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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?
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.
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
results
Overview of the results obtained from analyses
Information can be in text, table, or graphical form
Statistical information relaying findings regarding research questions
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
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
Examples:
Age of an individual
Household income
nominal/categorical
grouping, countable [ =, ≠]
Bar Graph
ordinal/ranking
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
ratio
zero has meaning, magnitude [*, /]
Using Class Intervals \n Histogram \n Stem-and-Leaf \n
Maintains Individual Values \n Polygon
dependent variable
variable being described
variable that is being measured as a result of experiment
independent variable
describing variables
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
mode > median > mean
positive skew
most people on lower end of scale
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
not appropriate for nominal variable scales, questionable with ordinal
median
middle value
appropriate for ordinal, interval, and ration variable scale
mode
most common value
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
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
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.)
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
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
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
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
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
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
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
Note 
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