Ask a question from expert

Ask now

Assignment on Quantitative Data Analysis

Present analysis of qualitative data findings and critically discuss challenges of analyzing qualitative data and producing rigorous findings.

18 Pages3759 Words381 Views
   

Added on  2021-04-17

Assignment on Quantitative Data Analysis

Present analysis of qualitative data findings and critically discuss challenges of analyzing qualitative data and producing rigorous findings.

   Added on 2021-04-17

BookmarkShareRelated Documents
Running head: Assignment _ Quantitative Data AnalysisAssignment_ Quantitative Data analysisName of StudentName of UniversityAuthor note
Assignment on Quantitative Data Analysis_1
Assignment _ Quantitative Data AnalysisPart 1: Quantitative Analysis(B) Null hypothesis significance testingStatistical Theory:The bottom line of any statistical investigation is to draw some inference regarding the underlying probability law of the phenomenon of interest on the basis of available, observable data (Cohen, Manion & Morrison, 2013). According to statistical theory, observations form the foundation on which any assertion, conjecture or research hypothesis could be analysed and inferred upon. A statistical hypothesis testing method is a tool to evaluate the validity of a conjecture regardingthe parameter of the probability distribution which is assumed to be underlying the phenomenon being considered in the hypothesis (Casella & Berger, 2013).. This is done on the basis of a sample statistic. The procedure takes into consideration two contesting hypothesis, namely the null hypothesis and the alternate hypothesis (Levine, 2014). The null hypothesis assumes a position of no difference with respectto the population parameter(s) involved in the conjecture when compared to a specific value or one another. The alternate hypothesis challenges the assertion of the null hypothesis (Zacks, 2014). Drawing on the fact that the process is dependent on observable values and based upon probability theory, the task is then to look at the sample evidence and determine whether there is reasonable doubt on the validity of the assumption. The rule or test which determines whether the null shall be rejected or not, isbased upon the sampling distribution of the test statistic (Casella & Berger, 2013).Consider the following example. It is of interest to test the validity of the claim that babies born to mothers who are regular smokers have lower weight at birth on an average than those born to mothers who do not. Then mean weight at birth for babies born to mothers who are regular smokers could be compared with the mean birth weight of those born to mothers who do not smoke. According Page 1 of 19ID: 31860125Module DHR.529 Code2750
Assignment on Quantitative Data Analysis_2
Assignment _ Quantitative Data Analysisto null hypothesis testing method, then mean or average weight at birth would be the statistic of interest (Salkind, 2016). According to central limit theorem, large sample distribution of mean is normal with mean equal to the population mean, μ and variance equal to σ2/n where σ2 is the population variance of weights of the babies at birth (Casella & Berger, 2013). Then assuming that specification of labelling parameter asserted by null hypothesis is true, if the probability that observed value of mean falls within the critical region is less than level of significance, α, which is a set probability is determined beforehand, the null is rejected at 100α% level of significance (Lowry, 2014). The following figure depictsthe situation when the test fails to reject null.Figure 1.1.aLet us refer to the observed of mean weight as tobs. Had the observed value of the test statistictobs, been greater than the critical value tα, which is the value which marks critical region, then P (T>tobs |Page 2 of 19ID: 31860125Module DHR.529 Code2750
Assignment on Quantitative Data Analysis_3
Assignment _ Quantitative Data AnalysisH0 is true) which is defined as the p-value, would be less than the level of significance leading to rejectionof null hypothesis (Lehmann & Romano, 2012). Figure 1 however shows the situation when theprobability is greater than α. This shows how statistical hypothesis testing considers how likely a hypothesis is to be true orfalse. Four cases is likely to be the outcome of a testing procedure as depicted in the following table:TruthNull hypothesis istrueNull hypothesis is not trueDecisionReject Null HypothesisIncorrectType I error ( = α)CorrectFail to reject null hypothesisCorrectIncorrectType II errorTable 1.1.aThis level of significance is the probability of type I error (Wasserman, 2013). The probability oftype I error is defined as the probability of rejecting the null hypothesis when it is true. The type II errorcan be used to compute how powerful the test is. The value (1-probability of type II error) gives thepower of the test which is a measure of how good the test is (Park, 2015). The main aim in determiningthe optimum test usually is to choose the test which has minimum probability of type I error whilekeeping type II error in check. This is usually best balanced with α=0.05 (Dancey & Reidy, 2007). This is inline with the intuition that rejection null hypothesis would have more severe consequences thanacceptance of an alternate which is false.Page 3 of 19ID: 31860125Module DHR.529 Code2750
Assignment on Quantitative Data Analysis_4

End of preview

Want to access all the pages? Upload your documents or become a member.

Related Documents
Financial Statistics | Assignment
|4
|662
|32

A Guide to Statistical Inference Question Answer 2022
|18
|4061
|28

Understanding Null Hypothesis, Alternative Hypothesis, Type I and Type II Errors in Statistics
|12
|1692
|79

Pearson Linear Correlation Test: Assumptions and Key Concepts
|4
|664
|141

Data Analysis | Assignment-1
|8
|1466
|10

Data Analysis for Smoking Growth Rate using AUTOS and FTND Methods
|6
|1048
|210