Coyne and Messina Articles, Part 2 Statistical Assessment
Details:
1) Write a paper of 1,000-1,250 words regarding the statistical significance of outcomes as presented in Messina’s, et al. article “The Relationship between Patient Satisfaction and Inpatient Admissions Across Teaching and Nonteaching Hospitals.”
2) Assess the appropriateness of the statistics used by referring to the chart presented in the Module 4 lecture and the resource “Statistical Assessment.”
3) Discuss the value of statistical significance vs. pragmatic usefulness.
4) Prepare this assignment according to the APA guidelines found in the APA Style Guide located in the Student Success Center. An abstract is not required.
5) This assignment uses a grading rubric. Instructors will be using the rubric to grade the assignment; therefore, students should review the rubric prior to beginning the assignment to become familiar with the assignment criteria and expectations for successful completion of the assignment.
Statistics: What you Need to Know
Introduction
Often, when people begin a statistics course, they worry about doing advanced mathematics or their math phobias kick in. Understanding that statistics as addressed in this course is not a math course at all is important. The only math you will do is addition, subtraction, multiplication, and division. In these days of computer capability, you generally don’t even have to do that much, since Excel is set up to do basic statistics for you. The key elements for the student in this course is to understand the various types of statistics, what their requirements are, what they do, and how you can use and interpret the results. Referring back to the basic components of a valid research study, which statistic a researcher uses depends on several things:
- The research question itself
- The sample size
- The type of data you have collected
- The type of statistic called for by the design
All quantitative studies require a data set. Qualitative studies may use a data set or may use observations with no numerical data at all. For the purposes of the next modules, our focus will be on quantitative studies.
Types of Statistics
There are several types of statistics available to the researcher. Descriptive statistics provide a basic description of the data set. This includes the measures of central tendency: means, medians, and modes, and the measures of dispersion, including variances and standard deviations. Descriptive statistics also include the sample size, or “N”, and the frequency with which each data point occurs in the data set.
Inferential statistics allow the researcher to make predictions, estimations, and generalizations about the data set, the sample, and the population from which the sample was drawn. They allow you to draw inferences, generalizations, and possibilities regarding the relationship between the independent variable and the dependent variable to indicate how those inferences answer the research question. Researchers can make predictions and estimations about how the results will fit the overall population. Statistics can also be described in terms of the types of data they can analyze. Non-parametric statistics can be used with nominal or ordinal data, while parametric statistics can be used with interval and ratio data types.
Types of Data
There are four types of data that a researcher may collect.
Nominal Data Sets
The Nominal data set includes simple classifications of data into categories which are all of equal weight and value. Examples of categories that are equal to each other include gender (male, female), state of birth (Arizona, Wyoming, etc.), membership in a group (yes, no). Each of these categories is equivalent to the other, without value judgments.
Ordinal Data Sets
Ordinal data sets also have data classified into categories, but these categories have some form or order or ranking attached, often of some sort of value / value perception. Examples include rankings of poor, fair, good, excellent, very satisfied to very dissatisfied, etc. While the categories may be rank ordered, there are not equal intervals between the categories. The difference between poor and fair is not necessarily the same difference between good and excellent, for example.
Interval Data Sets
Interval data sets have equal intervals between the units of measure, although they lack a true zero. For example, test scores of 50 and 60 have the same interval between them as test scores of 70 and 80. Degrees of body fever have the same difference between a temperature of 97.5 and 98.5 as between a temperature of 99 and 100. However, the body does not reach a true zero temperature. IQ scores have the same interval between 75 and 100 as they do between 100 and 125.
Ratio Data Sets
Ratio data sets have equal intervals, and a true zero to the scale. Examples include water temperatures when the temperature of the water has the same interval between 20 and 25 degrees as between 30 and 35 degrees, with a true zero at the point water freezes solid (in Celsius; Fahrenheit is 32 degrees above Fahrenheit “0”). Another example may be the level of a certain drug in the blood stream. There is a true zero, and the level of drug at 100 mcg/cc is exactly double the level of drug at 50 mcg/cc.
A Review of Data Sets:
Nominal − Data into categories with equal weight and value
Ordinal − Data into categories with rank ordering
Interval − Data with equal intervals between all data points, but no true zero
Ratio − Data with equal intervals between all data points, plus a true zero on the scale
Knowing what data type is being used in a statistical analysis is important because all data types cannot be used by all statistics. As noted above in Types of Statistics, nominal and ordinal data can be analyzed with non-parametric statistics, while interval and ratio data can be analyzed by parametric statistics. As a rule of thumb, you should use the highest statistic your data set will allow to extract as much information as possible.
Choosing the Right Statistics
In order to select the appropriate statistic for a research study, start with the basics.
What Does the Research Question Ask?
If you are comparing one data set to another or one group to another, use a method of description to see if they are alike. If you are asking if one group is different from another in a meaningful way, use methods of inference. For example, let’s say you have two samples of staff intention to stay on their jobs. In the first sample, the staff has received a raise. In the second, they have not. The samples are described as follows:
Sample 1 − mean score of 95, standard deviation + or − 4, range of scores 91-99 (meaning a likelihood they will stay)
Sample 2 − mean score of 80, standard deviation + or − 16, range of scores 64-96 (meaning a lower, and wider ranging, likelihood of staying)
If you are asked just to compare the two data samples, you use the data to say that the mean score in Sample 1 shows higher intent to stay on the job than the mean score in Sample 2. Also, the standard deviation shows that there is more consistency in the scores in Sample 1 (smaller deviation) than in Sample 2 (larger deviation). These are methods of description from which you can draw some conclusions. You can answer the question: what do the data sets look like? However, if you are asked to determine whether Sample 1 is significantly higher than Sample 2 in intention to stay on their jobs, you would need to use statistics such as a t-test or ANOVA (analysis of variance) to determine whether the difference is statistically significant. If you had been asked to determine whether it was likely that the raise contributed to the differences in intention to stay on the job, you would also need to use an inferential statistic, such as t-test or ANOVA, which enabled you to draw that inference. So, if the research question asks what a data set looks like, you can use the descriptive statistics. If you want to know what the variables listed are inferring, you must use the inferential statistics, as well.
What is the Sample Size?
Some statistics are designed to be used with small sample sizes, generally less than 30, such as t-tests. Others fit better with larger sample sizes, such as ANOVAs. For many statistics, sample size is not a critical factor, but it is helpful to know if the sample is large enough to warrant the use of the statistics used.
What Type of Data is Used?
Again, nominal and ordinal data can be analyzed with non-parametric statistics, while interval and ratio data can be analyzed by parametric statistics. The key data type is in the dependent variable. If you have interval or ratio data in the dependent variable, you can use parametric statistics for your analysis.
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