SEM 4 - EBP (wk 1-2)

Week 1-2 done completely// only class slides+pollev for wk 2

Variables

A property that can take on different values

Continuous variables

can have any value along a continuum within a defined range • Weight, height, ROM

Discrete variable

Described only in whole units BPM, children Dichotomous variables can only take on two values Yes or No

Types of variables: Ratio

• distance

• age

• time

• decibles

• weight

• numbers represent units with equal intervals measured from zero

Types of variables: interval

numbers that have equal intervals, but no true zero

calendar years and degress of F or C

Types of variables: ordinal

numbers indicate rank in order

MMT, px, function

Types of variables: nominal

numerals are category labels

• gender, blood type, gender

Nominal Variables

Classification: categorical

• Mutually exclusive categories

• No relative order

• Eg, employment status, marital status, gender,, blood type, eye color

Dichotomous: special case of nominal

Ordinal Variables

Rank-ordered categories > and <

1. relationship for adjacent categories

2. intervals inconsistent or not known

MMT: zero < trace < poor < fair < good < normal 2. Income categories 3. Hypo/normal/hyper 4. Pain?

Interval Variables

1. Rank-ordered 2. Equal intervals 3. No true zero

• Year of birth • shoe size • degrees in C or F

Ratio Variables

Interval scale with true zero Therefore, no negative values

1. ROM 2. height weight age 3. distance

INDEPENDENT variable: X

What you manipulate or specify

• Called factors

> 2 lvls or groups

Dependent variable: Y

What you measure

Attribute v. Active

Attribute - Gender is an attribute variable, cannot be manipulated

Active - Treatment is an active variable: the researcher manipulates the levels of treatment

Repeated v. Independent

Repeated factors

• same people measured at all levels of IV

• synonymous with within-subjects factors

• used in repeated measures designs

• subjects are used as their own controls

2. Independent factors

• different groups of people for each level

• synonymous with between-subjects factors

Independent Variables 1 vs 2

• One IV: single-factor design

• Two or more IVs: multifactorial design

Dependent Variables: one v. more than one

Univariate Designs 1. only one dependent variable 2. measure only ROM or force or BMI

Multivariate Designs 1. more than one dependent variable 2. measure ROM and force and BMI

Population

The entire set of people in the group of interest

Statistical characteristic of population is a parameter

Sample

Subset of the population chosen for study

Statistical characteristic of sample is a statistic

Inferential Statistic

Used to make inference about population

• Eg. p-value, mean difference with confidence interval

Descriptive Statistic

Used to describe sample 2.

Mean, standard deviation, range

Frequency Distribution (3 types)

Descriptive statistics aims to describe or summarize data

• raw data - just a table of all participants (1 box for every participant)

• grouped frequency distribution - ranges and how frequently they occur (percent and times)

• stem and leaf plot - first digit is the stem and second digit is the leaf

____ of the scores are within ± 1 SD of the mean

____ of the scores are within ± 2 SD of the mean

___ of the scores are within ± 3 SD of the mean

68%

95

99

skew to right

most of its on the left - positive

skewed to left

most on right and neg

best numeric choice for symetrical data

mean because extreme scores affect it

best numeric choice for unsymetrical data

median because its not affected by extreme scores

mode is used for

nominal or ordinal

Variability

Spread of the distribution

if the graph is left skewed the mean and median are

to the left of the mode

if the graph is right skewed the mean and median are

to the right of the mode

Range

difference between highest and lowest score (eg, 3, 21

Percentiles

a score’s position within the distribution (divides distribution into 100 parts

Quartiles

Divides distribution into 4 equal part

Interquartile range (IQR)

difference between 25th and 75th percentile; often used with median

Box Plots

• Box represents the interquartile range

• Horizontal line at median

• “Whiskers” show minimum and maximum scores

in a left skewed bell curve then the median

is left on a bell curve and right on a box and whisker

in a right skewed bell curve then the median

is right on a bell curve and left on a box and whisker

Variance equation

• Variance (S² is square of the SD S)

Coefficient of Variation (CV)

Ratio of SD to mean, expressed as percentage

Probability

The likelihood that any one event will occur, given all the possible outcomes - Implies uncertainty—what is likely to happen

Standard Error of the Mean (SEM)

• Estimated from the sampling data

• Serves as an estimate of the population SD

• Basis for statistical inference

• Allows us to estimate population parameters

Standard Error of the Mean will ____ as sample size _____

decrease, increases

You want to measure an individual’s heart rate and record it in beats per minute. Beats per minute would be considered which of the following types of variables?

Dichotomous

Ordinal

Nominal

Discrete

Discrete

Your patient reports that their blood type is AB. What level of measurement is blood types?

Interval

Ordinal

Nominal

Ratio

Nominal

You test a patients lower trapezius strength and score it as a manual muscle test grade of 3. Manual muscle testing is which level of measurements?

Ordinal

Nominal

Interval

Ratio

Nominal

You test a patients lower trapezius strength and score it as a manual muscle test grade of 3. Manual muscle testing is which level of measurements?

Group of answer choices

Interval

Nominal

Ratio

Ordinal

Ordinal

You are performing the 6-minute walk test on an individual with Parkinson’s disease, and they can go a distance of 150 feet. Distance is which of the following type of variable?

Interval

Ratio

Nominal

Ordinal

Ratio

A researcher performs a study investigating the effects of 8 visits of manual therapy, exercise, and ultrasound on increasing quad muscle strength in college aged athletes who had undergone an anterior cruciate ligament reconstruction. In this study the dependent variable is?

Anterior cruciate ligament reconstruction

Treatment

Quad strength

College aged athletes

Quad strength

You are performing a study comparing the effects of treadmill running, trail running, and road running on running speed and jumping height in health male adults. In this study the independent variable has how many levels?

2

3

1

4

3

You decide to design a 2 X 3 factorial design. How many independent variables are there in this type of study design?

Group of answer choices

2

1

4

3

2

You select a sample of individuals for a study and the mean height for the group is 5 feet 9 inches. You determine your sample has a normal distribution. If this is correct, 5 feet 9 inches plus or minus 1 standard deviation would include what percentage of the sample?

98

78

58

68

68

You are reading a research article and Figure 2 is an image of a box plot and you are examining the “whiskers”. The whiskers represent what in a box plot?

Group of answer choices

Minimum and maximum values

95% CI

Mean

Median

Minimum and maximum values

While searching the literature you come across a randomized clinical trial with 60 subjects comparing the effects of 30 mins of walking per day (n=30) compared to no walking (n=30) for individuals with congestive heart failure. The researcher wants to determine if walking reduces blood pressure in this population. You are reading the results and find the mean difference between groups and the 95% confidence interval. Which of the following is used to determine if the findings in the study are representative of the target population?

Inferential statistics

Prescriptive statistics

Mechanistic statistics

Descriptive statistics

Inferential statistics

Point Estimate (mean)

a single value that represents the best estimate of the population value

Confidence Interval

a range of values that we are confident contains the population parameter

• Width concerns the precision of the estimate

• It is NOT correct to say that there is a 95% probability that the population mean falls within an obtained confidence interval.

• means that you are 95% confident that the populations true value falls between this range

• mean should fall in between the conference interval

z score is

almost 2 SD

Estimation Equation

Increased precision (narrowed) or narrow confidence intrval increased by…

1. Larger sample size

2. Less variance

3. Lower selected level of confidence

(90% vs. 95%)

smaller confidence interval is…. the more ____ it is

precise

Hypothesis Testing

Does this difference represent a “real” difference in the population?

2. Or is it just sampling error?

A null hypothesis

a statement in research and statistics that assumes no effect, no relationship, or no difference between variables

Difference represents sampling error (p > a)

Hypothesis Testing Alternative Hypothesis

Difference represents a “real” difference (p ≤ a)

There is a difference • May be stated with or without direction

Disproving” the null hypothesis

Reject vs Do not reject

Reject - not true, observed difference is true of the population

Do not reject - in reality there is no difference between the groups Type I

Type I errors

mistakenly finding a difference (when in reality there is no difference)

Type II errors

mistakenly finding no difference ( when there is a difference)

what type of error is it when null hypothesis is true but you reject it

type 1 error (alpha)

what typr of error is it when the null hypothesis is false but dont reject it

type 2 error (beta)

Mistakenly finding a difference is also called a

False-positive

Alpha (α) or type 1 error or false positive

probability of making a Type I error

Maximum probability of type 1 error

Set by researcher before running statistics

Usually set to 0.05 (max chance of type 1 error = 5%)

The p value is

is the probability of finding an effect as big as the one observed when the null hypothesis is true.

Probability of Type 1 error, if the null hypothesis is true

a type 2 error is also called

Beta (β)

False-negative

Beta

Probability of making a Type II error

Statistical power

1- B

Power is the probability that a test will lead to rejection of the null hypothesis, or the probability of attaining statistical significance.

Type I error can only happen when ___ < ___

p value is less than or equal to alpha

**Rejecting the Ho when Ho is true

Finding a significant difference when none exists in the target population

Type II error can only happen when ___ > ___

p value is grater than or equal to alpha

i.e. Failing to find a significant difference when there is one in the target population

decision rule

if p value is less than or greater than a, reject the null

if the p value is greater than a, do not reject the hypothesis

when are p value and alpha values set

Alpha is set ahead of time by researcher

P-value is calculated after the study and compared to alpha

If we “fail to reject” (accept) Ho, we attribute any observed difference to____ only

sampling error

We don’t interpret non-significant differences as _____ (maybe not even as trends)

real

We understand that a non-significant difference is attributable only to chance. If we repeated the experiment tomorrow, we might very well get the same magnitude of difference but in the ______

opposite direction.

flip

“We must be careful to avoid using the magnitude of p as an indication of the degree of validity of the research hypothesis. Don’t use “highly significant or more significant” because they imply that the value of p is a measure of experimental effect, which it is not.”

“Once the decision is made, the magnitude of p reflects only the relative _____ that can be placed in that decision”

degree of confidence

if the confidence interval includes 0 is it significant

it is non significant.

if the p value is less than alpha and the CI does not cross zero, what does that infer?

that the data is significant

Statistical Power

The probability of finding a statistically significant difference if such a difference exists in the real world

*****if H0 is false and I reject the null hypotheis (im correct)

1-B

Determinants of Statistical Power

1. P = power (1 – β)

2. A = alpha level of significance

3. N = sample size

4. E = effect size

Knowing three of these four will allow for determination of the fourth

why shouldn’t you just increase your alpha value to increase the statistical power

because you are accepting the higher probability of a type 1 error

Effect Size

‘Effect size’ is simply a way of quantifying the

effectiveness of a particular intervention, relative

to some comparison intervention.

it means that the intervention woul have a larger effect than the other intervention

2. Allows for comparison of changes on a common scale.

Effect Size norms

.20 is considered small

2. .50 is considered medium

3. .80 is considered large

best way to increase statistical power

increasing the sample size!

how to increase power

• increase sample size, alpha, and effect size

• decrease variance

how to decrease power

• increase variance

• decrease sample size, alpha, and effect size

A priori analysis

Estimating sample size before

Before we collect data, is our design powerful enough, based on n, a, Cohens d (effect size), SD.

Post hoc analysis

Determining power after

Only an issue if you fail to reject Ho

If you find a difference, the power issue is moot

If you don’t find a difference, the power issue is HUGE

A priori – Sample Size Estimation

Used to figure out how many subjects to use before a study is started

Hold power constant (.80) and determine “n” required for .80 power with a given alpha, effect size, and variance (SD)

Post-hoc Analysis: 2 Ways to Determine

• Compute with traditional Cohen approach ( > 0.8 is default)

• Determine with Confidence Interval Analysis of the effect size (better way)

what is the cohens approach based on

Sample size

• Alpha

• Variance (observed)

• Effect size (use MCID, not observed)

Post-hoc: Confidence Interval Analysis

If MCID excluded from CI: adequate power

If MCID included within CI: inadequate power

You are reading a study examining the effects of 2 stretching techniques on hamstring flexibility as measured by knee angle during the 90-90 test. The mean difference between groups is 14 degrees. 14 degrees is the?

Interquartile score

Range

Confidence interval

Point estimate

Point estimate

A range of values in which we believe contains the population value is known as?

Confidence interval

Range

Interquartile score

Point estimate

Confidence interval