Course name and number
STATISTICS FOR THE BEHAVIORAL AND SCIENCES 12
Coursename and number
Datesubmitted
Statisticsfor the Behavioral and Social Sciences
Part1
EssayQuestion One
Theresearch was conducted to establish whether there is a significantdifference between the two vaccines namely, a shot and the nasalspray used to prevent flue infections. In this regard, the researchquestion can be formulated as “between nasal spray and shot spray,which one is more effective in safeguarding individuals from flueinfections?” The following procedures will be followed in anobjective of answering the research question. First, is to examinethe difference of the effects of the shot and the nasal spray vaccineusing observation. The study will have the following two hypotheses:
NullHypotheses: shot spray is equal effective than nasal spray
AlternativeHypotheses: shot spray is more effective than nasal spray
Theresearch used the Z test instead of the T test the hypothesis becausethe sample size was greater than 30 (n=500). The pooled estimatedenoted by P=20
Z=(P_{1}– P_{2})/ SQRT (P*1P *(1/N_{1}+ 1/N_{2})
= 0.08 /0.025
=3.2
P(Z < – 3.2) = 0.0008
Pvalue = 0.0008 < 0.05(level of significance)
Thesolution above indicates that the null hypothesis will be rejected at5% level of significance. Thus, there is a difference between the twovaccines with the shot vaccines being more effective.
N* P_{1}> 5, prove that the test is correct. However, if we conductanother calculation on the alternative hypothesis, the values of Zand P remain the same, and thus the alternative hypothesis cannot besupported on the basis of the findings (P_{1}> 5). The rule of the thumb advocates for the use of a sample sizegreater than 500, but in this case the sample size used N=500,therefore it does not meet the threshold of a good research. Thereare two limitations in this study, first there is no evidence thatthe data normally distributed as required by the thumb rule. Second,the calculations do not ascertain which of the two vaccinationmethods is more effective because the P and Z values are similar forboth(Hayes& Preacher, 2014).
Thefollow up test will be conducted by subjecting the same person to thetwo vaccines, this is because different people react differently andhave dissimilar physical characteristics. A pair test will beconducted with the use of the chisquare the 2*2 contingency tablewill be used(Hayes& Preacher, 2014).
Statisticalsignificance is based on mathematics and it is derived from thesample size and the chosen confidence level on which the test inconducted. On the other hand, practical significance is based factorssuch as cost, objectives and requirements of the research.
Statisticalsignificance depends on the sample size. For a big sample size, adifference of 3% between men (61%) and women (59%) in a sample isstatistically significant and thus will affect decision making,however in terms of practical significance is not important(Hayes& Preacher, 2014).
A30% percent difference for example, (90% for women less 60% for men)may be practically significant and therefore it will considered I thedecision making process whereas the same difference when approachedfor a statistical significance point of view, will not be importantand thus not featured in the decision making process(Hayes & Preacher, 2014).On the other hand, a difference of 30% would be practicallysignificant whereas it would not important in statisticalsignificance.
EssayQuestion Two
Thefindings of the researcher in the question above indicate that thereis a strong correlation between the intelligence quotient (IQ) andgrade point average (GPA). The r = 0.75 is the research confirm theexistence of a positive relationship between IQ and GPA.
Ther=0.75 only give us the relationship between the two variables, rgives us the value of the coefficient of determination R^{2}=0.56. The R^{2}meansthat only 56 percent of the level of IQ is explained by GPA,remaining 44% is accounted for by other factors outside the modelused for this research(Hayes & Preacher, 2014).The other factors might include, level of education, time dedicatedfor studies by the student, family background and academic resourcesavailable. This correlation illustrated by the research depict apositive relationship between IQ and GPA that is, the higher thelevel of IQ the more the GPA recorded by the student. However,increase in IQ might not increase GPA directly due to the influenceof other factors such as the environment for study and familybackground.
Thelimitation of correlation is that it only whether the relationship ispositive or negative, thus it cannot be used to quantify the results.As a result, a regression (causation) analysis is required toquantify the outcome from the research above. There are six variablesthat affect the size of correlation between IQ and GPA namely: thevariability between IQ and GPA. Thereare six variables affecting size of correlation, the differences inthe distribution of the two variables, absence of a linearrelationship, the error of measurement and characteristics of thesampling method used to compute correlation(Hayes & Preacher, 2014).Regression analysis method will be adopted to quantify therelationship between IQ and GPA this is because regression method isable to depict the exact relationship between the variables inquestion.
EssayQuestion Three
Thetable below show the data arranged into meaning full sets.
2.2 
4.7 
7.3 
4.1 
9.5 
15.2 
4.3 
9.5 
2.7 
3.1 
9.2 
2.9 
8.2 
7.6 
3.5 
2.5 
9.3 
4.8 
8.5 
8.1 
Thefigures were tabulated using the excel application, and thesolutions are displayed below

Themean of the data shown on the table illustrate that on overage,persons have a reaction time of 6.36 seconds. The mean is a goodmeasure for this type of data because of the existence of an outlier.Therefore, the median is more suitable to measure the reaction time.
Inthe event we omit the outlier in the data (15.2), the descriptivestatistics will be as follows
Mean 
5.894736842 
Standard Error 
0.632107479 
Median 
4.8 
Mode 
9.5 
Standard Deviation 
2.755292621 
Sample Variance 
7.591637427 
Kurtosis 
1.795892701 
Skewedness 
0.060172236 
Range 
7.3 
Sum 
112 
Confidence Level (95.0%) 
1.328008534 
Computingthe data without outliers we get a smaller mean (5.84) of responsetime the prior mean (6.36).
Group1Group 2

Descriptivestatistics for group 1 and 2 are as shown below.
Group 1 
  
  
  
Mean 
3.48 
Standard Error 
0.297695 
Median 
3.3 
Standard Deviation 
0.941394 
Sample Variance 
0.886222 
Kurtosis 
1.5709 
Skewedness 
0.190223 
Range 
2.6 
Sum 
34.8 
Group 2 
  
  
  
Mean 
9.24 
Standard Error 
0.707452 
Median 
8.85 
Mode 
9.5 
Standard Deviation 
2.237161 
Sample Variance 
5.004889 
Kurtosis 
6.86883 
Skewedness 
2.443916 
Range 
7.9 
Sum 
92.4 
Fromthe tables above, it is evident that all variables are unique in eachgroup, for example, mean, median, and standard deviation kurtosis.The standard error in group 2 increases the average response time.
Whenthe two samples are doubled, the results will be as presented in thetable below
Group 1 
Group 2 
2.2 
7.3 
2.5 
7.6 
2.7 
8.1 
2.9 
8.2 
3.1 
8.5 
3.5 
9.2 
4.1 
9.3 
4.3 
9.5 
4.7 
9.5 
4.8 
15.2 
2.2 
7.3 
2.5 
7.6 
2.7 
8.1 
2.9 
8.2 
3.1 
8.5 
3.5 
9.2 
4.1 
9.3 
4.3 
9.5 
4.7 
9.5 
4.8 
15.2 
Descriptivestatistics after doubling the samples is as shown below.
Group 1 
Group 2 

  
  
  
  
Mean 
3.48 
Mean 
9.24 
Standard Error 
0.204888 
Standard Error 
0.486902 
Median 
3.3 
Median 
8.85 
Mode 
2.2 
Mode 
9.5 
Standard Deviation 
0.916285 
Standard Deviation 
2.177493 
Sample Variance 
0.839579 
Sample Variance 
4.741474 
Kurtosis 
1.49733 
Kurtosis 
4.727574 
Skewedness 
0.17372 
Skewedness 
2.231898 
Range 
2.6 
Range 
7.9 
Sum 
69.6 
Sum 
184.8 
Fromthe chart above, it is evident that doubling the sample leads to achange in the values of the kurtosis, skewedness, standard error andstandard deviation. Increasing the sample size decreases all thevalues and thus makes the data more powerful due to minimization ofthe variance and standard deviation.
Part2
Theresearch paper cited above investigated the relationship between landownership and domestic violence against women in Nicaragua. Thehypothesis was set establish whether the ownership of land by womeninstigated domestics violence in Nicaragua. Previous studies by theinternational center cite that domestic violence is fuelled by thesocietal position of women in the household and disregards landownership as the main determinant. On the contrary, possession ofland was found to empower women and bolster their position as well astheir ability to seek legal redress against domestic violence.
Theresearch paper had the following null hypothesis: first, there is nodifferent between the two groups of women in the study, there is nodifference in the level of employment and domestic violence in thegroups, and last there exist no link between women empowerment, landownership and domestic violence.
Methodof Data Collection and Discussion
Thehousehold survey method was used to collect data in this study thesurvey was conducted to two groups of women. First, to the women whoare land owners and second, to the women who are not predominantowners of land. The study adopted the random sampling technique topick the sample from the total population of 380 women who had beenassisted by the government to own land. Out of the whole group, 174of them was randomly selected
Theresearcher used interviews which were conducted in private in orderto get the correct information and to make the intervieweescomfortable (Hayes& Preacher, 2014).Structured questionnaires were also administered to the targetpopulation. Before collection of the information from the samplegroup, the subjects were required to provide an oral consent on theiracceptance to take part on the study.
Theresearch was conducted in two areas, the first region was where thewomen had been assisted by the government to establish newsettlements and land ownership was facilitated by the state in theresettlement process. The government in collaboration with otherinternational firms conscious on gender equality assisted them to getland registered on their names and gave them jurisdiction over theirnew acquired property granted from the state. The organizations thattook part in the resettlement offered training to the women on genderequality and the ways through which a woman can be empowered in a bidto fight domestic violence. Data from this group revealed that casesof domestic violence were minimal, their chances of occurrencereduced as women derived more rights ownership of property in thehousehold. The other group comprised of women who had no any form ofland ownership and had no say in the property owned by the household.Among the second group, cases of domestic violence were prevalent ascompared to the first group.
Researchstudies on the second group revealed that domestic violence wasfueled by customary practices that bound women to their traditionalroles in the family men are buoyed by the customs of the societywhich prohibit women from any kind of property ownership in thehousehold. A majority of women in group two do not own land and havenot joined any of the women empowerment organizations. On the otherhand, majority of women in group one were found to collaborate withwomen empowerment organizations through which they enrolled for landownership programs and trainings. The research was conducted onwomen from all the communities in Nicaragua to ensure the sample wastrue representative of the study population (Hayes& Preacher, 2014).
Results
Thestudy conducted the research using the analysis of variance tests andthe following results were arrived at. The test done above revealedthat the women who are predominant land owners had a high level ofempowerment than their counterparts who did not own land. Theanalysis of variance method use d revealed that the two weredifferent on the some parameters including : Gender dogma F (1, 308)= 69.60, P< .00, sexual relation power F (1, 308) = 14.72, P<.00, partner mobility F(1, 308) = 2.76, P< .10 decision making at the household level F(1, 308) = 5.99, P< .02 financial decisions F(1,308) = 2.79, P<.10 autonomy F(1, 308) = 3.62, P< .06 and selfesteem F(1, 308) = 5.40, P< .03. The results above depict that women who are landowners aremore empowered compared to their counterparts with not access to anyform of land ownership.
Conclusion
Thediscussion above depict that there is an important link between landownership and women empowerment, land ownership among women leads toa decline in the prevalence and occurrence of domestic violence andthus improve the social welfare of families in Nicaragua. Landownership is a base for women to feel empowered and not to becondemned to their traditional roles in the marriage set up, thus itis one of the fundamental ways through which gender inequality can beeradicated in the society. The government should commission moreresearch on policies that remove barriers curtailing women’sefforts to become land owners in the society. This will go a long wayto assist in the fight against genders inequality and domesticviolence in the society.
References
Hayes,A. F., & Preacher, K. J. (2014). Statistical mediation analysiswith a multicategorical independent variable. BritishJournal of Mathematical and Statistical Psychology, 67(3),451470.
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