# Sample Undergraduate Agriculture Statistical Analysis

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## Introduction

This report has been formulated to carry out a detailed statistical analysis of the data provided related to the knowledge of people regarding the genetically modified crops and the information regarding the crops provided by the scientists, politicians, and mass media.

The data has been gathered and coded into numbers to carry out statistical analysis in an efficient manner. This report has included a comprehensive discussion regarding the methodology that the researcher has employed.

The analysis is carried out based on the details mentioned in the report’s methodology section. Based on the analysis, this report also includes a comprehensive discussion and recommendations.

Lastly, this report includes a conclusion based on the information that has been extracted from the analysis of this dataset. Based on the information that is available on the GM crops and the opinion of the public, the following objectives have been formed:

- To investigate how social, socioeconomic, environmental, governmental, and health-related factors and their risks and benefits influence opinion and acceptance of genetically modified crops.
- To fail to reject the alternative hypothesis.

## Methodology

This research has followed quantitative grounds to collect the data and then provide analysis based on the data. The researcher has used primary data to extract information with the help of a survey questionnaire as the research instrument.

By utilising the survey questionnaire as the research instrument, the researcher has promptly and conveniently obtained information from the respondents.

The questionnaire included seventeen questions altogether, out of which some of them were divided further into sub-questions. Some of the questions were based on the Likert scale, and some were comments based while some were simply yes-no questions.

A total of 163 respondents were selected to carry out the data collection. The sample size for this research was selected with the help of a convenience sampling method where the researcher considered convenience and ease (Etikan, Musa, and Alkassim, 2016, p. 4).

After collecting data from the respondents, the data was coded into numbers to analyse it. The data analysis of this research is carried out with the help of excel and different statistical tests. Following are the tests which have been carried out for the analysis of this dataset.

## Mann Whitney U Test

This statistical tool is considered to be a non-parametric version of the two-sample T-test. This test is more flexible than the two-sample T-test because it does not consider any assumption regarding the distribution of the population (McKnight and Najab, 2010).

This test is carried out to compare two populations the formula for calculating U-statistic for Mann Whitney test is explained below:

**Where,**

**R= sum of ranks in the sample**

**N= number of items in the sample**

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## Kruskal Wallis test

This test is often considered to be the non-parametric version of one-way ANOVA. Because of its non-parametric nature does not assume that the data follow any kind of pattern or distribution (Wu and Guan, 2015, p. 556).

This test is used when the dataset does not meet the assumption such as normality of distribution. This test makes use of the ranks of the data values rather than utilising the data values. The formula for H-statistic is below:

**Where,**

**N= sum of sample sizes**

**C= number of samples**

**Tj= sum of ranks in the jth sample**

**Nj= size of jth sample**

## Spearman Correlation

This statistical test is used to find correlation among two variables based on the difference of their ranks (Myers and Sirois, 2006). It can be said that the spearman correlation among two variables is equal to the Pearson correlation among the rank of these two variables.

The Spearman correlation coefficient tends to assess the monotonic relationship (Hauke and Kossowski, 2011, p. 93). A perfect +1 or -1 Spearman correlation occurs if there is no repetition in the values of the data set; however, this rarely happens. This kind of correlation is appropriate for both continuous and discrete variables.

## Analysis

## Spearman Correlation

To carry out the correlation analysis of this data set, excel has been used where Spearman’s coefficient has been calculated to assess the interdependence. The correlation is assessed among two variables of the data, i.e., age and seeking of education on genetically modified crops. Based on these two variables, the hypotheses of this test are:

**H _{o} **= There is no significant correlation among the age of the respondents and information seeking of respondents regarding genetically modified crops

**H _{a}** = There is a significant correlation among the age of the respondents and information seeking of respondents regarding genetically modified crops

The pressing reason for the assessment of interdependence among these two variables is that it will allow terms of drawing out a conclusion regarding age having a significant relationship with the urge of respondents to know about genetically modified crops.

For this data set, the correlation has been measured for the variables age and information-seeking of genetically modified crops. For each variable first rank was assigned, then the Spearman correlation coefficient was calculated.

The calculated Spearman coefficient was calculated to be 0.0855. The sign for the coefficient is positive, which means a positive relationship among both the variables.

The strength of correlation among the variables under study can be interpreted by the value of the Spearman correlation coefficient, which for this model is 0.0855.

To prove that the relationship among the variables is strong, the value of the Spearman coefficient needs to be greater than 0.70. For this model, the value of the Spearman correlation coefficient is 0.085, which means that the relationship among both variables is very weak. Irrespective of the existence of a relationship among both variables, the strength of the relationship is quite weak.

## Mann Whitney U test

This test has been carried out for this data set for comparing two variables alienated public opinion and the information provided by scientists, politicians, and mass media regarding the GM crops.

The purpose of comparing both the variables is to depict whether the mean for both the groups is equal or not. Based on the above assumption following are the hypotheses which are tested from the Mann Whitney U test:

**H _{0}**: The median of Alienated Public Opinion and information provided by the scientists, politicians, and mass media are not the same

**H _{a}**: The median of Alienated Public Opinion and information provided by the scientists, politicians, and mass media are the same

The fundamental aim of considering both the variables to carry out this test is that the researcher aims to analyse the difference in both the independent and dependent variables.

In this case, the independent variable is information given by scientists, politicians, and mass media. The dependent variable of the research is the public opinion regarding genetically modified crops. Following are results that have been obtained from carrying out the Mann-Whitney U test on the data set.

As indicated by the formula, n1 refers to the number of samples for group 1, and n2 refers to the number of samples for group2, which is 24 for each group.

The U1 value represents the U-statistics for the group “alienated public opinion,” which is calculated by the formula specified in the prior part of the report. U2 is the U-stat for group 2, which is “information provided by scientists, politicians, and mass media”.

By finding out the difference of U1 and U2 the U statistic is calculated to be -497. The standard deviation calculated for this test is 48.49 which means that the data is deviated from mean value by 48.49 units.

The value of z-score in the above table shows that the standard deviation is above the mean level. As p in the above table is less than the acceptance value of 0.05, the null hypothesis is rejected.

## Kruskal Wallis

For this data set, the Kruskal-Wallis test is carried out to determine one-way ANOVA between three groups: alienated public opinion regarding GM crops, information provided by scientists, politicians and mass media, and education level of the respondents.

To conduct this test, two independent variables are required and one dependent variable is required which is ordinal. The two independent variables of this model are alienated public opinion and the information provided regarding genetically manufactured crops. The dependent variable of this model is education level of the respondents.

The researcher has aimed to find out the impact of alienated public opinion and information regarding GM crops on the educational level of the respondents. Based on this information, the following hypotheses are tested through the Kruskal Wallis test.

**Ho=** All groups are derived from identical populations

**Ha=** At least one of the groups has disproportionately large share of higher numbers

This test has been carried out for this data analysis because it is assumed that the two variables above might impact the respondents’ educational qualification. Following are the results of the test which is obtained from excel.

The major value that needs to be interpreted to deduce the Kruskal Wallis test results is H-statistic and the critical value. The critical value of the dataset should be less than the calculated value of H-statistic.

As for this data set the H-stat value calculated by ranking each of the groups mentioned above. The formula mentioned in the above section of the report is 11953.

The p value for this data set is 0.000 which is less than the value of alpha hence the null hypothesis for the test is rejected. If the critical value of test is significantly lower than the H-stat value then it means that difference among the rankings of within the sample group is significant.

For this data set, it can be concluded that as the value of Kruskal Wallis test is higher than the critical chi-square value, the null hypothesis is rejected, which means that at least one of the groups has a disproportionately larger share of higher numbers.

# Conclusion

Conclusively, it can be said that this report has analysed the data set efficiently with the help of range of different statistical tests. The test results conclude that there is a significant impact of alienated public opinion and the biased information provided by scientists, politicians, and mass media.

For all the different tests carried out for this data analysis report, the null hypothesis has been rejected, which shows that the analysis has shown desirable results.

For the correlation analysis it has been found that irrespective of the existence of relationship among age and information seeking the strength of relationship is quite weak. The Mann Whitney U test results show that the mean value of alienated public opinion and the information regarding genetically manufactured crops are not equal.

The results of Kruskal Wallis test shows that the value of Kruskal Wallis test is higher than the critical chi-square value hence the null hypothesis is rejected which means that At least one of the groups has disproportionately large share of higher numbers.

## References

Bain, L., 2017. *Statistical analysis of reliability and life-testing models: theory and methods*. Routledge.

Hess, A.S. and Hess, J.R., 2017. Understanding tests of the association of categorical variables: the Pearson chi‐square test and Fisher’s exact test. *Transfusion*, *57*(4), pp.877-879.

McKnight, P.E. and Najab, J., 2010. Mann‐Whitney U Test. *Corsini Encyclopedia of Psychology*.

Myers, L. and Sirois, M.J., 2006. Spearman correlation coefficients, differences between. *Wiley StatsRef: Statistics Reference Online*.

Wu, B. and Guan, W., 2015. Reader reaction on the generalized Kruskal–Wallis test for genetic association studies incorporating group uncertainty. *Biometrics*, *71*(2), pp.556-557.

Etikan, I., Musa, S.A. and Alkassim, R.S., 2016. Comparison of convenience sampling and purposive sampling. American Journal of Theoretical and Applied Statistics, 5(1), pp.1-4.

**Frequently Asked Questions**

**To perform undergraduate agriculture statistical analysis:**

1. Collect relevant data on agricultural variables.

2. Clean and organize the data.

3. Choose appropriate statistical tests.

4. Analyze the data using software like R or SPSS.

5. Interpret the results and draw conclusions.

6. Present findings in a clear and concise manner.