Experimentsand Independent Samples

Choosetwo studies that have been in the media during the last year.

Variousstatistical researches has been discussed widely over the past years.One example is the study on the impact of the media on eatingdisorders in children and adolescents. The second study is assessingthe effectiveness of various types of therapy for depression. In thefirst one, the media utilized independent measures whereby differentparticipants were used for each condition of the independentvariables. That is, the media used sample individuals to assess theeffects of media on eating disorders on children. The second studyincorporated the use of matched pairs type of experimental designsthis is where the media experts utilized distinct participants, butthey were matched using essential features, such as, age, gender, andage. To improve the experimental designs, researcher`s needs toincrease the sample size, repeating the experiments, randomizing thesamples as well as increasing the repeated measurements of variousitems under study. The proposed changes will improve the quality ofresearch in that increasing the sample size enhances the possibilitythat what is assessed is indicative of the entire population (Slutz,& Hess, 2011). Randomizing samples reduces the biases during thestudy. Repeating the experiments increases the accuracy of thesurvey.

One-wayAnalysis of Variance verses two-way Analysis of Variance.

Oneway ANOVA is utilized when there is only one explanatory variablewith several groups, levels or categories. On the other hand Two-way,ANOVA is employed where there are two independent variables each withseveral levels and a single response variable. The two-way ANOVAassess the impact of every explanatory variable on the sole outcomevariables and establishes if there is any relationship impact amongthe explanatory variables. Both the one-way and two- way ANOVAanalyses a normally distributed data. Also, both the two-way andone-way variances are used to test a hypothesis regarding theexperimental data. They analyze the relationships between two groups(Bradley, 2011).

Multinomialexperiments

Amultinomial analysis is a statistical test with the followingfeatures the test comprises of n recurring trials. Every test has adiscrete number of probable results. In each trial, the probabilitythat a particular outcome will occur is constant. Also, the tests areindependent in that result in one trial has no effect on the othertrials. Examples of the studies that exhibit the multinomialcharacteristics include a study that was conducted by the ministry oftransport to assess the number of individuals who were involved inbicycle accidents for the past five years. The surveyors were simplyselecting an individual randomly from the population and determiningif the person suffered a head injury or not, that is event A. Event Bwas if the individual was wearing a helmet during the occurrence ofthe accident, or not. The sample size was represented by n from thepopulation the multinomial distribution parameters are presented asn. The second study involves the Boston Hospital last year wherethey wanted to assess the effectiveness of a particular drug. In theassessment, the hospital staff selected a sample of patients who hadbeen administered with that drug. Event A represented those patientswho had been healed after using the drug. Event B showed thosepatients whom the drug had no effect on them. These studies areexamples multinomial experiments since in both cases, the trials areindependent of each other. Also, each trial has a discreet number ofprobable outcomes, that is, a certain patient selected may have thedrug may be effective or not.

Fromwhat you can discover, do they satisfy the chi-square goodness-of-fittest?

Chi-squaregoodness of fit measures how strongly the sample statistics suit aspecific hypothesized distribution. In this case, the above-discussedstudies can be assessed using Chi-square distribution, we will havetwo observed frequencies, that is, f_{1}which will be the number of individuals who suffered a head injuryand f_{2}will the number of individuals involved in the accidents and werewearing a helmet. In the second study, f_{1}will be the number of patients whom the drug was effective and f_{2}will the number of patients whom the drug was ineffective. Theformula in this case will be =(Bowermanet al, 2012)

Chi-squaretest for independence and how it is used

Theanalysis is utilized to assess if there is a significant associationbetween two variables. The occurrence of one variable is comparedwith different values of the second nominal variable. To compute it,the first step includes finding the expected value of the twovariables. The second step involves applying the formula to computethe chi-square value. The last step is calculating the criticalChi-square from the Chi-square table and comparing with thecalculated figure to make the decision. If the computed value for theChi-square is greater than the critical value, we reject the nullhypothesis and conclude there is an association between the twovariables. The formula is where the observed frequency count is and is the expected frequency count.

References

Bradley,H(2011) *Theanalysis of Covariance and alternative: Statistical Methods for*

*ExperimentsQuasi-Experiments Quasi-Experiments and single-case Studies*.John Wiley& Sons

Bowerman,B.L., Murphree, E.S., O’Connell, R.T., & Orris, J.B. (2012)*Essentialsof Business *

* Statistics*(4th Ed.). New York, NY: McGraw- Hill Irwin.

Slutz,S & Hess, K (2011) *Increasingthe Ability of an Experiment to measure an Effect*.

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