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Module 5/6 Creating Inferential Statistics Report
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Module 5/6 Creating Inferential Statistics Report

Introduction

My group and I designed a survey to learn about the current education level of nurses, and their plans for further education.  We also were interested in finding any relationships between their current education levels, plans to continue their education, their years in nursing, and their current age.  Our population was those currently working in the nursing field, including Certified Nursing Assistants, in the United States.  We did not obtain a random sample for this survey.  Instead we surveyed co-workers in the nursing field at the various facilities where we work.  My nurses were given a paper survey form with our questions to fill out.  Others in my group may have used different methods of obtaining the answers to the survey questions.  This would be considered a convenience sample, with a voluntary response aspect, as not everyone we asked took the time to respond.  Also, there was some reluctance to take the survey and reveal age, even though they were told their responses would only be used for a class project, and they would remain anonymous.  Also, with age there is the possibility that they may not have listed their age as honestly as we would have liked.  I believe there is also a time factor which comes in to play here, as life changes, opportunities in the nursing field open up, and jobs change and evolve, a nurse may be more likely to continue their education in the future, but may have indicated that they had no intention to do so at this time - on this survey.

We asked the following questions on our survey:

1. The highest level of education in the nursing field you have obtained is

     Professional Certification          [   ]

     Associate Degree                     [   ]

     Bachelor Degree                      [   ]

     Master Degree                         [   ]

     Doctorate Degree                    [   ]

2. Are you planning to continue your education in the nursing field?   

    Yes             [   ]

     No            [   ]

3. How many years have you been in the nursing field?  ___

4. What is your age in years? ___

Looking at the Categorical-Variable -- Are You Planning to Continue Your Education in the Nursing Field.

The responses to the question “Are you planning to continue your education in the nursing field?” are shown in the pie chart below.

Result 1: Pie Chart of Plan to Continue Education in Nursing   [Info]
Right click to copy

On the pie chart above, one can say that 58 of the 132 nurses who responded to our survey, or about 43.9% said "yes", they planned to continue their education in the nursing field.  Nurses responding "no", to this question is represented by 74 of the nurses surveyed, or 56.1%. 

Result 2: One Sample Prop. Summary of Plan to Continue Education   [Info]
One sample proportion confidence interval:
p : Proportion of successes
Method: Standard-Wald

95% confidence interval results:
ProportionCountTotalSample Prop.Std. Err.L. LimitU. Limit
p581320.439393940.0431985290.354726380.5240615

The chart above shows the 95% confidence interval for the proportion of our sample nurse group that answered “yes” to the question: “Are you planning to continue your education in the nursing field”.  In our sample, the proportion of “yes” responses to total responses is 0.439, so we would say p hat is 0.439.  From the chart, we see that the lower limit is 0.355, and the upper limit is 0.524.  The 0.95 or 95% confidence interval estimate of the population proportion of nurses, p, is represented by 0.355 < p < 0.524.  This means we are 95% confident that the interval from 0.355 to 0.524 actually does contain the true value of the nursing population proportion p.  Notice our sample proportion 0.439, does fit in this interval. If we were to select many different samples of size n=132 and construct the corresponding confidence intervals, 95% of them would actually contain the value of the nurse population proportion p.  We are 95% confident that the proportion of nurses in our population of nurses who would answer “yes” that they are "planning to continue their education in the nursing field", lies between 0.355 and 0.524.  We can calculate our margin of error E as (0.524 – 0.355)/2 = 0.169/2 = 0.085.

Looking at the Numerical Variable of Years in the Nursing Field

The responses to our question: “How many years have you been in the nursing field?” are shown in the histogram and box plot of the data, along with the summary statistics below.

Result 3: Histogram of Years in Nursing Field   [Info]
Right click to copy

Result 4: Boxplot of Years in Nursing   [Info]
Right click to copy

Result 5: Summary Stats for Years in Nursing   [Info]
Summary statistics:
ColumnnMeanVarianceStd. dev.MedianRangeMinMaxQ1Q3
Yrs. in Field13212.784091103.6534110.18103210391404.519

A 95% confidence interval for the population mean µ, is shown below

Result 6: One Sample T for Years in Nursing   [Info]
One sample T confidence interval:
μ : Mean of variable

95% confidence interval results:
VariableSample MeanStd. Err.DFL. LimitU. Limit
Yrs. in Field12.7840910.8861450813111.03108514.537097

The 95% confidence interval means that if we were to survey many different nurses of sample size n=132, approximately 95% of these samples would result in confidence intervals that contain the true population mean μ.  We can also say, we are 95% confident that the mean of the nurse population in “years in the nursing field” will lie between 11.03 years and 14.54 years.  Our sample mean is x bar=12.78.  Because we do not know the population mean of all nurses in the United States, we were forced to use the t-interval method for this calculation, with a degrees of freedom of n-1, or 132-1 which gives us 131 degrees of freedom.  This wider interval, produced by the t method over the z method, is the price we had to pay for only having a sample mean to use in our calculations.

 

HTML link:
<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=69279">Module 5/6 Creating Inferential Statistics Report</A>

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