Strategy, Math and Research Methods Flashcards
How do you add numbers in scientific notation?
Make the exponents the same and then add/subtract the bases?
Multiply numbers in scientific notation
add the exponent; if same base add exponents, if different bases multiply the bases and raise to power
Divide two numbers in scientific notation
keep the base and subtract the exponents
Raise a number in scientific notation to a power
raise the base to the exponent and multiple the second portion by the exponent
Sin (0)=
0
Sin (30)=
1/2
Sin (45)=
sqrt 2/ (2)
Sin (60)
sqrt 3/ (2)
Sin (90)=
1
Cos (0)
1
Cos (30)`
sqrt 3/ (2)
Cos (45)
sqrt 2/ (2)
Cos (60)
1/2
Cos (90)
0
Trig Rules
SOH CAH TOA
Tan (theta)
sin (theta)/cos (theta)
sin^2x + cos^2x=
1
Area of a circle
pi r^2
Circumference of a circle
C=pi(d) or C=2pi(r)
Area of a triangle
1/2 bh
Volume of a sphere
V= 3/4 (pi)(r^3)
Pythagorean Theorem
A^2 +B^2 = C^2
All angles in a triangle must add up to
180 degrees
Converting degrees to radians RULES
pi radians= 180 degrees
2pi radians =360 degrees
approx. 6 radians in one circle
12 rad/s =2 rev/s
DECI- SI UNIT
1/10, 10^-1
CENTI- SI UNIT
10^-2
MILLI- SI UNIT
10^-3
MICRO-SI UNIT
10^-6
NANO-SI UNIT
10^-9
PICO- SI UNIT
10^-12
FEMTO-SI UNIT
10^-15
DECA-SI UNIT
10^1
HECTO-SI UNIT
10^2
KILLO-SI UNIT
10^3
MEGA-SI UNIT
10^6
GIGA-SI UNIT
10^9
TETRA-SI UNIT
10^12
Linear vs Non-linear graphs
- if both contain squares/cubes graph will be linear
- if they are different vs variable –> graph will be non-linear
Steps for choosing a graph:
1) does y-value start high or low? (max/min values)
2) what is the slope and what does it represent?
3) what is the sign of the y-axis? is it always pos/neg? does it cross the x-axis?
Displacement vs. Time=
velocity
Velocity vs. time=
acceleration
Log- log graph
has a logarithmic scale on both axes
Semi-log graph
log scale on one axis, linear on the other
When to manipulate and equation:
1) If x doubles, what happens to y =?
2) 2 trials: predict change on a 2nd variable
3) data charts: look at chart and calculate factor
4) half in passage, half in question “volume doubled”
5) Ratio between A and B ***most difficult
Peer review
research is submitted 1st, reviewed and critiqued by colleagues
Verification
also known as replication, or the ability to reproduce results
Experimental or Basic Science– RESEARCH
lab research under controlled conditions
Human Subjects– RESEARCH
outside of lab on humans
ex: drug trials
2 types of human subjects research
- experimental: specific intervention given
- observational: observes data without direct control over variables or implementation of interventions
Beneficence
do good; end study because of positive results that could potentially help other patients
Non-maleficience
do no harm; end study because of negative results
Types of Observation studies
Cohort, Cross-sectional, and Case-control
Cohort Study
longitudinal study observing characteristics (risk factors) across time
Cross-sectional study
analysis of data collected from population in a specific time
Case-control study
observational study of individuals in population with condition present and compare to a control group without the disease (reference group)
Independent Variable
the variable MANIPULATED or directly changed
“predictor variable”
Dependent Variable
the variable MEASURED as a response to change
“outcome or effect” variable
Control group
all conditions and environmental factors are IDENTICAL to the treatment group, but they are not receiving the treatment
Positive Control
group is given treatment with a known outcome that can then be used to compare the the outcome of the treatment being studied
Negative Control
group that does not receive any treatment; the known treatment has no effect or outcome
-ensures there is no response to the treatment
Selection Bias (and types)
selection of participants is not truly random and do not represent the population accurately types: -specific real area -Self-selection -prescreening/advertising -exclusion bias -healthy-user -Berkson's fallacy -Overmatching
Specific real area bias
bias introduced by conducting study in a specific area that does include a representative sample
Self-selection bias
introduced when a participant in study has the choice to participate or not, or to determine level of involvement
Prescreening/advertising Bias
occurs when screening or advertising process results in an unrepresentative sample
Exclusion Bias
to the exclusion of an entire group from a population
Healthy-user Bias
persons included in the study are healthier than general population
ex: choosing triathlon runners for study of CV disease
Berkson’s Fallacy
participants are less healthy than the general population
ex: choosing hospital patients
Overmatching
negative outcome resulting from what is normally good practice; matching for potentially confounding variables
Observer Bias
observers or researchers know the goals of the study or hypotheses and allow this knowledge to influence their observations during the study
Demand Characteristics
participants form an interpretation of experiments purpose and unconsciously change their behavior to fit this model
Information Bias
wrong or inexact recording of variables or data
- continuous variable (blood pressure): called measurement error
- categorical variable (disease state): called misclassification
Confounding Variable
extraneous variable that influences variables being studied, but is not a part of the expected correlation
Placebo effect
example of a confounding variable; participants are given a placebo and experience real or perceived health benefits as a result of their belief that they are being treated
Detection Bias
differences between groups caused by inconsistencies in the method of detection or diagnosis
Performance Bias
difference between groups in terms of care receives or treatment
Experimenter Bias
errors introduced to expectations of investigator
types:
-confirmation bias
-reporting bias
Conformation Bias
tendency to favor info that confirms ones hypothesis and dismiss others that go against it
Reporting Bias
some findings are reported others are not; withholding or ignoring data
Accuracy
difference between measurement and the actual value
Precision
variation in measurement seen when recording
Reliability
consistent and repeatable results
Test-Retest Reliability
consistent and repeatable results
Inter-Rater reliability
extent to which two or more raters (observers) agree
Validity
test or experiment tests what it is supposed to measure and uses methods that meet scientific standards; internal and external validity
Internal Validity
extent to which study findings of truth or causation are justifiable; the scientific rigor of the study
External Validity
generalizability; degree to which findings can be extrapolated to general population
Correlation Coefficient (r^2)
- Linear regresson: correlation coefficient related to linear regression analysis
- r^2 is a measure of how tightly the data fits the line– closer to the data, as a whole, the higher the r^2 value
- r^2=1 is a perfect fit
Hill’s Criteria is used for what?
whether or not a causal relationship exists
Hills Criteria and definitions
- Specificity: single cause produces a single effect
- Plausability: reasonable path to link outcome to exposure
- Dose-response: increase amount of exposure, increase the risk
- Testable by experiment: condition can be altered with different treatments
- Coherence: association should be compatible with existing theory and knowledge, including knowledge of past causes and epid. studies
- Analogy: similar association are known to exist that are analogous to associations being made
Single-bling experiments
subjects are blinded to the purpose, treatment and control group
Double-blind experiments
experimenters and subjects are blinded to the purpose, treatment, and control
Sample
portion of a population that is included in the data
Population
all members in the group or category being sampled (ex: all US veterans)
Statistic
measure or data point that is calculated for the sample (average income among veterans)
Parameter
a measure that is calculated for the entire population, not just the sample
Mean, median, mode
Mean- the average value
median- middle of the data
mode- most frequently occurring data point
range- the minimum data point to the maximum data point
Standard Deviations
how tightly associated the data are to the mean; small means narrow set of data, close to the mean. Large SD indicated greater spread of the data around the mean
Standard Deviations
1 SD= 68%
2SD=95%
3SD=99%
Probability RULES
o Assumption = Outcomes are independent (i.e., do NOT influence one another) and are also mutually
exclusive (i.e., they cannot occur together). o AND vs. OR
▪ AND = MULTIPLY the probabilities of individual events to get the overall probability of all events occurring.
▪ OR=ADDtheprobabilitiesofeachindividualeventtogethertogettheoverallprobabilityofANY of the events occurring.
Null Hypothesis
H0 is the LACK OF A RELATIONSHIP OR GROUP DIFFERENCE; no statistically significant differences between groups– no relationship
Alternative Hypothesis
opposite of the Null; there is PRESENCE OF A RELATIONSHIP OR GROUP DIFFERENCE; there is a difference between groups— there is a relationship
T or Z test –> P value
- test statistic is calculated
- result is compared to a table of t-values or z-values
- table indicated the significance level
Significance Level (alpha)
alpha=0.05; 0.01, 0.001
p< 0.05 means that we can be 95% confident that the results are real
p<0.01 means we can be 99% confident
If hypothesis is directional (A is larger than B)
- if p> alpha CANNOT reject H0=NO STATISTICAL significance
- of p< 0.05 we REJECT H0=STATISTICALLY significant
If hypothesis is non-directional (there is a difference between A and B. no assertion made as to whether it is larger or smaller)
- If p> alpha/2 we CANNOT reject H0=NO STATISTICAL SIGNIFICANCE
- if p< alpha/2 REJECT H0-STATISTICALLY SIGNIFICANT
Type 1 errors
researchers claimed a difference between groups when none existed (they rejected H0 but should not have)
“false positive”
Type 2 errors
researchers did not claim a difference between groups when one DID exist
aka “false negative”
(should have rejected H0 but did not)
Confidence Interval
95% is standard
(z score)(SD)= error margin
C.I.= Mean +/- Error margin
Standard Error of the Mean (SEM)
a quantification of how precisely the mean represents the true mean of the population; SEM decreases as sample size increases
