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 / val.

1. 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

2. 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.

3. 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

4. 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 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.
In order to help you review studies in terms of their selection of
statistics, refer to the following chart:
Using Statistical Assessment
Statistic
Data Type

5. Sample Size
Research Question
Mean and Standard Deviation
Interval or ratio
>2
What does the data set look like?
Frequency Distribution
Nominal-Ratio
>2
What does the data set look like?
Chi-Square
Nominal-Ordinal
>4
Is the variance of one variable equal to or different from
another variable
Correlation Coefficient
Interval-Ratio
>4
What is the relationship between two variables?
t-Test
Interval-Ratio
<30
Is there a significant difference between two groups? May be
intrinsic or may be experimental
ANOVA (Analysis of Variance)
Interval-Ratio
>30
Is there a significant difference between 2 or more groups?
Regression Analysis
Interval-Ratio
>30
How much of the change in the dependent variable is predicted
by the independent variable or variables?
Statistical Significance
The concept of statistical significance is a part of inferential
statistics. When you are looking for differences or changes in

6. data sets as a result of the impact of an independent variable,
you need to be able to determine if the changes are significant
or resulting from random chance. Statistical significance
answers the question: What is the probability that the results
seen in this study are due to the effects of the independent
variable on the dependent variable rather than random chance?
Significance is also expressed as Type I Error, which is the
possibility of rejecting a true finding as false. It is depicted in
statistics as an alpha character (Greek), or "α." It can also be
expressed as p<0.05. The level at which alpha is set will tell
you that the probability of the finding being attributable to
chance itself is less than (<) 0.05%. Other common settings for
the alpha include 0.01% or even 0.001%. Most studies require at
least an alpha of 0.05% in order for the results to be deemed
significant.
Referring to the research study in Coyne et al (Coyne, Richards,
Short, Shultz, and Singh, 2009) on hospital cost and efficiency
and the effects of hospital size and ownership, the research
question asked if size and ownership type made a difference in
the efficiency and cost results of hospitals in the State of
Washington. The sample size was 100 hospitals. The dependent
variables, efficiency and cost measures, used numbers with a
true zero (cost, occupancy, revenue, etc) so that the data would
be classified as a ratio. The independent variables were hospital
size and ownership type, which could be classified as ordinal
for size (small, medium, large) and nominal for ownership type
(not for profit; government owned). The statistic selected was
an ANOVA (good choice), and the statistical significance was
set as 0.05% alpha. Read the results on page 168, Table 3, to
determine which results were significant, or less than 0.05%.
Note that bed size made a significant difference in two of the
efficiency ratios and two of the cost ratios. Also note which
ownership affected one of the efficiency ratios and two of the
cost ratios. The interaction of the two independent variables
affected two of the efficiency ratios.
Conclusion

7. Picking the correct statistic to answer the research question, fit
the sample size, and fit the data types is an essential element of
a useful and valid research study. When these are correctly
done, the results and their statistical significance can give you a
better sense of elements you want to translate into evidence-
based practice based on solid research.
References
"Hospital Cost and Efficiency: Do Hospital Size and Ownership
Really Matter?" by Coyne, Richards, Short, Shultz, and Singh,
from the Journal of Healthcare Management (2009), located in
the GCU eLibrary at
http://library.gcu.edu:2048/login?url=http://proquest.umi.com.li
brary.gcu.edu:2048/pqdweb?did=1752526591&sid=1&Fmt=4&c
lientId=48377&RQT=309&VName=PQD
Statistical Assessment
Use the chart in the Module 4 lecture to complete the table
below to assess the appropriateness of the statistics used, and
determine the statistical significance of outcomes in Messina’s,
et al., article “The Relationship Between Patient Satisfaction
and Inpatient Admissions Across Teaching and Nonteaching
Hospitals” . Refer specifically to the discussion on pages 189-
90 of the article.
Messina, D., Scotti, D., Ganey, R., Zipp, G., & Mathis, L.
(2009). The Relationship Between Patient Satisfaction and
Inpatient Admissions Across Teaching and Nonteaching
Hospitals. Journal of Healthcare Management, 54(3), 177-89,
discussion 189-90. Retrieved from
http://library.gcu.edu:2048/login?url=http://proquest.umi.com.li
brary.gcu.edu:2048/pqdweb?did=1752526601&sid=1&Fmt=4&c
lientId=48377&RQT=309&VName=PQD

8. Statistic
Data type
Sample Size
Research Question
Statistical Significance:
There were three errors in Table 4 on page 185. In your
identification of significant findings, can/did you find them?

9. The chart from the Module 4 Readings:
Statistic
Data Type
Sample Size
Research Question
Mean and Standard Deviation
Interval or ratio
>2
What does the data set look like?
Frequency Distribution
Nominal-Ratio
>2
What does the data set look like?
Chi-Square
Nominal-Ordinal
>4
Is the variance of one variable equal to or different from
another variable
Correlation Coefficient
Interval-Ratio
>4
What is the relationship between two variables?
t-Test
Interval-Ratio
<30
Is there a significant difference between two groups? May be
intrinsic or may be experimental
ANOVA (Analysis of Variance)
Interval-Ratio
>30
Is there a significant difference between 2 or more groups?
Regression Analysis
Interval-Ratio
>30
How much of the change in the dependent variable is predicted

10. by the independent variable or variables?
Refer to the Module 4 Readings for explanation of the chart.
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