· Quantitative Data Analysis: Statistics Introduction Understanding the use of basic statistical strategies is part of being a critical consumer of published research literature. Unless they plan to conduct research themselves, it is not as important for counselors to understand the mathematical calculations of the statistical techniques as it is to be able to recognize the names of the common ones and what kind of information they provide. There are several commercially-available software packages for analyzing quantitative data, one of which is described in detail in Chapter 14 of Counseling Research: Quantitative, Qualitative, and Mixed Methods . Descriptive and Inferential Statistics In quantitative studies, statistical techniques are used for data analysis. The two main categories of statistics are descriptive and inferential. Descriptive statistics are used to summarize the data. Some common descriptive statistics are the measures of central tendency: the mean, median, and mode. They provide information about where the middle is in distribution of scores. On the normal distribution, the mean, median, and mode are the same. Distributions are said to be skewed when extreme scores draw the mean away from the middle of the distribution. Measures of variability, such as the range, variance, and standard deviation, provide information about how widely a distribution of scores is dispersed (Erford, 2015, p. 250). The standard deviation is a measure of how the scores cluster around the mean. The greater the standard deviation, the greater the spread of scores. Toggle DrawerHide Full Introduction Inferential statistics are used to make inferences from the sample to the population. All inferential statistical procedures are based on probability theory. They are used to test hypotheses. Three commonly used inferential statistics are chi square, t-test, and analysis of variance (ANOVA). Chi square is used with nominal data to determine if the observed expected frequency differs significantly from the expected frequency. A t-test is used to determine whether there is a statistically significant difference between the means of two groups. ANOVA is used to determine whether there is a statistically significant difference between the means of three or more groups. Statistical Significance When a quantitative study tests a hypothesis, it is technically the null hypothesis being tested. The null hypothesis says there is no difference between the groups, or relationship between the variables (depending on the research design). If the statistical procedure indicates there is statistical significance, the null hypothesis is rejected, meaning that the probability is high that there really is a group difference or strong relationship between the variables. Rejecting the null hypothesis is not equivalent to proving the research or alternative hypothesis. Researchers can embrace the research hypothesis as one plausible explanation, but because only .

1. ·
Quantitative Data Analysis: Statistics
Introduction
Understanding the use of basic statistical strategies is part of
being a critical consumer of published research literature.
Unless they plan to conduct research themselves, it is not as
important for counselors to understand the mathematical
calculations of the statistical techniques as it is to be able to
recognize the names of the common ones and what kind of
information they provide. There are several commercially-
available software packages for analyzing quantitative data, one
of which is described in detail in Chapter 14 of
Counseling Research: Quantitative, Qualitative, and Mixed
Methods
.
Descriptive and Inferential Statistics
In quantitative studies, statistical techniques are used for data
analysis. The two main categories of statistics are descriptive
and inferential. Descriptive statistics are used to summarize the
data. Some common descriptive statistics are the measures of
central tendency: the mean, median, and mode. They provide
information about where the middle is in distribution of scores.
On the normal distribution, the mean, median, and mode are the
same. Distributions are said to be skewed when extreme scores
draw the mean away from the middle of the distribution.
Measures of variability, such as the range, variance, and
standard deviation, provide information about how widely a
distribution of scores is dispersed (Erford, 2015, p. 250). The
standard deviation is a measure of how the scores cluster around

2. the mean. The greater the standard deviation, the greater the
spread of scores.
Toggle DrawerHide Full Introduction
Inferential statistics are used to make inferences from the
sample to the population. All inferential statistical procedures
are based on probability theory. They are used to test
hypotheses. Three commonly used inferential statistics are chi
square, t-test, and analysis of variance (ANOVA). Chi square is
used with nominal data to determine if the observed expected
frequency differs significantly from the expected frequency. A
t-test is used to determine whether there is a statistically
significant difference between the means of two groups.
ANOVA is used to determine whether there is a statistically
significant difference between the means of three or more
groups.
Statistical Significance
When a quantitative study tests a hypothesis, it is technically
the null hypothesis being tested. The null hypothesis says there
is no difference between the groups, or relationship between the
variables (depending on the research design). If the statistical
procedure indicates there is statistical significance, the null
hypothesis is rejected, meaning that the probability is high that
there really is a group difference or strong relationship between
the variables.
Rejecting the null hypothesis is not equivalent to proving the
research or alternative hypothesis. Researchers can embrace the
research hypothesis as one plausible explanation, but because
only the null hypothesis can be tested, the researcher cannot be
completely certain. That is why it is inaccurate to say that a
study proves something. It is more prudent and correct to state
that the findings from this study lend support to the theory, or

3. the results fail to support the theory.
Validity
The concept of validity has several applications to research.
External validity is the extent to which the research findings
can be generalized from the sample to the population. Internal
validity is the extent to which we can trust that the changes in
the dependent variable are due to the effect of the independent
variable. There exist multiple threats to external validity and
internal validity. One of the threats to internal validity has to do
with instrumentation, which is the quality of the measurement
instrument being used to collect data.
When instruments are used to assess one or more variables,
consideration must be given to their validity and reliability.
These are some of the concepts with which to be familiar: face
validity, content validity, criterion validity, construct validity,
inter-rater reliability, internal consistency reliability, equivalent
forms reliability, and test-retest reliability.
Reference
Erford, B. T. (2015).
Research and evaluation in counseling
(2nd ed.). Stamford, CT: Cengage.
Objectives
To successfully complete this learning unit, you will be
expected to:
1.
Describe descriptive and inferential statistical concepts in a
research study

4. Assignment
Quantitative Data Analysis: Statistical Techniques
Resources
After studying the introduction to this unit and completing the
study activities, summarize the quantitative research article you
selected. Include enough detail to provide the context for the
main focus of this post, the statistical techniques that were used
in the study. Identify a descriptive statistic from the study.
Also, describe the statistical technique that was used to answer
the research question or test the hypothesis. The description
should be in your own words, not direct quotes from the article.
Cite and reference the course text to demonstrate that you are
incorporating material from an authoritative source on research
methods.