The Scientific Method for Falsifiable Testing - myassignmenthelp

Question: Discuss about theThe Scientific Method for Falsifiable Testing Procedures. Answer: Introduction The scientific method is the name given to a series of procedures for obtaining new knowledge or updating existing knowledge about the varied phenomena which typically involves empirical and measurable or verifiable source of observation. The father of scientific methodology is said by some to be the Arab polymath Ibn al-Haytham who first argued the importance of questioning phenomena and validating them through formally testing them. The principal steps involved in the scientific method are:(i)detailed observation of events or phenomena, (ii) asking relevant questions about the cause and/or effect of the phenomena, (iii) formulating testable hypotheses based on the observations (iv) develop testable predictions based on the hypotheses framed (v) testing the validity of the predictions using empirical and falsifiable testing procedures (vi) formulating effective theories, if the tests in the previous step are positive/ reformulate hypiotheses and predictions and retest those. Thus, w e see that scientific method is more of a cyclic and continuous process over time.(Science Made Simple. 2016). The scientific method, at least since the time of Galileo, has produced innumerable advancements in human knowledge and thinking, the fruits of which we are enjoying at the present moment. In this project, though, we look and critique at the scientific method with reference to the statistical perspective in a typical experimental setup, taking a published journal article for our reference. T-Test, Anova And Regression Analysis The three most prominent statistical terms that are being used in practice in statistical analyses, and are being critically examined with respect to their application in this report are: the t-test, analysis of variance(ANOVA) and regression analysis. It is important to know the details of these three terms before we try to critique the journal article. In a sense, all the three terms can be included under the broad category of regression analysis, which is used to compare the statistical difference between two or more different samples or variables.(Paret, M., 2016) , (Lomax, R. G. 2007)Typically, the analysis is used to find out the relationship(s) between one dependent and one or more independent variables in a population. In regression analysis, the dependent variable is assumed to be a function of the independent variables with respect to certain parameters, the number of which depends of the type of regression we use, like linear or non-linear or multilinear. In mathematical t erminology, we can say that regression analysis hinges on two things: (i)Correlation, or the problem of finding the form of the function where where is the dependent variable and are dependent variables, being the parameters which is usually determined in linear and general linear cases by a factor known as correlation coefficent which is a ratio of product of covariances(deviation from means) to the product of standard deviations In this step, an additional terminology used is the error in prediction, denoted by which is minimized by a method commonly known as method of least squares. (ii) The testing of statistical significance of the above estimated function by calculating the conditional probability of the model being false and comparing the obtained value with that of a known standard probability distribution. Two additional terminologies used in this step are the null and alternative hypothesis. The null hypothesis is the assumption that the dependency of the dependent variable on the independent variable is not real but accidental and the alternative hypothesis is that the dependency is actual. In this context, the two most widely used probability distributions are the t-distribution and F-distribution. When the t-distribution is used, the statistical test is said to be a t-test, and when the F-distribution is used, the test is said to be an F-test. The analysis of variance(ANOVA) is determining the interdependence and statistical difference between a set of more than two variables using an F-test applied to the ratio of variance between the group of interdependent variables and variance within of group of variables. Note that the statistical tests like t-test and F-test are not limited only to regression analysis, rather can also be performed on sample statistics which are assumed to follow the Students-t or Snedecor-F distribution.(NLREG., 2017), (Montgomery, D. C. 2012) In addition, for the analysis that we will use in this article, we also need some terminology from the sampling theory. The most common sampling methods used in experiments are: simple random sampling, stratified random sampling and multistage random sampling. In simple random sampling, each and every unit in the population is equally likely to be a part of the sample chosen. In stratified random sampling, the population is stratified, or classified beforehand into strata or classes based on certain parameters and then, the sample is constructed by simple random sampling from amongst the strata. In multistage random sampling, the sample is chosen in multiple steps. This type of sampling is quite useful in cases where location based sampling is essential. In this type of sampling the population is first divided into regions from which the first simple random sampling is done. The second stage consists of simple random sampling from dividing the hitherto divided regions into further sm aller regions, and so on. Thus, in this type of sampling, we are more localising the population to be sampled.(Yale University ., 2017) the article chosen for critical analysis The article that is chosen for this critical report is Pandey, M., Singh, J., Mangal, G., Yadav, P.,(2014),Evaluation of awareness regarding orthodontic procedures among a group of preadolescents in a cross-sectional study, Journal of International Society of Preventive and Community Dentistry,4(1),44-47. The article is an open access article, available on PubMed Central with PMCID:PMC4015160. In the article, statistical analysis is done regarding the awareness and know-how of orthodontic and other dental procedures among a group of preadolescents from rural and urban areas in Bilaspur district, Chattisgarh State, India. The objective of the paper says that the study was conducted as there was a high prevalence of malocclusion, which is a dental anomaly characterized by large abnormalities in the tooth position. The method employed by the authors of the paper was a cross-sectional study of about 1010 subjects(students) with average age somewhere around 13.02 years with standard devia tion of 2.1 years using a questionnaire consisting of questions pertaining know how of orthodontical procedures. The questionnaire was validated by using a pilot study consisting of nine items. Finally, to test the statistical significance, t-test and ANAOVA were conducteed at a significance level of 0.05. The broad results of the study were that students aged 14 years were more aware than other students, that girl students were significantly more aware of the orthodontic procedures and that students from urban background were similarly more aware than their rural counterparts. The Experimental Design Used In The Article The method of design of the study used by the authors requires some mention. The Methods section of the article says that first, an epidemological survey was taken in the Bilaspur district during the period between September and December, 2013; and then later a multistage random sampling was done to select six schools consisting of three in urban and three in rural areas in the same district. We see that preliminary epidemological survey, done in this case is quite important, as it helps to determine the local variations amongst the population effectively. Sampling before assessing the local properties of the population may lead to enormous difficulties in proper data sampling and may even lead to biased sample. The next thing we note is the use of multistage random sampling to select the six schools. Note that this is a very crucial part of the reseearch. If simple random sampling or, stratified random sampling would have been made, there could have been drastic changes in the resul t. We note that the method adopted by the authors is well suited to the purpose, as the population that is used to study is a very large one, and simple random sampling could be representative of a very small part of population. Stratified sampling, though better than simple random sampling in this case, gives the problem of stratification of the population, which is another complex issue having various parameters. Thus, the via media solution is to employ multistage random sampling that effectively tries to capture the population of Bilaspur district. We also note that a dual stratification has also been done by the authors by including equal samples from urban and rural areas. This is because, the urban students, having good access to modern information, may be well equipped with orthodontic procedures, whereas, those with a rural background may not be as aware as their urban counterparts. Thus, to ensure evenness, equal samples were selected from both the urban and rural areas. W e also note that pilot study was conducted to validate the questionnaire beforehand. Pilot study is a small scale reliability test of the sample to evaluate the feasibility, time, cost, adverse events, and statistical variability of the sample. This is quite essential, because, in spite of the precautions taken while choosing the sample, like multistage sampling and stratification into urban and rural parts, it may so happen that the sample is thoroughly biased, for example, it may so happen that a particular school chosen may be the only one where the students are exceptionally educated as regards dental procedures due to the fact of there being a qualified dentist and better infrastructural facility in the school and hence report to the questionnaire more faithfully and correctly in comparison with other schools, where the students may just randomly guess the answer to questionnaires based on their whims and fancies. To ensure fairness, a pilot study is essential before embarking to the full detailed questionnaire. The article states that the intra-examiner reliability factor, =0.87. We note that there is a good intra-examiner reliability, as the cohens kappa is close to 1.(Sapiens 2010). Now, the authors state that after the pilot study was performed amongst the chosen samples, the main sample was chosen excluding those undergoing orthodontic treatments. This latter step is added to ensure unbiasedness, as those students would be naturally more aware of orthodontic procedures. Statistical Analysis Used In The Article The article states that after the questionnaire was successfully answered by the volunteer students, the statistical analysis of the scored data was done using SPSS 16.0 software. The details that were recorded were descriptive statistics including mean percentage scores, standard deviations, frequency scores, students t-test and ANOVA to test the statistical significance of means, and finally multiple linear regression. Here, we note the authors are using a complete approach to statistically analysing the data. The descriptive statistics are as much important to analyse the data as much as the quantitative tests used. The descriptive statistics proivide us a qualitative description of the data, which is quite useful to understand a priori as to which statistical test to apply to investigate the data more thoroughly. Now, we see the results obtained. We see that amongst the 1010 students selected for the study, 556 were boys and 454 were girls, 606 were from urban areas and 404 from rural areas and the ages varied from 12 to 15 years. We observe that here the dependent variable is the nominal binary awareness of the orthodontic procedure, whereas the independent variables are age, location(urban/rural) and gender. From Table1 in the article, we can also find out that the number of 12 year olds is 254, 13 year olds 200, 14 year olds 252 and 15 year olds 304. Thus, we see that there are roughly equal proportion of students in each of subcategories of each of the independent variables. Thus, the sample chosen is well suited to the variables chosen. The study also revelead that the overall awareness of orthodontic procedures among the students is about 45.1%. The mean scores of awareness of orthodontic procedures amongst girls(4.46) with a standard deviation of 1.71 was found to be significantly higher than that of boys (4.00) with standard deviation of 1.489 using t-test. We need to understand here that the awareness as a whole gave a rough account of know how of the orthodontic procedures among the students, whereas the mean scores calculated on the basis of grouping the sample gives us a better command over the distinction of the same over the various sub-categories of the sample. In addition, the t-test also gives us conclusive evidence that the mean scores are significantly different and not due to pure chance alone, which is seen from Table 2 in the article, where p-value is seen to be 0. Though theoretically p-value cannot be equal to 0, but the zero value is indicative of a very low value in the SPSS software. What this implies in the context of t-test is that the probability of the difference of means of the two subcategories in the sample(boys and girls in case of Table 2) being zero assuming the null hypothesis that they are equal is close to zero. We need to note that the level of significance of the test, or the threshold value of the value of Students-t distribution chosen before the study began was 0.05. But, the observed value of probability is found to be close to 0, which is indicative that the original assumption of the null hypothesis that the means of the genders are equal is false and needs to be rejected. This simple test shows the power of statistical logic, which is not to be obtained in a casual prima facie study. Similarly, the t-test applied to subcategories according to location gave significant difference amongst the mean scores in urban(4.43 with standard deviation 1.606) and rural locations(4.00 with a standard deviation 1.578), with a p-value close to zero or exactly zero in the SPSS software. The next observation in the results section we need to consider is the ANOVA table. Here, in addition to the p-value, we have additional column showing the F-value. What the F-value actually shows is the ratio of between the group variances(the age groups in Table 1) and within the group variances(variance of awareness in a single age group). We see that if the null hypothesis that the mean of the groups according to ages are equal, which is assumed, were true, then the between the group variances would be dominated by or equal to the within the group variances, thus giving us an F-value of close to 1 or less than 1. But, that this is not the case is shown by the high value of F-value in all the four subcategories of age parameter, being well above 1 in all the four cases(seen to be 57.61, 81.48, 69.21, 51.81 respectively for 12, 13, 14 and 15 year olds). This, combined with the p-values being close to zero, proves the significance of the difference in the mean scores of the different age groups between different, with the observed mean score of 5.20 with a standard deviation of 0.747 for 14 year olds to be the highest . The last analysis we take up is the regression analysis between the three different variables of age, location and gender. We note that the t-test is a subset of F-test(ANOVA) in the two dimensional case, or in other words, when we compare only two variables or subgroups within a sample, the F-test is nothing but the t-test as, the Snedecor-F distribution with 1 degree of freedom is the Students-t distribution. Again, the ANAOVA is nothing but the regression analysis of the variances. Thus, in ANOVA and t-tests done, the authors compared the subcategories in the independent variables of Age(12 to 15 year olds), Gender(Boys and Girls) and Location(Urban and Rural), in the final regression analysis they are comparing the mean scores in the three main categories of variables themselves. Thus, ANOAVA and t-tests were a regression analysis done on the subcategories within the independent variables. In the regression analysis, we find that age, gender and location, in that order of preference affect the dependent variable of awareness of orthodontic procedures. This is ensured by comparing the value, which is nothing but the multiple correlation coefficient computed by taking into account the individual correlation coefficients involving the individual independent variables with the dependent variable as in a correlation matrix. The scores obtained keeping only age constant is less than that obtained keeping both age and gender constant which is less than that obtained keeping all the three constant. The F-values being significantly greater than 1, and p-values being close to zero, gives us the validity of the differential effect of the three independent variables on the dependent variable. Conclusion And Summary We see that the authors of the journal article have made a thorough statistical analysis of the awraeness of orthodontic procedures amongst the student in an attempt to better understand the prevalence of malocclusion. The way the sample was chosen, the way the validation was conducted, the statistical analyses conducted and the results and conclusions drawn, were, from a statistical and analytical perspective, quite appreciable. But, as in statistics, there are bound to errors in the study. The first error might have crept in from the choice of schools and the volunteers that participated. In spite of wisdom in sampling and conducting the pilot study, there might have been biases in the selection of schools due to political, or, similar reasons, like better infrastructure in schools and enthusiasm in students. It might be the case that within the group variances in the ANOVA and regression analyses be very small and insignificant as compared to the between group variances just becau se of the reason that the volunteers were of a homogenous nature, thus giving ahigh F-value, in spite of there being no significant difference in the means. Again, this has to do with sample selection. We think that it might have improved the statistical analysis if two way ANOVA be done to improve the test and an ANOCOVA(Analysis of Covariance) be performed. (Kass, R. E . 1 February 2011). Overall, the study made by authors can be a suitable model which could be implemented in statistical studies. References Pandey, M., Singh, J., Mangal, G., Yadav, P.,(2014),Evaluation of awareness regarding orthodontic procedures among a group of preadolescents in a cross-sectional study, Journal of International Society of Preventive and Community Dentistry,4(1),44-47. Kass, R. E (1 February 2011). 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