**OTD 8161: Evidence and OT Practice**

Winter Semester - 2016

Week 7

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

: Please read this brief 1/2 page pdf article to reinforce your understanding of the differences between Descriptive and Inferential Statistics

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

years down the road

!

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.

(from Copyright ©1997 The McGraw-Hill Companies http://www.mhhe.com/socscience/intro/cafe/common/stat/descrp.htm )

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.

(from Copyright ©1997 The McGraw-Hill Companies http://www.mhhe.com/socscience/intro/cafe/common/stat/descrp.htm )

Mandatory-please read this 1/2 page intro article on variance and standard deviation to reinforce your understanding

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?