Exam 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 

sections that make up a journal article

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

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

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?

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Hypotheses

* Sometimes explicitly stated
* Other times must be inferred from text

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.

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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

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Generally, this presents the Statistical Methods used

results

Overview of the results obtained from analyses

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Information can be in text, table, or graphical form

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Statistical information relaying findings regarding research questions

discussion

Authors’ conclusions, understanding, or interpretation of the findings

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

The author will sometimes provide reasoning about the findings

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

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

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.)

continuous

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

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Examples:

Age of an individual

Household income

nominal/categorical

grouping, countable \[ =, ≠\]

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Bar Graph

ordinal/ranking

direction, comparable \[

interval

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

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

Maintains Individual Values \n Polygon

ratio

zero has meaning, magnitude \[\*, /\] 

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

Maintains Individual Values \n Polygon

dependent variable

variable being described

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variable that is being measured as a result of experiment

independent variable

describing variables

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variable being manipulated in study

predictor

provides information on an associated dependent variable regarding a particular outcome

covariate

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

population

total set of individuals or items of interest

parameter

measured characteristics of population

sample

a subset of the population taken as representative of population

statistic

measured characteristics of sample

data

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

systematic differences

Individual Differences Explained by Group Membership. \n

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

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

descriptive statistics

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

Graphical and Numerical representations of sample characteristics

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

negative skew

most people on higher end of scale

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mode > median > mean

positive skew

most people on lower end of scale

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mean > median > mode

kurtosis

* Peakedness of a distribution 
* Positive leptokurtic 
* Symmetrical mesokurtic 


* Negative platykurtic 

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 

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not appropriate for nominal variable scales, questionable with ordinal 

median

middle value

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appropriate for ordinal, interval, and ration variable scale

mode

most common value

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appropriate for any variable scale

z score formula

Z = X - μ / σ

standard deviation formula

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)

scatterplot

* Direction of relationship  
* Linear relationship is monotonic with constant rate of change 

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Flat 

* Changes in one 
* No effect on changes in the other 

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Positive 

* Both variables change in the same direction 
* As X increases, Y increases 

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Negatives 

* Variable change in opposite directions 
* As X decreases, Y increases and vice versa 

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Can be non-monotonic (move in multiple directions) 

* Cannot discern if its positive or negative 

strength of relationship in scatterplot

* How much dispersion about a line 
* Stronger = more determined 
* Stronger correlation when dots are closer to a line 

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 

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 

Spearman rho

* monotonic but non-linear relationships Ordinal, interval, or ratio variables 
* Helps when outliers are present 

Point Biserial

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

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

Biserial

* One artificial dichotomy with interval or ratio variables
* Usually ranked as high or low
* Line represents means of each group

Tetrachoric

* Two artificial dichotomies

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

Coefficient phi

* With two true dichotomous variables
* Y & N

Cramer’s V

* With two nominal variables (>2 categories)

reliability vs validity

**reliability**

measures consistently and predictably 

necessary but not sufficient condition for validity

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**validity**

how appropriately/accurately a construct is measured

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 

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

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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 

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 

inter-rater reliability

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

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Same scores have high inter-rater reliability 

intra rater reliability

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

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intra-rater reliability - How consistent same judge is

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 

response process

* e.g., giving a **higher rating** on an item reflects stronger feeling about the topic expressed in the question 


* Scores 1-5 responses 

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 

based on other constructs

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

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 

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.

criterion related validity

* Does a measure have an empirical relationship with various other indicators of a construct; 
* Concurrent & predictive 

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

* Predicting another outcome based on first one 

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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 

construct valildity

* does a measure behave the way our theory about a construct implies it would; 
* Convergent & Divergent 

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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 

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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