my Azizul Yadi Yaakop Faculty of Management and Economics, Universiti Malaysia Terengganu 21030 Kuala Terengganu, Malaysia e-mail: azizul_yadi@umt.edu.my (Received: 9-11-11/ Accepted: 30-11-11) Abstract The widespread use of mobile phones, the various information access means that it provided to its users, and the vast presence and significant impact of mobile phone on users’ daily life make mobile phones important devices to study. This paper focuses on studying the importance of different choice criteria in mobile phone selection among Malaysian consumers. A quantitative study drawing data from 376 university students was employed. The collected data were analyzed using SPSS. Descriptive statistics, factor analysis, and Friedman test have been employed in the study. The principal components factor analysis resulted in seven independent dimensions: (1) innovative features, (2) image, (3) price, (4) personal recommendation, (5) durability and portable aspects, (6) media influence, and (7) post-sales service. The top three most important factors influencing consumer choice of mobile phones are: innovative features, recommendation and price. Several managerial implications are drawn from the results and future research suggestions are provided. Keywords: Mobile phone, Choice criteria, Malaysia. 1. Introduction The development of mobile communication technology (e.g. wireless Internet, the mobile phone, MP3 player, GPS navigation system) has been a long journey......

Words: 5202 - Pages: 21

#### Weak Form Efficiency Test of Dse

...Form Market Efficiency of Dhaka Stock Exchange (DSE), Bangladesh ABU TAHER MOLLIK Economics & Finance, Regional School of Business, Faculty of Law and Management, La-Trobe University, Bendigo, VIC 3550, Australia. Email:abumollik@yahoo.com.au; a.mollik@latrobe.edu.au M KHOKAN BEPARI PhD Student School of Commerce and Marketing Faculty of Arts, Business, Informatics and Education Central Queensland University, Australia Email: k.bepari@cqu.edu.au; khokan552@yahoo.com Phone:+610402917968 Weak Form Market Efficiency of Dhaka Stock Exchange (DSE), Bangladesh Abstract This paper examines the weak-form efficiency in Dhaka Stock Exchange (DSE) of Bangladesh adjusting for thin trading problem. Both non-parametric tests and parametric tests are used. The data sets consist of daily DSE General Index (DSE-GEN) and DSE 20 Index for the period ranging from January 1, 2002 to December 31, 2007. The results of the study reveal that DSE return series are not normally distributed. Both the return series are stationary and do not follow a random walk. Overall, the study rejects the weak form efficiency of DSE. Key words: Efficient Market Hypothesis; Dhaka Stock Exchange; Random Walk Model; Weak Form of Efficiency; Return autocorrelation. JEL classification: G14, N25, G 34 Weak Form Market Efficiency of Dhaka Stock Exchange (DSE), Bangladesh 1. Introduction The theory of efficient market hypothesis (EMH) proposed by Fama (1965) was a ‘water......

Words: 7750 - Pages: 31

#### Test

...Testing Life Cycle (STLC). The different stages in Software Test Life Cycle - Each of these stages have a definite Entry and Exit criteria  , Activities & Deliverables associat In an Ideal world you will not enter the next stage until the exit criteria for the previous stage practically this is not always possible. So for this tutorial , we will focus of activities and delive different stages in STLC. Lets look into them in detail. http://www.guru99.com/software­testing­life­cycle.html 1/12 6/28/2015 Software Testing Life Cycle STLC Requirement Analysis During this phase, test team studies the requirements from a testing point of view to identify requirements. The QA team may interact with various stakeholders (Client, Business Analyst, System Architects etc) to understand the requirements in detail. Requirements could be eith (defining what the software must do) or Non Functional (defining system performance /secur .Automation feasibility for the given testing project is also done in this stage. Activities Identify types of tests to be performed.  Gather details about testing priorities and focus. Prepare Requirement Traceability Matrix (RTM). Identify test environment details where testing is supposed to be carried out.  Automation feasibility analysis (if required). Deliverables RTM Automation feasibility report. (if applicable) Test Planning This phase is also called Test Strategy phase. Typically , in this stage, a......

Words: 1712 - Pages: 7