Descriptive and Inferential Statistics
April 11, 2013
Importance of Statistics in Nursing
Researchers link the statistical analyses they
choose with the research question, design,
and level of data collected.
Allows us to critically analyze the results.
Provide organization and meaning to data.
Where Do You Find Them?
Methods section will contain the planned
Results section will provide the data
generated from testing the hypothesis or
Data is the analysis using descriptive and
Levels of Measurement
Measurement is the process of assigning
numbers to variables.
For example: Males and females in a study.
Males would be assigned as 1 and females assigned
Every variable in research study that is assigned a
specific number must be similar to every other
variable assigned that number.
Levels of Measurement
Nominal- aka categorical, naming or classifying.
Either does or does not have the characteristic.
Lowest level of measurement and allows for the
least amount of statistical information.
Examples- gender, marital status, religious
Can you think of one?
Used to show relative rankings of variables or events.
Ranks in order from high to low, but does not
indicate how much higher or how much lower.
Intervals are not necessarily equal and there is no
Limited in the amount of mathematical manipulation
Examples- class rank, levels of wellness, levels of
Shows rankings of events or variables on a
scale with equal intervals between.
Zero point remains arbitrary and not absolute.
Allows for more mathematical manipulation of
Examples- test scores and temperature on a
Shows rankings of events or variables on
scales with equal interval and absolute zero.
Most often used in physical sciences.
Highest level of measurement, allows for most
manipulation of data.
Number represents the actual amount of the
property the object possesses.
Example- height, weight, pulse and BP.
Procedures that allow researchers to describe
and summarize data you definitely know
(describes the sample).
Examples: Demographics, clinical data.
Frequency distribution is one way to display data.
See page 313.
Measures of central tendency are used to describe
the pattern of responses among a sample.
Mean- most frequently used average, add up
numbers (sum) and then divide by the #. Defined
as a balance point in a distribution of scores.
Median-50% are above and 50% are below the
score. Defined as the middle point in a
distribution. Insensitive to extreme scores.
Mode-Most frequently occurring score. May have
more than one mode.
Most important curve (Bell-shaped).
Most often found in nature and used as the basis
for a number of inferential statistics.
Mean, median and mode are equal.
Measure of Variability
Concerned with the spread of data.
Range- the difference between the highest and lowest
Semiinterquartile range- indicates the range of the
middle 50% of the scores.
Standard Deviation-most stable and most useful,
provides an overall measurement of how much
participants scores differ from the mean of the group.
Z score-used to compare different measurements,
scores are converted to Z scores and them compared.
Data collection procedures that allow
researchers to estimate how reliably they can
make predictions and generalize findings.
Allows us to compare groups and test
Answer research question in a study.
Parameter- a characteristic of a population.
Statistic- characteristic of a sample.
Not possible to study the whole population so
we study a sample and make predictions or
statements related to our findings.
2 important qualifications must be conducted
to use inferential statistics.
Sample must be representative (drawn with
probability, some form of random selection).
Scale used must be either interval or ratio
level of measurement.
If nonprobability sampling occurs techniques
such as power analysis are used to
compensate for this.
Researchers are able to make objective
decisions about the outcome of their study by
using statistical hypothesis testing.
Scientific hypothesis is what the researcher
believes will be the outcome of the study.
Null hypothesis is what can actually be tested
by the statistical methods.
Inferential stats use the null hypothesis to test
the validity of a scientific hypothesis.
Probability- the notion that in a repeated
trial/study under the same conditions we
would get the same results.
Statistical probability is based on sampling
error. The tendency for stastics to fluctuate
from one sample to another is known as
Type I and Type II Errors
2 types of errors in statistical inference.
Type I- researcher rejects a null hypothesis when it is actually
Type II- researcher accepts a null hypothesis that is actually
Type I errors are considered more serious because if a
researcher declares that differences exist when none are
present the potential exists for patient care to be adversely
Type II errors occur when sample is too small.
Level of Significance
The probability of making a type I error.
Minimum accepted level for nursing research
“ If I conduct this study 100 times, the
decision to reject the null hypothesis would be
wrong 5 times out of 100”
If wanting to assume smaller risk level will be
set at 0.01.
Meaning researcher is willing to be wrong only
once in 100 trials.
Decision to use alpha level 0.05 or 0.01
depends of the study significance.
Decreasing the risk of making a type I error
increases the risk of making a type II error.
Parametric and Nonparametric Statistics are
used to determine significance.
Parametric have 3 attributes:
1. Estimation of at least one population parameter.
2. Require measurement on at least an interval scale.
3. Involve certain assumptions about the variables being
Variable is normally distributed in the overall
Most researchers prefer parametric statistic when
possible because they are more powerful and more
Not based on the estimation of population
parameters; usually applied when variable
measured on a nominal or ordinal scale , or
distribution of scores is severely skewed.
Table 14.3 and Table 14.4, page 324. Most
commonly used inferential statistics.
Most Commonly Used Inferential Statistics
used in nursing
research, tests whether
2 group means are
Chi-square- used when
data is at the nominal
groups. Robust and
used with small
Tests of Relationships
Interested in exploring the relationship
between 2 or more variables.
Studies would use statistics to determine the
correlation or degree of association between 2
or more variables.
Pearson r, the sign test, the Wilcoxon matched
pairs, signed rank test and multiple regression.
1. Statistics are used in nursing research to :
a. Help us organize and understand the data
b. Help us to publish our study results.
c. Help us to analyze data that can be useful in
d. Help us to determine if results have practical
2. List the four levels of measurement:
3. The level of measurement that allows for the
most manipulation of data and is used most
often in the physical sciences is?
4. Give 2 examples of this level of measurement:
5. Define descriptive statistics.
6. Define inferential statistics.
7.List the measures of central tendency.
8. The bell shaped curve is:
a. Used often in inferential statistics.
b. Known for the mean, median and mode
c. Found most often in nature.
d. All of the above
e. A & B.
9. Type ____ errors are most serious because
they can negatively impact patient care.
10. Rejecting the null hypothesis when it is true
is what type error?
11. What is the lowest level of measurement