Statistics Assignment Samples

Assignment Sample On Statistics

Question:-  

Analyse à Descriptive à frequencies (choose statistics and charts to do the right stats and the histogram)

Analyse à Descriptive à Q-Q Plot?

Analyse à Descriptive à Correlate à Bivariate?

Analyse à Descriptive à Scale à Reliability Analysis?   

Answer:-

Activity 1

The data from the Excel spreadsheet are appropriately entered in the SPSS worksheet under the respective variable names (Te Grotenhuis, and Matthijssen, 2015).The Student_ID is entered as string variable whereas all the others are numeric variables.

Activity 2

The variable Student_ID is of string type. Hence, any calculations or graphs cannot be produced for this variable. The calculations are done with ten variables from the given dataset.

1. A histogram represents the distribution of the data points through graphical representation. It helps to estimate the probability distribution of a variable that is continuous. Karl Pearson was the first to introduce it. A frequency histogram is a type of histogram that represents the frequency distribution of the various observations in the data set. The height of the vertical bars is proportional to the frequency of the corresponding data point.

The normal q-q plot is a type of probability plot. It is a graphical technique to observe the deviation of the data from the normality by plotting the quantiles. It helps to identify the outliers in the data set (Cleophas, and Zwinderman, 2015). The graph is plotted as such that the x-axis has the observed values whereas the y-axis has the expected values supposing that the data follows a normal distribution. If the data is a normal, then the graph will give a straight line.

The detrended normal q-q plot is a graphical representation to observe the deviation of the data points from the normal (Babbie, et al., 2015). The x-axis plots the observed values and the y-axis plots the difference between the expected and observed values. It sometimes makes to decipher the pattern of data set.

From all the graphs, it can be said that the data follows a normal distribution except for three data points with deviates extremely from normality.

Generally, by the term Mean we understand Arithmetic mean. It gives the nothing but the average of the data points in the sample. Moreover, it is when the data is normal; it is an appropriate measure of central tendency (Ho, and Carol, 2015). But, it fails to indicate the centre of the data if the dataset is skewed or contains extreme outliers.

Standard deviation is a measure to calculate the deviation of the data from the measure of central tendency. In general the standard deviation is obtained for the mean of the data (Bickel, and Doksum, 2015).

The descriptive statistics Minimum and Maximum denotes the minimum and the maximum value of the data points in the dataset.

   Year_Enrolled

HI001_Final_Exam

HI001_Assignment_01

 HI001_Assignment_02

HI002_Final_Exam

HI002_Assignment_01

HI002_Assignment_02

HI003_Final_Exam

HI003_Assignment_01

HI003_Assignment_02

Activity 3

The term correlation is used to study the dependence or the relation between the two data sets. The Pearsonian Product-moment correlation coefficient is one of the common measures of correlation. The term positive correlation means that the datasets are directly proportional to each other. And the term negative correlation means the two data sets are inversely proportional to each other (Weiss, and Weiss, 2012). The value of the correlation coefficient varies between -1 to 1. The value -1 or 1 defines a perfect correlation and is termed as a totally negative and total positive correlation.

Correlation between HI001 FINAL EXAM and HI001 ASSIGNMENT 01

From the above table, it can be determined that the final exam and assignment 1 is positively correlated. But the strength of the correlation is questionable. Moreover, the correlation coefficient is significant at 99% confidence interval which means that 99% confidence interval carries this value of correlation.

Correlation between HI001 FINAL EXAM and HI001 ASSIGNMENT 02

The final exam and assignment 2 has a moderately positive correlation between each other. The correlation coefficient is significant at 99% confidence interval. The 99% confidence interval contains this value of correlation coefficient (Nimon, 2015).

Correlation between HI001 ASSIGNMENT 01 and HI001 ASSIGNMENT 02

The correlation between assignment 1 and assignment 2 is more than a moderate positive relation. Moreover, the correlation coefficient is significant at 99% confidence interval. Hence, it can be said that the 99% confidence interval contains this value of correlation.

Correlation between HI002 FINAL EXAM and HI001 ASSIGNMENT 01

The final exam and assignment 1 has a very poor positive correlation between each other. The 95% confidence interval does not contain this value of correlation coefficient that implies that the correlation coefficient is insignificant at 95% confidence interval.

Correlation between HI002 FINAL EXAM and HI001 ASSIGNMENT 02

From the above table, it can be determined that the final exam and assignment 2 is positively correlated. But the strength of the correlation is questionable. Moreover, the correlation coefficient is significant at 99% confidence interval which means that 99% confidence interval carries this value of correlation.

Correlation between HI002 ASSIGNMENT 01 and HI002 ASSIGNMENT 02

The correlation between assignment 1 and assignment 2 is more than a moderate positive relation. Moreover, the correlation coefficient is significant at 99% confidence interval. Hence, it can be said that the 99% confidence interval contains this value of correlation.

Correlation between HI002 FINAL EXAM and HI001 ASSIGNMENT 01

The final exam and assignment 1 has a negligible positive correlation between each other (Jarman, 2015). The correlation coefficient is insignificant at 5% level of significance. This implies that 95% confidence interval does not contain this value of correlation coefficient.

Correlation between HI002 FINAL EXAM and HI001 ASSIGNMENT 02

From the above table, it can be determined that the final exam and assignment 2 is positively correlated. But the strength of the correlation is extremely poor. Moreover, the correlation coefficient is not significant at 95% confidence interval which means that 95% confidence interval does not carry this value of correlation.

Correlation between HI002 ASSIGNMENT 01 and HI002 ASSIGNMENT 02

The assignment 1 and assignment 2 is positively correlated to each other. They have a moderate correlation. And this correlation is significant in 1% level of significance which implies that this value of correlation is contained in 99% confidence interval.

Correlation between HI001 FINAL EXAM and HI002 FINAL EXAM

There is an almost negligible positive relation between HI001 the final exam and HI002 final exam. Moreover, the correlation coefficient is insignificant at 5% level of confidence, which implies that the 95% confidence interval does not contain this value of correlation coefficient (Morgan, et al., 2012).

Activity 4

The overall consistency of data is measured by reliability. If an experiment gives similar outcomes when performed under the same conditions, then a high reliability of the data can be observed (Meeker, and Escobar, 2014). Cronbach’s alpha and Cohen’s Kappa are some of the common tools to measure the consistency of the data. The measure used in this problem is Cronbach’s alpha measure.

The internal reliability or consistency is most commonly measured with the help of Cronbach’s alpha. The analysis of a 5 point Likert scale questionnaire is usually done by the help of Cronbach’s alpha. High reliability of the data set is given by a high value of the Cronbach’s alpha. The formulae for Cronbach’s alpha is defined as

Where N = the total number of data points.

             c_bar = the inter-item covariance of the data points

              v_bar = average variance of the data points.

It can be concluded from the formulae that Cronbach's alpha is dependent on the number of data points used in the analysis (Gwet, 2014). It also has a direct proportionality with the inter-item covariance. This implies that the value of alpha also increases if the inter-item covariance increases, keeping the size of the data set constant.

The Cronbach’s alpha for the given data set is

From the above table, it can be observed that the value of Cronbach's alpha is 0.443. This implies that the internal consistency of the data is very poor. It can be concluded that the reliability of the data is not acceptable.

The following data shows that if any of the variables is deleted whether the Cronbach’s alpha is improved or not.

From the above table it can be seen that the if the items HI002 ASSIGNMENT 01 and HI003 ASSIGNMENT 01 are removed from the variable list then the reliability of the data can be improved (Elliott, and Woodward, 2015). But if the variables HI001 FINAL EXAM and HI003 FINAL EXAM are removed from the variable list then the reliability of the data will fall drastically. Hence, these two variables must not be deleted from the variables set Horwitz, S. M., (Hoagwood, et al., 2014).

If the two variables HI002 ASSIGNMENT 01 and HI003 ASSIGNMENT 01are deleted, then the maximum reliability is obtained.

It is observed that if the two variables are removed then the reliability of the data increases from 0.443 to 0.469. This is the maximum reliability that can be obtained from the given data set.

References

Babbie, E., Wagner III, W. E., and Zaino, J. (2015). Adventures in social research: Data analysis using IBM® SPSS® Statistics. Sage Publications.

Bhushan, M., and Ketchen, M. B. (2015). Basic Statistics and Data Visualization. In CMOS Test and Evaluation (pp. 311-345). Springer New York.

Bickel, P. J., and Doksum, K. A. (2015). Mathematical Statistics: Basic Ideas and Selected Topics, volume I (Vol. 117). CRC Press.

Cleophas, T. J., and Zwinderman, A. H. (2015). Quantile-Quantile Plots, a Good Start for Looking at Your Medical Data (50 Cholesterol Measurements and 58 Patients). In Machine Learning in Medicine-a Complete Overview (pp. 253-259). Springer International Publishing.

Elliott, A. C., and Woodward, W. A. (2015). IBM SPSS by Example: A Practical Guide to Statistical Data Analysis. SAGE Publications.

Gwet, K. L. (2014). Handbook of inter-rater reliability: The definitive guide to measuring the extent of agreement among raters. Advanced Analytics, LLC.

Ho, A. D., and Carol, C. Y. (2015). Descriptive Statistics for Modern Test Score Distributions Skewness, Kurtosis, Discreteness, and Ceiling Effects.Educational and Psychological Measurement, 75(3), 365-388.

Horwitz, S. M., Hoagwood, K., Stiffman, A. R., Summerfeld, T., Weisz, J. R., Costello, E. J., ... and Norquist, G. (2014). Reliability of the services assessment for children and adolescents. Psychiatric Services.

Jarman, K. H. (2015). Beyond Basic Statistics: Tips, Tricks, and Techniques Every Data Analyst Should Know. John Wiley and Sons.

Meeker, W. Q., and Escobar, L. A. (2014). Statistical methods for reliability data. John Wiley and Sons.

Morgan, G. A., Leech, N. L., Gloeckner, G. W., and Barrett, K. C. (2012). IBM SPSS for introductory statistics: Use and interpretation. Routledge.

Nimon, K. (2015). Secondary Data Analyses From Published Descriptive Statistics Implications for Human Resource Development Theory, Research, and Practice. Advances in Developing Human Resources, 17(1), 26-39.

Rachel, and Bosley, M. (2015). Active learning with graphs and charts. Primary Teacher Update, 2015(41), 31-34.

Te Grotenhuis, M., and Matthijssen, A. (2015). Basic SPSS Tutorial. Sage Publications.

Weisburd, D., and Britt, C. (2014). Representing and Displaying Data. InStatistics in Criminal Justice (pp. 36-64). Springer US.

Weiss, N. A., and Weiss, C. A. (2012). Introductory statistics. Pearson Education.