MCAT Math/Research/Ethics notes

skewed distribution

A ________ is one that contains a tail on one side or the other of the data set.

population

A _________ is the complete group of every individual that satisfies the attributes of interest.

hypothesis

A __________ is the proposed explanation or proposed answer to our testable question. It is often in the form of an if-then statement, which will be tested in subsequent steps.

bimodal

A distribution containing two peaks with a valley in between is called ____________

autonomy

respect for patient _______, or the responsibility to respect patients' decisions and choices about their own healthcare

beneficence

the obligation to act in the patient's best interest

confidence.

the probability of correctly failing to reject a true null hypothesis (reporting no difference between two populations when one does not exist) is referred to as _______

1.10 (all of them!)

what are the sig digits of 1.10

exhaustive

when a set of outcomes is _______, there are no other possible outcomes

fail to reject the null hypothesis; then we reject the null hypothesis and state that there is a statistically significant difference

For a directional test, if the p-value is greater than α, then we ____________, which means that there is not a statistically significant difference between the two populations. If the p-value is less than α, ____________ between the two groups.

multiplied

For a number that is raised to an exponent and then raised again to another exponent, the two exponents are ________

root of the number

For fractional exponents, the numerator can be treated as the exponent, and the denominator represents the _________

P(A ∩ B) = P(A and B) = P(A) × P(B)

For independent events, the probability of two or more events occurring at the same time is the product of their probabilities alone

Temporality, strength, dose-response relationship, consistency, plausibility, consideration of alternate explanations, experiment, specificity, coherence

Hill's criteria

clinical significance

However, even the smallest difference between two treatments may be significant mathematically. For example, a decrease in systolic blood pressure of one millimeter of mercury could be statistically significant; however, it is not likely to change patient outcomes. In this way, we must assess whether there is ___________—a notable or worthwhile change in health status as a result of our intervention.

single-blind

In ________ experiments, only the patient or the assessor (the person who makes measurements on the patient or performs subjective evaluations) is blinded

double-blind

In _________ experiments, the investigator, subject, and assessor all do not know the subject's group.

equipoise

In addition, in studies comparing two potential treatment options, one cannot approach the research with the knowledge that one treatment is superior to the other. This is termed __________. If it becomes evident that one treatment option is clearly superior before a study is scheduled to finish, the trial must be stopped because providing an inferior treatment is a net harm.

independent; dependent

In basic science research, we manipulate an ________ variable, and measure or observe a _______variable.

X^A × X^B = X^(A + B)

In cases of multiplication and division, the exponents can be manipulated directly, as long as the base number is the same. When multiplying two numbers with the same base, the exponents are added to determine the new number:

institutional review boards

In current practice, hospital or university ________________have put into place systematic protections against unethical studies.

mean of the two central data points.

In data sets with an odd number of values, the median will actually be one of the data points. In data sets with an even number of values, the median will be the _________

subtract

In division, we ______ the exponent of the denominator from the exponent in the numerator to find the exponent in the quotient, as long as all bases are the same:

placebo effect

In drug trials, a negative control group is often used to assess for the _______—an observed or reported change when an individual is given a sugar pill or sham intervention.

statistically significant

In research, the primary marker of success is being able to generate results that are ____________—that is, not the result of random chance.

Mutual exclusivity

Independence is a condition of events wherein the outcome of one event has no effect on the outcome of the other. _________ is a condition wherein two outcomes cannot occur simultaneously.

statistic

Information about a sample is called a ________________.

parameter

Information that is calculated using every person in a population is called a ________.

outlier

Mean values are a good indicator of central tendency when all of the values tend to be fairly close to one another. Having an _________—an extremely large or extremely small value compared to the other data values—can shift the mean toward one end of the range.

independent; dependent

On a graph the_______variable belongs on the x-axis and the _________variable belongs on the y-axis.

Semilog graphs *note log-log changes both axes

Semilog graphs are a specialized representation of a logarithmic data set. They can be easier to interpret because the otherwise curved nature of the logarithmic data is made linear by a change in the axis ratio.

sin theta/ cos theta

Tan theta =

median

The ________ value for a set of data is its midpoint, where half of data points are greater than the value and half are smaller.

mode

The ________, quite simply, is the number that appears the most often in a set of data. There may be multiple modes in a data set, or—if all numbers appear equally—there can even be no mode for a data set.

Hawthorne effect

The ___________, or observation bias, posits that the behavior of study participants is altered simply because they recognize that they are being studied.

range

The _______of a data set is the difference between its largest and smallest values: range = xmax − xmin

1.5 you would have to times 1.5 by the interquartile range, then see how far above or below the 1st and 3rd quartile it is - and that would set the boundary; anything outside the boundary would be an outlier

The interquartile range can be used to determine outliers. Any value that falls more than_______ interquartile ranges below the first quartile or above the third quartile is considered an outlier.

IQR = Q3 - Q1

The interquartile range is then calculated by subtracting the value of the first quartile from the value of the third quartile:

selection bias

The most prevalent type of bias is _______, in which the subjects used for the study are not representative of the target population.

true

The position of the median can be calculated as follows:

P(A ∪ B) = P(A or B) = P(A) + P(B) − P(A and B)

The probability of at least one of two events occurring is equal to the sum of their initial probabilities, minus the probability that they will both occur.

1 − β

The probability of correctly rejecting a false null hypothesis (reporting a difference between two populations when one actually exists) is referred to as power, and is equal to_______

three

The standard deviation can also be used to determine whether a data point is an outlier. If the data point falls more than ________standard deviations from the mean, it is considered an outlier.

standard distribution

The standard normal distribution is a special case of the normal distribution . It is the distribution that occurs when a normal random variable has a mean of zero and a standard deviation of one.

Sine = Opposite ÷ Hypotenuse Cosine = Adjacent ÷ Hypotenuse Tangent = Opposite ÷ Adjacent

Trigonometric ratios: SOH CAH TOA:

numerator and denominato

When a fraction is raised to an exponent, the exponent is distributed to the _______r:

both numbers in the same direction

When rounding numbers to be multiplied, round one number up and one number down to compensate. When rounding numbers to be divided, round ___________ to compensate.

sample

Working with a population is generally not feasible, even for smaller groups. Therefore, we make generalizations about populations based on sample data. A ______is any group taken from a population that does not include all individuals from the population.

Box plots he box of a box-and-whisker plot is bounded by Q1 and Q3; Q2 (the median) is the line in the middle of the box. The ends of the whiskers correspond to maximum and minimum value of the data set. Alternatively, outliers can be presented as individual points, with the ends of the whiskers corresponding to the largest and smallest values in the data set that are still within 1.5 × IQR of the median. Box-and-whisker plots are especially useful for comparing data because they contain a large amount of data in a small amount of space, and multiple plots can be oriented on a single axis.

______ are used to show the range, median, quartiles and outliers for a set of data. A labeled box plot, also called a box-and-whisker

Independent events

______ do not impact each other, so their probabilities are never expected to change.

Precision

______, also called reliability, is the ability of the instrument to read consistently, or within a narrow range.

nonmaleficence

______, or the obligation to avoid treatments or interventions in which the potential for harm outweighs the potential for benefit

Positive controls

_______ are those that ensure a change in the dependent variable when it is expected.

Bar charts

_______ are used for categorical data, which sort data points based on predetermined categories.

justice

_______, or the responsibility to treat similar patients with similar care, and to distribute healthcare resources fairly.

Mutually exclusive outcomes

________ cannot occur at the same time. One cannot flip both heads and tails in one throw, or be both ten and twenty years old. The probability of two mutually exclusive outcomes occurring together is 0%.

Standard deviation

________ is calculated by taking the difference between each data point and the mean, squaring this value, dividing the sum of all of these squared values by the number of points in the data set minus one, and then taking the square root of the result. Expressed mathematically,

Randomization

________ is the method used to control for differences between subject groups in biomedical research.

Detection bias

________ results from educated professionals using their knowledge in an inconsistent way. Because prior studies have indicated that there is a correlation between two variables, finding one of them increases the likelihood that the researcher will search for the second.

Accuracy

________, also called validity, is the ability of an instrument to measure a true value.

informed consent

________, in which a patient must be adequately counseled on the procedures, risks and benefits, and goals of a study to make a knowledgeable decision about whether or not to participate in the study.

cohort studies

_________ are those in which subjects are sorted into two groups based on differences in risk factors (exposures), and then assessed at various intervals to determine how many subjects in each group had a certain outcome.

Negative controls

_________, in contrast, ensure no change in the dependent variable when no change is expected.

Vulnerable persons

_________, which include children, pregnant women, and prisoners, require special protections above and beyond those taken with the general population.

Measures of central tendency

__________ are those that describe the middle of a sample

Morally relevant differences

____________ are defined as those differences between individuals that are considered an appropriate reason to treat them differently. For example, age is a significant moral difference in ethical deliberations: all else being equal, a transplant that is as likely to benefit a young child or an elderly adult may be given to the child because of a longer life expectancy.

Cross-sectional studies

__________attempt to categorize patients into different groups at a single point in time. For example, a study to determine the prevalence of lung cancer in smokers and nonsmokers at a given point in time would be an example of a cross-sectional study.

Case-control studies

__________start by identifying the number of subjects with or without a particular outcome, and then look backwards to assess how many subjects in each group had exposure to a particular risk factor.

Dependent events

________do have an impact on one another, such that the order changes the probability. Consider a container with five red balls and five blue balls. The probability that one will choose a red ball is 5/10 If a red ball is indeed chosen, then the probability of drawing another red ball is 4/9

Pie or circle charts

_______are used to represent relative amounts of entities and are especially popular in demographics. They may be labeled with raw numerical values or with percent values. The primary downside to pie charts is that as the number of represented categories increases, the visual representation loses impact and becomes confusing.

Hill's criteria

_______describe the components of an observed relationship that increase the likelihood of causality in the relationship. While only the first criterion is necessary for the relationship to be causal, it is not sufficient. The more criteria that are satisfied by a relationship, the likelier it is that the relationship is causal. Hill's criteria do not provide an absolute guideline on whether a relationship is causal, thus for any observational study, the relationship should be described as a correlation.

type II error β

_______occurs when we incorrectly fail to reject the null hypothesis. In other words, a type II error is the likelihood that we report no difference between two populations when one actually exists.

Basic science research

_______—the kind conducted in a laboratory, and not on people—is generally the easiest to design because the experimenter has the most control.

test statistic; p-value

a _______ is calculated and compared to a table to determine the likelihood that that statistic was obtained by random chance (under the assumption that our null hypothesis is true) This is our _________

type I error

a _______ is the likelihood that we report a difference between two populations when one does not actually exist

Confidence intervals

a range of values so defined that there is a specified probability that the value of a parameter lies within it. e.g. "we are 95% confident that the true mean age of the population from which this sample is drawn is between 24.12 and 35.88."

To calculate the position of the third quartile (Q3), multiply n by 3/4 Again, if this is a whole number, take the mean of this position and the next. If it is a decimal, round up to the next whole number, and take that as the quartile position.

calc 3rd quartile

To calculate the position of the first quartile (Q1) in a set of data sorted in ascending order, multiply n by 1/4 2. If this is a whole number, the quartile is the mean of the value at this position and the next highest position. 3. If this is a decimal, round up to the next whole number, and take that as the quartile position.

calc first quartile

external validity

it is the extent to which the results of a study can be generalized to other situations and to other people.

Skewed Distributions (a) Negatively skewed distribution, with mean lower than median; (b) Positively skewed distribution, with mean higher than median.

left tailed = neg right tailed -pos

log (n × 10^m) ≈ m + 0.n −log (n × 10^−m) ≈ m − 0.n

log shortcut

internal validity

refers to how well an experiment is done, especially whether it avoids confounding (more than one possible independent variable [cause] acting at the same time). The less chance for confounding in a study, the higher its__________ is.