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1

the importance of statistics in evidence-based practice

Formulating a well-thought question

Identify evidence-based resources that help answer that question

Critically appraise the evidence to assess its validity

Applying the evidence

Re-evaluate the application of evidence and areas for improvement

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sections that make up a journal article

abstract, introduction (background and hypotheses), methods, results, discussion,

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abstract

Brief summary of the article at beginning

– Usually contains fewer than 150 words

Provides an overview of the study’s purpose, methods, and findings

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introduction

background

Statement of Purpose: Why did the author conduct the study?

Review of Literature most relevant for the presented study

What is the goal of the study?

Hypotheses

Sometimes explicitly stated

Other times must be inferred from text

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methods

How was the study conducted?

Participants/Subjects/Sample: Who was in the Study

Sample Size

Selection Methods

Materials: What was used to collect data

Instruments or Apparatuses used to collect data

e.g., Questionnaires, Lab Equipment, etc.

Procedures: the protocol for data collection

What did participants do; When and Where was data collected

Data Analysis Plan: Once data is collected how will the researchers analyze it to come up with their findings; Results not reported here

Generally, this presents the Statistical Methods used

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results

Overview of the results obtained from analyses

Information can be in text, table, or graphical form

Statistical information relaying findings regarding research questions

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discussion

Authors’ conclusions, understanding, or interpretation of the findings

Interprets results section in the context of the purpose of the study

The author will sometimes provide reasoning about the findings

Limitations of the study are discussed as well as potential future research

Where one is most likely to find the relevance of research findings to practice may be referred to as Implications for Practice

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discrete

Variable **cannot** take on a Value between Successive Observed Values

Examples: Number of kids in household \n Type of material used for construction (e.g., wood, brick, etc.)

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continuous

Variable **can** take on a Value between Successive Observed Values

Examples:

Age of an individual

Household income

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nominal/categorical

grouping, countable [ =, ≠]

Bar Graph

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ordinal/ranking

direction, comparable \[

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interval

equidistant, zero does not mean zero, degree of difference [+, -]

Using Class Intervals \n Histogram \n Stem-and-Leaf \n

Maintains Individual Values \n Polygon

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ratio

zero has meaning, magnitude [*, /]

Using Class Intervals \n Histogram \n Stem-and-Leaf \n

Maintains Individual Values \n Polygon

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dependent variable

variable being described

variable that is being measured as a result of experiment

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independent variable

describing variables

variable being manipulated in study

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predictor

provides information on an associated dependent variable regarding a particular outcome

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covariate

an independent variable that can influence the outcome of a given statistical trial, but which is not of direct interest

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population

total set of individuals or items of interest

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parameter

measured characteristics of population

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sample

a subset of the population taken as representative of population

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statistic

measured characteristics of sample

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data

collected pieces of information about observations on people, lab samples, etc.

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systematic differences

Individual Differences Explained by Group Membership. \n

E.G., In general, Elderly Individuals may require longer recovery time.

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random variation

Within a Group there may be Unexplained Differences between Individuals \n

E.G., Louisa had a recovery time shorter than what is typical for Other Elderly Individuals

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descriptive statistics

Describe a Sample; Summarize, Organize, and Simplify Data \n

Graphical and Numerical representations of sample characteristics

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inferential statistics

Make inferences from a Sample to a Population; Derive generalizations about a Population based on a Sample from that Population \n

Statistical Tests and Levels of Confidence in Estimation of \n Parameters

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negative skew

most people on higher end of scale

mode > median > mean

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positive skew

most people on lower end of scale

mean > median > mode

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kurtosis

Peakedness of a distribution

Positive leptokurtic

Symmetrical mesokurtic

Negative platykurtic

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mean

Evenly divide the total amount of something amongst everyone in a group

Can be affected by extreme values (outliers)

Adding or removing a value will change it unless the value is equal to it

Adding or subtracting a constant, it will change by that constant

Multiply or diving by a factor it will also change by that factor

not appropriate for nominal variable scales, questionable with ordinal

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median

middle value

appropriate for ordinal, interval, and ration variable scale

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mode

most common value

appropriate for any variable scale

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z score formula

Z = X - μ / σ

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standard deviation formula

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empirical rule

a statistical rule that states that almost all observed data for a normal distribution will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ)

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scatterplot

Direction of relationship

Linear relationship is monotonic with constant rate of change

Flat

Changes in one

No effect on changes in the other

Positive

Both variables change in the same direction

As X increases, Y increases

Negatives

Variable change in opposite directions

As X decreases, Y increases and vice versa

Can be non-monotonic (move in multiple directions)

Cannot discern if its positive or negative

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strength of relationship in scatterplot

How much dispersion about a line

Stronger = more determined

Stronger correlation when dots are closer to a line

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correlation coefficient

Often denoted as r

-1 ≤ r ≤ 1

The closer to –1 or 1 the straighter the line, and stronger the relationship

The closer to 0 the weaker the relationship

R can take on negative, positive, or zero linear directionality

0.1 - 0.3 relationship – small correlation

0.3 - 0.5 - medium correlation

0.5+ - strong correlation

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coefficient of determination

R2 serves as an index measuring the strength (not direction of angle) of the linear relationship (how closely do points follow a straight line)

If we have r=0.5 then r2 = 0.25 as 25% if the variance between two variables

R2 does not measure direction of correlation

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Spearman rho

monotonic but non-linear relationships Ordinal, interval, or ratio variables

Helps when outliers are present

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Point Biserial

True dichotomy with interval or ratio variable (treatment groups, term class taken, sex, etc.)

ex. student type (graduate vs undergrad) and amount of sleep (in hours)

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Biserial

One artificial dichotomy with interval or ratio variables

Usually ranked as high or low

Line represents means of each group

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Tetrachoric

Two artificial dichotomies

ex. income (high & low) education level (college & less than college)

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Coefficient phi

With two true dichotomous variables

Y & N

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Cramer’s V

With two nominal variables (>2 categories)

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reliability vs validity

**reliability**

measures consistently and predictably

necessary but not sufficient condition for validity

**validity**

how appropriately/accurately a construct is measured

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internal consistency

homogeneity of items within a scale; items on scale work well together

“Are items on scale doing equally well at measuring a construct”

Internal consistency is a type of reliability

**Scale is internally consistent when responses across items provided by individuals are similar thus exhibit correlations with one another & overall scale scores

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alternate forms

Correlation of scores for the same individuals amongst different versions of the same scale;

If different forms of instrument are truly measuring the same construct, then we would expect the correlation of the scores to be high

why we want them

Briefer form of a longer scale

Different forms for a Pre- & Post-test to avoid pretest sensitization (performance upon administration influences performance on next administration perhaps by memorization)

Prevent Cheating on Tests

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test-retest

if same basic score is expected across measurement occasions (as with traits), correlation of scores across different time points should be high

Measuring resting heart rate every month, in general should be similar

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inter-rater reliability

the extent to which ratings of a phenomena emerging from different judges on the same occasion are in agreement

Same scores have high inter-rater reliability

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intra rater reliability

the extent to which ratings of a phenomena emerging from a single judge across multiple occasions are in agreement

intra-rater reliability - How consistent same judge is

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content of measure

an item asking if an individual has “friends who could help them in a time of need” assesses social support defined as having a network of others upon which they can rely on

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response process

e.g., giving a

**higher rating**on an item reflects stronger feeling about the topic expressed in the questionScores 1-5 responses

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internal structure

e.g., depression scale has items tapping into each the cognitive, emotional, social, and physical dimensions of depression

How detailed and if it is reaching every aspect of abstract variables

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based on other constructs

e.g., college readiness exam scores should be related to other indicators of academic achievement

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based on consequences

e.g., would a diagnostic assessment tool erroneously lead to a misdiagnosis which may in turn unnecessarily subject an individual to a risky treatment

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content validity

How well does a measure represent the components of a construct;

Expert review of how accurately items tap into aspects of a construct & content sampling;

e.g., if we wanted to assess a person’s Overall Health Well-Being, we may want to sample across health content, such as energy levels, experience of pain, frequency of sickness, etc.

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criterion related validity

Does a measure have an empirical relationship with various other indicators of a construct;

Concurrent & predictive

Predictive: scores on a college admission test should predict college freshman GPA

Predicting another outcome based on first one

Concurrent: since both SAT and ACT are used for college admissions, then if one scores high on the ACT we would also expect that they score high on SAT

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construct valildity

does a measure behave the way our theory about a construct implies it would;

Convergent & Divergent

Convergent: Stress and Blood Pressure are known to have a positive correlation with one. A researcher checks to see if the scores on their Stress Scale correlate to Blood Pressure Levels.

If stressed then BP should be higher

Divergent: Word problems on a Math Exam are meant to reflect Math Comprehension more so than Reading Ability. To assure this, it was examined whether scores on other measures of Math Comprehension were more strongly correlated with Word Problem scores than to Reading Skill Scores

If measure stress and height those should not be related

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