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# T test for two independent samples and induction

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### T test for two independent samples and induction

1. 1. T Test For Two Independent Samples - Presentation Transcript1. Week 9:Independent t -test t test for Two Independent Samples 12. Independent Samples t - test The reason for hypothesis testing is to gain knowledge about an unknown population. Independent samples t-test is applied when we have two independent samples and want to make a comparison between two groups of individuals. The parameters are unknown. How is this different than a Z-test and One Sample t- test? 23. Independent t - test We are interested in the difference between two independent groups. As such, we are comparing two populations by evaluating the mean difference. In order to evaluate the mean difference between two populations, we sample from each population and compare the sample means on a given variable. Must have two independent groups (i.e.samples) and one dependent variable that is continuous to compare them on. 34. Examples: Do males and females significantly differ on their level of math anxiety? IV: Gender (2 groups: males and females) DV: Level of math anxiety Do older people exercise significantly less frequently than younger people? IV: Age (2 groups: older people and younger people) DV: Frequency of getting exercise 45. Examples: Do 8th graders have significantly more unexcused absences than 7th graders in Toledo junior highs? IV: Grade (2 groups: 8th grade and 7th grade) DV: Unexcused absences Note that Independent t-test can be applied to answer each research question when the independent variable is dichotomous with only two groups and the dependent variable is continuous. 56. Generate examples of research questions requiring an Independent Samples t-test: What are some examples that you can come up with? Remember- you need two independent samples and one dependent variable that is continuous. 67. Assumptions The two groups are independent of one another. The dependent variable is normally distributed. Examine skewness and kurtosis (peak) of distribution Leptokurtosis vs. platykurtosis vs. mesokurtosis The two groups have approximately equal variance on the dependent variable. (When n1 = n2 [equal sample sizes] ,the violation of this assumption has been shown to be unimportant.) 78. Steps in Independent Samples t-test 89. Step 1: State the hypotheses Ho: The null hypothesis states that the two samples come from the same population. In other words, There is no statistically significant difference between the two groups on the dependent variable. Symbols: Non-directional: Ho: μ1 = μ2 Directional: H 0:µ ≥ µ1 2 or H 0:µ ≤ µ 1 2 • If the null hypothesis is tenable, the two group means differ only by sampling fluctuation – how much the statistic’s value varies from sample to sample or chance. 910. Ha: The alternative hypothesis states that the two samples come from different populations. In other words, There is a statistically significant difference between the two groups on the dependent variable. Symbols: Non- directional: H 1:µ ≠ µ 1 2 Directional: H 1:µ > µ 1 2 H 1:µ < µ 1 2 1011. Step 2: Set a Criterion for Rejecting Ho Compute degrees of freedom Set alpha level Identify critical value(s) Table C. 3 (page 638 of text) 1112. Computing Degrees of Freedom Calculate degrees of freedom (df) to determine rejection region. n n df = 1 + 2 − 2 -2 sample size for sample1+ sample size for sample2 • df describe the number of scores in a sample that are free to vary. • We subtract 2 because in this case we have 2 samples. 1213. More on Degrees of Freedom • In an Independent samples t-test, each sample mean places a restriction on the value of one score in the sample, hence the sample lost one degree of freedom and there are n-1 degrees of freedom for the sample. 1314. Set alpha level Set at .001, .01 , .05, or .10, etc. 1415. Identify critical value(s) Directional or non-directional? Look at page 638 Table C.3. To determine your CV(s) you need to know: df – if df are not in the table, use the next lowest number to be conservative directionality of the test alpha level 1516. Step 3: Collect data and Calculate t statistic t= x −x 1 2  ( − 1) + ( − 1)  1 2 2  variance s n 1 1 s n  + 1 2 2   n +n −2  n n   1 2  1 2 Whereby: n: Sample size s2 = variance df x :Sample mean subscript1 = sample 1 or group 1 subscript2 = sample 2 or group 2 1617. Step 4: Compare test statistic to criterion df = 18 α = .05 , two-tailed test in this example • critical values are ± 2.101 in this example 1718. Step 5: Make Decision Fail to reject the null hypothesis and conclude that there is no statistically significant difference between the two groups on the dependent variable, t = , p > α. OR Reject the null hypothesis and conclude that there is a statistically significant difference between the two groups on the dependent variable, t = , p < α. • If directional, indicate which group is higher or lower (greater, or less 18 than, etc.).19. Interpreting Output Table: Mean APGAR Sample size SCORE Levene’s tests the assumption of equal variances – if p < .05, then variances t-value Degrees of are not equal and use a different test freedom to modify this: Here, we have met the assumption so use first row. CI p - value Observed difference 19 Retrieved on July 12, 2007 from SPSSShortManual.html between the groups20. Interpreting APA table: 2021. Variable Math anxiety t Gender Male 3.66 Female 3.98 3.35*** Age Under 40 years 3.32 Over 41 years 3.64 2.67** Note. **p < .01. ***p < .001. 21
2. 2. 22. Examples and Practice See attached document. Create the following index cards from this lecture: When to conduct a t-test (purpose, conditions, and assumptions) t-test statistic formula for computation t-test statistic formula df formula 22 shoffma5 + Follow 47247 views, 5 favs, 4 embeds Related Two sample t-test 5366 views Two Sample Tests 1295 views Small Sampling Theory Presentation1 3388 views Sample B_Book Typesetting 534 views Z And T Tests 2707 views Chi2 Anova 1199 views Ch11 1612 views Freq distribution 288 views Part3 175 views One Way Anova 13103 views
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6. 6. people are likely to be discontented, unlikely to give of their best, and end up leavingvoluntarily or involuntarily when their unsuitability becomes evident. They will not offer theflexibility and commitment that many organisations seek. Managers and supervisors will haveto spend extra time on further recruitment exercises, when what is needed in the first placeis a systematic process to assess the role to be filled, and the type of skills and abilitiesneeded to fill it.Most recruitment systems will be simple, with stages that can be followed as a routinewhenever there is a vacancy to be filled, and which can be monitored and adapted in the lightof experience.This booklet describes the main features of such systems, and other related issues. Systemsshould be: efficient - cost effective in methods and sources effective - producing enough suitable candidates without excess and ensuring the identification of the best fitted for the job and the organisation fair - ensuring that right through the process decisions are made on merit alone.The importance of fairnessThe employer has the legal responsibility to ensure that no unlawful discrimination occurs inthe recruitment and selection process on the grounds of sex, race, disability, age, sexualorientation, and religion or belief. Equality of opportunity is an integral part of therecruitment and selection process, and to this end employers may offer training andencouragement to any under-represented groups. Examples include pre-applicationassistance for those who do not have English as their first language, or managementdevelopment training for women where they are under-represented in management grades(1).Job advertisements may also state that the employer encourages applications from thosegroups that are under- represented in the organisation.Employees and their representatives will also have an interest in fair, non-discriminatoryrecruitment and selection policies, and they should be fully consulted when new proceduresare introduced or existing procedures reviewed. The Sex Discrimination Act 1975, the RaceRelations Act 1976, the Employment Equality Regulations (covering sexual orientation,religion or belief, and age) and the Disability Discrimination Act 1995 set out the legalrequirements for employers.Organisations should be aware that the provisions of the Disability Discrimination Act 1995not only make it unlawful to discriminate against disabled individuals without justifiablereason but also require employers to make reasonable adjustments to the workplace orworking arrangements. Detailed guidance is available in the Code of Practice on theelimination of discrimination in employment. This can be obtained from The Stationery Office(2).The Acas Equality Direct helpline (tel: 08456 00 34 44 08456 00 34 44 ) can giveadvice on the best ways of implementing an equal opportunities policy.Advice is also offered to employers in small and medium sized organisations through theBusiness Link service (4) and through Acas training (5).Human resource planningRecruiters need to keep abreast of changes in the labour market to ensure that theirrecruitment efforts are not wasted or directed at too small a pool of labour. Skill shortages
8. 8. The balance of the labour force is changing, with some increase in the numbers of women,young people, and most particularly older workers available for work. Employers arebeginning to give serious consideration to the employment of older workers, and a voluntaryCode of Practice to counteract ageism in employment has been introduced by theGovernment (7). Jobcentres will not accept vacancies with age limits.The value of labour market information is that it gives employers some forecasts from whichthey can decide how best to plan for future recruitment. Should the organisation make apositive move to attract older workers? What might best be done to counter any shortage ofpotential recruits with particular skills? Should training new and existing workers move higherup the priority list in the firm?Should the organisation make the introduction of family-friendly policies a priority so as toattract the widest range of suitable staff? Looking at all the options means that recruitmentwill be better targeted and therefore more efficient and effective.Recruitment and selectionA Tesco case studyPage 1: IntroductionTesco is the biggest private sector employer in the UK. The company has more than 360,000employees worldwide. In the UK, Tesco stores range from small local Tesco Express sites tolarge Tesco Extras and superstores. Around 86% of all sales are from the UK.Tesco also operates in 12 countries outside the UK, including China, Japan and Turkey. Thecompany has recently opened stores in the United States. This international expansion is partof Tesco”s strategy to diversify and grow the business.In its non-UK operations Tesco builds on the strengths it has developed as market leader inthe UK supermarket sector. However, it also caters for local needs. In Thailand, for example,customers are used to shopping in “wet markets” where the produce is not packaged. Tescouses this approach in its Bangkok store rather than offering pre-packaged goods as it would inUK stores.Tesco needs people across a wide range of both store-based and non-store jobs: In stores, it needs checkout staff, stock handlers, supervisors as well as many specialists, such as pharmacists and bakers. Its distribution depots require people skilled in stock management and logistics.
9. 9. Head office provides the infrastructure to run Tesco efficiently. Roles here include human resources, legal services, property management, marketing, accounting and information technology.Tesco aims to ensure all roles work together to drive its business objectives.Tesco needs to ensure it has the right number of people in the right jobs at the right time. Todo this, it has a structured process for recruitment and selection to attract applicants for bothmanagerial and operational roles.Workforce planning is the process of analysing an organisation”s likely future needs forpeople in terms of numbers, skills and locations. It allows the organisation to plan how thoseneeds can be met through recruitment and training. It is vital for a company like Tesco to planahead. Because the company is growing, Tesco needs to recruit on a regular basis for both thefood and non-food parts of the business.Positions become available because: jobs are created as the company opens new stores in the UK and expands internationally vacancies arise as employees leave the company when they retire or resign or get promotion to other positions within Tesco new types of jobs can be created as the company changes its processes and technologyTesco uses a workforce planning table to establish the likely demand for new staff. Thisconsiders both managerial and non-managerial positions.
10. 10. In 2008/09, for example, Tesco calculates that to support its business growth there will be ademand for around 4,000 new managers.The planning processThis planning process runs each year from the last week in February. There are quarterlyreviews in May, August and November, so Tesco can adjust staffing levels and recruit wherenecessary. This allows Tesco sufficient time and flexibility to meet its demands for staff andallows the company to meet its strategic objectives, for example, to open new stores andmaintain customer service standards.Tesco seeks to fill many vacancies from within the company. It recognises the importance ofmotivating its staff to progress their careers with the company. Tesco practises what it calls“talent planning”. This encourages people to work their way through and up the organisation.Through an annual appraisal scheme, individuals can apply for “bigger” jobs. Employeesidentify roles in which they would like to develop their careers with Tesco. Their managersets out the technical skills, competencies and behaviours necessary for these roles, whattraining this will require and how long it will take the person to be ready to do the job. Thishelps Tesco to achieve its business objectives and employees to achieve their personal andcareer objectives.Job descriptions and person specificationsAn important element in workforce planning is to have clear job descriptions and personspecifications. A job description sets out: the title of the job to whom the job holder is responsible for whom the job holder is responsible a simple description of roles and responsibilitiesA person specification sets out the skills, characteristics and attributes that a person needs todo a particular job.Together, job descriptions and person specifications provide the basis for job advertisements.They help job applicants and post-holders to know what is expected of them. As they are sentto anyone applying for jobs, they should:
11. 11. contain enough information to attract suitable people act as a checking device to make sure that applicants with the right skills are chosen for interview set the targets and standards for job performanceAt Tesco these documents are combined:Job descriptions and person specifications show how a job-holder fits into the Tesco business.They help Tesco to recruit the right people. They also provide a benchmark for each job interms of responsibilities and skills. These help managers to assess if staff are carrying outjobs to the appropriate standardsSkills and behavioursTesco”s purpose is to serve its customers.Tescos organisational structure has the customer at the top. Tesco needs people with the rightskills at each level of this structure.There are six work levels within the organisation. This gives a clear structure for managingand controlling the organisation. Each level requires particular skills and behaviours.
12. 12. Work level 1 frontline jobs working directly with customers. Various in-store tasks, such as filling shelves with stock. Requires the ability to work accurately and with enthusiasm and to interact well with others. Work level 2 leading a team of employees who deal directly with customers. Requires the ability to manage resources, to set targets, to manage and motivate others. Work level 3 running an operating unit. Requires management skills, including planning, target setting and reporting. Work level 4 supporting operating units and recommending strategic change. Requires good knowledge of the business, the skills to analyse information and to make decisions, and the ability to lead others. Work level 5 responsible for the performance of Tesco as a whole. Requires the ability to lead and direct others, and to make major decisions. Work level 6 creating the purpose, values and goals for Tesco plc. Responsibility for Tesco”s performance. Requires a good overview of retailing, and the ability to build a vision for the future and lead the whole organisation.Tesco has a seven-part framework that describes the key skills and behaviours for each job atevery level in the company. This helps employees understand whether they have the rightknowledge, skills or resources to carry out their roles.Attracting and recruiting
13. 13. Recruitment involves attracting the right standard of applicants to apply for vacancies. Tescoadvertises jobs in different ways. The process varies depending on the job available.Internal recruitmentTesco first looks at its internal Talent Plan to fill a vacancy. This is a process that lists currentemployees looking for a move, either at the same level or on promotion. If there are nosuitable people in this Talent Plan or developing on the internal management developmentprogramme, Options, Tesco advertises the post internally on its intranet for two weeks.External recruitmentFor external recruitment, Tesco advertises vacancies via the Tesco website www.tesco-careers.com or through vacancy boards in stores. Applications are made online formanagerial positions. The chosen applicants have an interview followed by attendance at anassessment centre for the final stage of the selection process. People interested in store-basedjobs with Tesco can approach stores with their CV or register though Jobcentre Plus. Thestore prepares a waiting list of people applying in this way and calls them in as jobs becomeavailable.For harder-to-fill or more specialist jobs, such as bakers and pharmacists, Tesco advertisesexternally: through its website and offline media through television and radio by placing advertisements on Google or in magazines such as The Appointment Journal
14. 14. Tesco will seek the most cost-effective way of attracting the right applicants. It is expensiveto advertise on television and radio, and in some magazines, but sometimes this is necessaryto ensure the right type of people get to learn about the vacancies.Tesco makes it easy for applicants to find out about available jobs and has a simpleapplication process.By accessing the Tesco website, an applicant can find out about local jobs,management posts and head office positions. The website has an onlineapplication form for people to submit directly. SelectionSelection involves choosing the most suitable people from those that apply for a vacancy,whilst keeping to employment laws and regulations. Screening candidates is a very importantpart of the selection process. This ensures that those selected for interview have the best fitwith the job requirements.ScreeningIn the first stages of screening, Tesco selectors will look carefully at each applicant”scurriculum vitae (CV). The CV summarises the candidate”s education and job history to date.A well-written and positive CV helps Tesco to assess whether an applicant matches theperson specification for the job.The company also provides a “job type match” tool on its careers web page. People interestedin working for Tesco can see where they might fit in before applying.
15. 15. The process Tesco uses to select external management candidates has several stages.Assessment centresA candidate who passes screening attends an assessment centre. The assessment centres takeplace in store and are run by managers. They help to provide consistency in the selectionprocess. Applicants are given various exercises, including team-working activities orproblemsolving exercises. These involve examples of problems they might have to deal withat work.Candidates approved by the internal assessment centres then have an interview.Line managers for the job on offer take part in the interview to make sure thatthe candidate fits the ConclusionWorkforce planning is vital if a business is to meet its future demands for staff. It allows abusiness time to train existing staff to take on new responsibilities and to recruit new staff tofill vacancies or to meet skill shortages.Tesco is a major international company with many job opportunities, including management,graduate, school leaver and apprentice posts.