BTM8106 Week 7 Complete Solution use as a guide only
BTM8106 Week 7 Complete Solution use as a guide only
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Date Created: 11/05/15
1Compare and Contrast Internal and External Validity The internal validity depends over the accuracy of the results Hence if the sample does not select by random collection method then it could affect the internal validity because internal validity depends over the data collection method In the same manner the external validity includes the concepts of generalization to know the impacts of the results for the larger population Herek 2012 Hence it also depends over the data collection method as like internal validity There are some differences between the external validity and internal validity The internal validity generally makes some dealing with the research study without the help of other research elements On the other side external validity looks over that situation when one could take the outcomes of the research study and simplify it in a broader perspective The generalization also works with the help of external validity Kimmel 2007 It could be better understood with an example When researchers conduct a research study for the testing of drug the drug organization could not consist in the test population as the target population Suppose a research question that is quotTo identify the impact of changes in ecology on the living style of Hispanicquot Then for this research question the external validity could be a primary concern because this question focuses over the whole group of Hispanic instead of someone or a particular group But if the research question states that quotTo identify the impact of changes in ecology on the living style of teenagers Hispanicquot then it would be very difficult to generalize and simplify the outcomes of this question for the whole people of the Hispanic community In this situation internal validity is a primary concern because without it the result of the study could not be effective Herek 2012 For making strong claims in the context of applicability of ndings towards a target population the researchers use the random sampling method systematic samples and cluster sampling for gathering the information and data from the selected population Kimmel 2007 This strategy plays an effective role in the generalization of study outcomes because the sampling process based on probability always includes the high response rate that helps the researchers to apply the result of study in the broader manner 2Compare and Contrast Random Selection and Random Assignment The random selection and random assignment both are slightly relative terms The random selection describes how the research could draw the sample from the whole population related to the research study while the random assignment describes about the process of researchers that they use to assign and draw the sample from different groups of the population Trochim 2006 Due to this similarity both random assignment and selection could be applied to conduct a study It could be better understood with an example If a researcher draws 50 people from a group of 500 people with the help of random sample then it would call random sampling But the researcher selects 50 people for new treatment instead of remaining 450 people from whole population then it would be called random assignment In some situation when the researcher does not use the random sample to select the population but selected the some people for providing the different treatment then the random selection could not be applied but random assignment could be used McNabb 2010 But there are some difference between random selection and random assignment Random selection depends over sampling process and it is directly related to the external validity of the study results Trochim 2006 On the other hand the random assignment is related to the study design and also related to the internal validity of the study s result 3Sample Size and Likelihood of a Statistically Signi cance In the sense of statistics signi cance is also a statistical term which helps to ensure the difference and relationship takes place in two groups It also depends on the sample size StatPac Inc 2013 For example in a study 50 people are selected for a test and the merit would be decided on the basis of male and female category The males score 100 and the females score 98 The ttest gives the difference in signi cance is 001 At the same time there is no huge difference in 100 and 98 This result describes that there is small difference between the groups that could not make negative impact on the outcomes of the study Therefore it could be stated that the sample size makes the drastic impacts on the outcomes of the study whether the study is conducted for any population or for any cause The sample size also includes some errors If there is the small sample size then this situation could affect the likelihood of a statistically signi cant because it could not be encountered the possible errors and it could affect the outcomes of the study But the error could be decreased in that situation when the research takes a large group StatPac Inc 2013 Hence there is a relationship between sample size and likelihood of a statistically signi cant in the context of two groups It is because that when there is a large sample size the different types of likelihood such as the type and type II encounter the errors and also reduces them if the other study part is constructed carefully At the same time the large sample size also provides the rights to the researchers for increasing the signi cance level of study outcomes Biau Kern is amp Porcher 2008 Therefore it could be stated that if the sample size increases the likelihood of nding a statistically signi cant relationship also increases in the same manner because the large size represent the characteristics as like the population 4Probability and Nonprobability Sampling Probability Sampling This method is used to select choices with the help of the complete random process Hackley 2003 This sampling method is used for ensuring that the collected sample is not similar and totally random Advantages The main advantage of this sampling method is its fairness It is because that it describes that every selected participant has given the equal opportunities before the gathering of the sample Hence it also improves the validity of the research outcomes It is very effective for the smaller population and the sample could be free from bias McNabb 2010 Disadvantages This sampling method completely depends over the selected people so they could cheat or the research could face the situation related to possibility of flaws that could also affect the fairness of this sampling model Hackley 2003 It takes time so if the sample group is large then it would require too much patience and time Nonprobability Sampling The nonprobability sampling is the just different from probability sampling because in this method the sample could be selected by the systematic method As like the probability sampling it is also effective for the small population McNabb 2010 Following are some advantages and disadvantages of nonprobability sampling method Advantages This sampling method is more effective because this it helps the researcher to target the speci c group of people Hackley 2003 Disadvantages The main disadvantage of this method is its bias character It is because that the people are selected from the similar group so their view could not represent the view of whole populations Calculate the sample size needed given these factors onetailed ttest with two independent groups of equal size small effect size see Piasta SB amp Justice LM 2010 alpha 05 beta 2 Assume that the result is a sample size beyond what you can obtain Use the compromise function to compute alpha and beta for a sample half the size Indicate the resulting alpha and beta Present an argument that your study is worth doing with the smaller sample Solution a in GPower First we select in test family ttest And in statistical test we choice means Difference between two independent means two groups Also in type of power analysis we choice A priori Compute required sample size given a power and effect size And in input parameters In taiss one Effect size d 02 which is small effect size a err prob l 005 powerl B err prob 1 B 1 02 08 AS beta 02 Allocation ratio N2Nl 1 You will get the sample size needed which is 310 as you shown below Elle edit Eiew lasts Qalculatcir Help Central and ncincentral distrilciuticins pmmmi f pgwer analyses Ii39iit c ll t 155532 nqq if ma 4 it 13 ii iquot t inquot i Jquot is 12 l r A quotin M S quotin 5 hag HE E I I1 I I I 3 all 5 Te st f amilir Statistical test lttests VI Iiileans Difference between tch independent means twp grciups VI Type cif pciwer analirsis li39l39i priciri IScimpute required sample size given ct pciwer and effect size VI Input Parameters lCtlutput Parameters Tail s Cine V ancentraliw parameter S 24ESISIFSISI L Effect size 1 I12 critical t iecizszsci cai err prpp EH35 Df ISlE F39ciwer l 3 err prep 3913 Sample size grciupl 31 III Alicicaticin ratici NEW 1 Sample size grciup 2 31 III Tcital sample size ISEIII Actual pciwer 03002 El KT plcitfcir a range cifualues I Calculate i b After that in type of power analysis we choice compromise compute implied a amp power given Ba raito sample size and effect size And write the sample half size which is 3102 155 Then click calculate you will get the resulting alpha and beta Eile Edit Eiew Iests galculatcir Help Central and nencentral distributions pmmmi f pgwer anal39irrges Il39fitl39ic ll t 39 3555 Te st f amilir Statistic al test lttests VI Iiileans Difference between tch independent means twe grciups VI Ttrpe pf ppwer analysis lCemprcimise Icimpute implied ei Ea ppwer given EIII39ei ratici sample size and effect size VI Input Parameters lClutput Parameters Tailfs Cine v Nencentralitir parameter 5 150531 1 Effect size cl I12 Critical t iesssi as We ratie 4 if SUE Sample size greupi 155 e err prep LENSES432 Sample size greup 2 155 E err prep D345129 Fewer i 3 err prep 0553331 E i pletferarangeefualues Ialculate I As you see the resulting alpha and beta if we Use the compromise function to compute alpha and beta for a sample half the size 2 a Calculate the sample size needed given these factors ANOVA xed effects omnibus oneway small effect size alpha 05 beta 2 3 groups b Assume that the result is a sample size beyond what you can obtain Use the compromise function to compute alpha and beta for a sample approximately half the size Give your rationale for your selected betaalpha ratio Indicate the resulting alpha and beta Give an argument that your study is worth doing with the smaller sample 3 In a few sentences describe two designs that can address your research question The designs must involve two different statistical analyses For each design specify and justify each of the four factors and calculate the estimated sample size you ll need Give reasons for any parameters you need to specify for GPower Solution Select Test family ftests Statistical test ANOVA xed effects omnibus oneway Type of power analysis A priori lnput Effect size f 010 a err prob 005 Power 1b err prob 08 Number of groups 3 Output Noncentrality parameter l 99375000 Critical F 30540042 Numerator df 2 Denominator df 156 Total sample size 159 Actual Power 08048873 Eile Eclit Eiew lasts galculator elp Central ancl noncentral clistriputions Protocol of power analyses criitiicali F 3 1541 LE a 2 in MI u r Test family Statistical test lFtests VI IAND JA Fixecl effects omnipus one way vl Type of power analysis IA priori Iompute required sample size giyen or power ancl effect size VI Input Parameters IElutput Parameters Effect sizef I125 Noncentralityparameterh ELEISFSIZIEIEI on err prop ELIZIS Critics F 3EIS4EIII42 Power 1 3 err prop LEI Numerator clf 2 Number of groups 3 Denominator cif 155 Total sample size 15539 uctual power DED4EIE3 iii r plot for a range of yalues L Calculate L Eile Edit Eiew lasts galculatcur Help Central and npncentral distributicuns pmmmI f p wer anahrrgeg Jr39lit cjall F 2 3399 Test familtr Etatistical test IF tests VI IAND JA Fixed effects cumnilsus cine wayr vl Type pf pcuwer analtrsis lCcImprcImise Cpmpute implied ca Eh pcnwer given We raticu sample size and effect size VI Input Parameters EIJIutput Parameters L Effect sizef Ill ancentralituparameterl ELEIIIIIIIIIIIIIIIIII Elia ratio 4 Critical F rzzeasas Tptal sample size ED Numeratpr clf 2 Number pf grcuups 3 Denpminatpr df F can err prcntn EHFEFEIFS E err prptu BEEN494 Ppwer i 3 err prcutu 02928505 K r plptfprarangepfualues lJ Calculate L
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