Week 3 Descriptive Statistics

 

1.  Variables and Research Question

Write in the Independent (IV) and Dependent (DV) variables. Identify the level of measurement, Categorical or Numeric, with an X.

Write your Research Question

Research Question:

            RQ:  Is there an average difference in SAT verbal scores (DV) based on ethnicity

Since R studio was not installed in my computer, I proceeded to do the analysis using STATA version 13. The descriptive statistics for each numeric variable is presented below (see Table 2).

2.  Review the Data

Missing Values

A.  Where any data rows removed? Explain.

 

Evaluate Limits

B.  Were any data removed? Explain.

 

Evaluate Outliers

C. Were extreme outliers found? If yes, list their values. Were they removed?

 

Categorical Data

D. Were changes made to the categorical data? Explain.

 

3.  Excel Setup

The Excel file is to be submitted with this worksheet.

 

 

 

4.  Descriptive Statistic - Graphics

Histogram

Paste (Ctrl V) the image in Appendix A in this paper.

E.  What did your observation tell you about the numeric variable?

 

Bar Chart

Right click and Copy. Paste the bar chart to Appendix B in this paper.

F.  What did your observation tell you about the categorical variable?

 

Scatterplot

Right click and Copy. Paste the scatterplot to Appendix C in this paper.

G.  What did your observation tell you about the relationship between these two variables?

Not Applicable

 

Normality

Place the output in Appendix D in this document.

H. What was your observation for normality? Explain.

 

5.  Descriptive Statistics – Calculations

Fill in Table 1 from the Xuru normality test output in Appendix D.

 

The SAT Verbal Descriptive Statistics are not from the dataset.  

Table 1

Descriptive Statistics on Numeric Variables

Note. The confidence interval is applicable for normally distributed data.

The sample data was not from a normally distributed population based on the fact that the resultant p-value from the test was less than 0.05 level of significance thus falling in the rejection region, we therefore reject the null hypothesis that the population is normally distributed. The plotted qq plot supports the findings

 

6.  Descriptive Statistics - Interpretation

Interpretation

Numeric Variable Name

            The numeric variable is the SAT scores collected from both black and white students in colleges. It is a continuous variable.  The minimum score was 14 and the maximum was 1278. Most of the students scored 154 and the mean of the scores was not centralized since the population was not normally distributed.

 

Categorical Variable Name

            There were 32 students picked from each college, each had sat for the SAT and the sores had been recorded. Of these, 16 were black and 16 were white, of the black, 8 had taken a foreign language and 8 had not. Their SAT scores were recorded.

 

 

 

Next Steps

1.      Post your paper to the team by midnight Day 5 for member review.

2.      Review member papers and post your critique by midnight Day 6. 

3.      Make corrections to this paper based on the critique and member collaboration.

4.      Update your Business Research Paper (time permitting) by midnight Day 7.

5.      Submit this paper and your created member review papers by midnight Day 7.

 

 

 

 

 

Appendix D: STATA findings

 

1.      Shapiro_Wilk normal test

swilk SAT_scores

                   Shapiro-Wilk W test for normal data

    Variable |    Obs       W           V         z       Prob>z

-------------+--------------------------------------------------

  SAT_scores |    231    0.94541      9.237     5.152    0.00000

2.      QQ plot

. qnorm SAT_scores

 

 

3.      Summary statistics

. summarize SAT_scores

    Variable |       Obs        Mean    Std. Dev.       Min        Max

-------------+--------------------------------------------------------

  SAT_scores |       231    650.0303    362.3033         14       1278

 

4.      Median and quantiles

. tabstat SAT_scores, statistics( mean iqr median p95 p5 )

    variable |      mean       iqr       p50       p95        p5

-------------+--------------------------------------------------

  SAT_scores |  650.0303       622       683      1165        79

----------------------------------------------------------------

5.      Confidence intervals

. ci SAT_scores

    Variable |        Obs        Mean    Std. Err.       [95% Conf. Interval]

-------------+---------------------------------------------------------------

  SAT_scores |        231    650.0303    23.83781        603.0619    696.9987

 

 

 

 

 

Appendix E: Table of percentages

 

 

 

 

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