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# OTD 8161: Week 9 - Appraisal of Quantitative Evidence

Winter Semester - 2016
by

## Rick Davenport

on 13 February 2016

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#### Transcript of OTD 8161: Week 9 - Appraisal of Quantitative Evidence

OTD 8161: Evidence and OT Practice
Winter Semester - 2016
Week 7

Appraisal of Quantitative Evidence
Let us do a Quick Review:
Appraising the Quantitative Evidence
Let us start out with some basics ...Measures of Central Tendency
The Scientific process:
One of the 1st steps to analyzing Quantitative data is to know that there are two main branches of statistics:
Mean, Median, and Mode
This semester the goal is for you to gain the skills for you to become a critical consumer of the research
and today
you will officially begin to learn about Quantitative Evidence
Now you are going to get into the nuts and bolts
Descriptive statistics (when you know all the values of the data set)
Inferential statistics (when you know part of the value from your population and extrapolate to make guesses about your entire population)
Required material
Review both of these videos that focus on reinforcing your understanding of descriptive and inferential statistics...
Note be sure to know the terminology (e.g.
confidence interval)
"yea! I am going to learn about statistics!"
Looking past the retro style :) including the retro phone ....this video is a quick way to review what you learned in your prerequisite statistics class.
Good idea to know how to calculate all 3....
An important feature of a frequency distribution is that it presents a
complete summary of the scores
(or other measures).

Data are often
summarized by calculating a single numerical score
that can be used to describe the data for the whole group(s). This score, called a
measure of central tendency.
Median
The median is the
middle score
(or mid-point) of a set of scores.

When the scores are arranged from lowest to highest (or highest to lowest).

Find the median of the following
26, 17, 21, 18, 12, 17, 18, 24, 25, 17
(make sure you order it)
Mean
The mean is the arithmetical
average
of all the individual scores (or measures) in a set of scores. It is calculated by adding all the scores together and dividing the total by the number of scores.

Mean = sum of all scores / number of all scores

Find the mean of the following
26, 17, 21, 18, 12, 17, 18, 24, 25, 17

The mean may not always provide the most accurate measure of central tendency of a set of scores
Mode
The mode is the most frequently occurring score in a set of scores.

Find the mode of the following
26, 17, 21, 18, 12, 17, 18, 24, 25, 17
(make sure you order it)
When to use mean, median, mode

Generally, when
most of the scores in a set of data cluster around a central value
(that is, there tends to be a normal distribution),
the mean is a fairly reliable
indicator of a typical score; that is, it is a useful representation of the data.

When
extreme scores occur
in a set of data (that is, a skewed distribution), a
more representative
measure of central tendency is
the median
.

The mode
provides a useful indicator of a
‘common’ or ‘usual’ score
because it is the most frequently occurring score.
This is a Good tidbit to understand :) hint hint
Remember "Learning to critically appraise research is more challenging... partly because of a need to interpret
statistics
and understand a range of research designs." (MacDermid, 2008, p.35)

Let us get started in learning about
statistics
! Remember you want to learn this material so as you retain it
!
Estimates of Dispersion
(variability of the observed values)
Range and Standard Deviation
Why are estimates of dispersion (variability) important?
Statistics can be defined as the practice of collecting, organizing, describing, and analyzing data to draw conclusions from data.

There are two main branches of statistics:
Descriptive
and
Inferential
.
Again let us review the concepts of Descriptive and Inferential statistics
Its objective is to summarize a collection of data in a clear and understandable way.
There are 2 basic methods:
numerical
&
graphical
.
In other words, it describes patterns and general trends in a data set.
Histograms
Scatter Plots
Frequency Distribution
Descriptive statistics
Central Tendency ...is a way of using a Single Description (such as the average or typical score) to summarize the data of the whole group
Measures of Variability

Although a measure of central tendency is certainly important, it does not completely represent a distribution by itself. Given a measure of central tendency, you have an idea of where scores tend to fall, but you don’t know to what extent the scores differ from one another. A measure of the amount of dispersion contained within a data set is called a measure of variability. Except when all scores in a data set are identical, all sets of scores vary to some degree. Consider the members of your
occupational therapy
class. They would vary on a host of measures, including height, weight, and grade point average. Measures of variability include the range, the variance, and the standard deviation.
Range
Range

The range is the difference between the highest and lowest scores in a distribution. The range provides limited information, because distributions in which scores bunch up toward the beginning, middle, or end of the distribution might have the same range. Of course the range is useful as a rough estimate of how a score compares with the highest and lowest in a distribution.

Learning Check: A memory researcher would like to know how many digits a person can recall with only one presentation of a list. She creates random lists of digits and presents them to participants. The number of digits recalled by the first 10 participants are as follows: 5, 9, 6, 10, 9, 7, 8, 7, 9, 12. What is the range of this data set?
The range is the highest number minus the lowest number. In this case it is simply 12 - 5 = 7. The range is 7.
Reinforcing the concept of Estimates of Dispersion
The range is the difference between the largest and smallest values of a set.
In other word the range is simply the highest score minus the lowest score.

Example:

What is the range of the following group of numbers: 10, 2, 5, 6, 7, 3, 4?

Well, the highest number is 10, and the lowest number is 2, so 10 - 2 = 8.

So the

range is 8.
1. Range
The standard deviation is simply the square root of the variance.

The standard deviation is an especially useful measure of variability when the distribution is normal or approximately normal because the proportion of the distribution within a given number of standard deviations from the mean can be calculated.

And for a sample, the standard deviation is the square root of the sum of the squared deviations from the mean, divided by the number of samples minus 1.
Standard Deviation
Review this video to get an understanding behind the formula to calculate the standard deviation. Note while you will not be tested on the formula.... understanding it will solidify your conceptual understanding (refer to Polit & Beck 2014, pp. 219-220 to see application of Standard Deviation)
A conceptual question may be: Why do some SD formulas divide by "n-1". .
"I am beginning to understand statistics!"
Inferential Statistics
Hypothesis Testing
The Hypothesis Testing

Oftentimes we want to determine whether a claim is true or false. Such claim is called a
hypothesis.

Null Hypothesis:
It's a specific hypothesis to be tested in an experiment.

Alternative Hypothesis:
A hypothesis that is different from the null hypothesis, which we usually want to show that is true.

The
null hypothesis
is tested through the following procedure:
a) Determine the null hypothesis and an alternative hypothesis
b) Pick an appropriate sample.
c) Use measurements from the sample to determine the
likelihood of the null hypothesis.

If the null hypothesis is
true
but the sample mean is such that it is rejected, a
TYPE I
error occurs. Otherwise if the null hypothesis is
false
but the sample mean is such that the null hypothesis cannot be rejected, a
Type II
error occurs.

Or put another way:
A Type I error is rejecting Ho (null hypothesis) when, in reality, it is true.
A Type II error is failing to reject Ho (null hypothesis) when, in reality it is false.
Mandatory: please review this video to be sure you fully grasp:
Type I and Type II errors.
The End
There were some questions regarding non-directional hypotheses (refer to chp. 6 of Polit & Beck text book p. 109).
You will be an entry level practitioner -but the skills you learn in this course will help you be an advocate for OT
You have been learning how to search the literature, read the literature, including the ethical concerns in research
When you begin working as an OT practitioner - you want the skills to be able to critically consume the research
Question: Why do some SD formulas always divide by "n-1". (which is used when calculating for the "sample" standard deviation versus the "Population" standard deviation). Did they divide by "n-1" in the previous video? why not?
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