Physics and Math Chapter 10 & 11: Mathematics and Reasoning about Design and Execution Flashcards
Scientific notation
[significand] x 10^[Exponent]
Significand must be:
greater than or equal to 1 and less than 10
The exponent in scientific notation must be
an integer
Significant figures
include all nonzero digits and any trailing zeroes in a number with a decimal point
Sig figs in addition and subtraction
reduce the answer to have the same number of decimal places as the number with the fewest decimal places
Sig figs in multiplication and division
reduce the answer to have the same number of sig figs as the number with the fewest number of sig figs
Tips for estimating in multiplication and division
In multiplication, if one number is rounded up, the other should be rounded down in proportion.
In division, if one number is rounded up, the other should also be rounded up.
Exponents
A notation for repeated multiplication. They may be manipulated mathematically, especially when the bases are the same.
Logarithms
the inverse of exponents and are subject to similar mathematical manipulations.
Natural logarithms
use base e
Direct relationships
as one variable increases, the other increases in proportion
Inverse relationships
as one variable increases, the other decreases in proportion
Conversions between metric prefixes require:
multiplication by corresponding powers of 10.
Scientific method:
a series of 8 steps for the generation of new knowledge
- generate a testable hypothesis
- gather data and resources
- form a hypothesis
- collect new data
- analyze the data
- interpret the data and existing hypothesis
- publish
- verify results
FINER method
assesses the value of a research question on the basis of whether or not it is feasible, interesting, novel, ethical and relevant.
Positive controls
ensure that a change in the depended variable occurs when expected
Negative controls
ensure that no change in the dependent variable occurs when none is expected
Accuracy (validity)
quality of approximating the true value
Precision (reliability)
the quality of being consistent in approximations
Cohort studies
record exposures throughout time and then assess the rate of a certain outcome
Cross-sectional studies
assess both exposure and outcome at the same point in time.
Case-control studies
assess outcome status and then assess for exposure history
Hill’s criteria
- temporality
- strength
- dose-response relationship
- consistency
- plausibility
- consideration of alternate explanations
- experiments
- specificity
- coherence
Error
bias
confounding
random error
Bias
Systematic and results from problem during data collection.
Selection bias
The sample differs from the population, is most common in human subjects research
Detection bias
arises from educated professionals using their knowledge in an inconsistent way by searching for an outcome disproportionately in certain populations
Hawthorne effect
results from changes in behavior - by the subject, experimenter or both - that occur as a result of the knowledge that the subject is being observed.
Confounding
an error in data analysis that results from a common connection of both the dependent and independent variable to a third variable
Belmont Report
- Respect for persons - includes autonomy, informed consent and confidentiality
- Justice - dictates which study questions are worth pursuing and which subjects to use.
- Beneficence - do the most good with the least harm
Populations
all of the individuals who share a set of characteristics - sets parameters
samples
subset of a populations that are used to estimate population data
Internal validity
refers to the identification of causality in a study between the independent and dependent variables.
External validity
refers to the ability of a study to be generalized to the population it describes.
Statistical significance
refers to the low likelihood of the experimental findings being due to chance
Clinical significance
refers to the usefulness or importance of experimental findings to patient care or patient outcomes.
