Statistically Large Biostats quizlet

What is a population

the entire collection of individual/observational units that share a common property

What is a sample

a subset of the population

Observation

Set of one or more quantities (measurements) on a single observational unit

what is a parameter

a quantity describing a statistical population

what is an estimate

a calculated quantity describing a statistical population, aka statistic

what is a categorical variable

describes membership in a category our group, they do not have magnitude on a numerical scale

what are the types of categorical variables

nominal (name) or Ordinal (ordered)

example of nominal variable

survival (alive or dead), eye color, breed of dog

example of an ordinal variable

life stage, size class (sm,m,lg), severity score

are months and weekdays categorical?

yes, they are treated both nominally and ordinally depending on the context

what is a numerical varaible

characteristics of observations that have magnitude on a numerical scale

what are the types of numerical variables

continuous and discrete

what is a continuous variable

any real number value, ex. degrees celcius, cm

what is a discrete variable

only take individible units though they can be non integers, ex. age at death, # of eggs in a bird nest,

Can continuous variables have an exact value?

the probability of any exact value is zero, whereas it is nonzero with discrete variables

what is a graph

visual representation of a relationship between variables

What is a bar graph

columns (bars) representing the distribution of a numerical variable against one or more categorical variables (better than pie charts)

what is an experimental study

researcher randomly assigns observational units to different groups (treatments). Researcher controls the treatments

what is an explanatory variable

the treatment variable that has been manipulated by the researcher (independent variable)

what is a response variable

the measured effect of the treatment (dependent variable)

what is an observational study

researchers have no control over which observational unit falls into which treatment. Passive observation

what is a scatter plot

graphical display of two numerical variables, each observation is represented as a point on a graph with 2 or 3 axis.

what is a line graph

uses dots connected by line segments to display trends measured over time or other ordered states

what is a frequency distribution

a representation (either graphical or tabular) that displays the number of observations within a given interval of a quantitative variable

what is the mode

interval corresponding to the highest peak in the frequency distribution

what is Skew

asymmetry in the shape of a frequency distribution for a numerical variable

what is the primary goal of statistics

to infer/estimate an unknown characteristic of an entire population based on sample data

what does location tell us

something about the average/typical individual units

what does spread tell us

how many measurements vary among individual units (how widely scattered are the values around the centre/location)

what is the most important location statistic

the arithmetic mean

what are the most important spread statistics

variance and standard deviation

what is variance

average squared deviation of observations from the mean. measures the overall uncertainty/spread

what is the coefficient of variance (CV)

it tells us how hard it is to guess a typical value (mean/location) relative to size. Small CV means most values fall close to the target relative to magnitude, Large CV means guesses are more uncertain.

what is the median

the middle measurment/value of a distribution

what is the mean

arithmetic average, more sensitive to extreme values than the median

what is the median for an even number of observations

the average of the two central numbers

what is left skewed

few small values, >1/2 of values exceed the mean

what is right skewed

few large values, >1/2 of values are less than the mean

what is the interquartile range

the measure of spread for the median (Q3-Q1)

what are the advantages of a box plot

quickly shows where the most values lie (location) and how spread out the data are. Provides quick info on symmetry and skewness

what is accuracy

how close. anestimate is to the population parameter (mean median or standard deviation)

what is precision

how much estimates vary across samples

acurrate and precise

low sampling variation and low bias

accurate and imprecise

high sampling variation and low bias

inaccurate and precise

low sampling variation and high bias

inaccurate and imprecise

high sampling variation and high bias

random sampling

minimizes bias and allows to quantify sampling variation

sample bias

occurs when observational units in the target population have a higher or lower probability of being sampled than others, leads to inaccuracy

sampling variation

refers to the natural variation in statistics across different samples drawn from the same population

sampling of convenience

whomever you can get, some members of a population are systematically more likely to be selected in a sample than others, leads to inaccuracy

survivorship bias

occurs when we draw conclusions based on the individuals that remain observable (sample observations) while ignoring those that did not survive, failed, or disappeared (unobserved)

what is μ

population mean (mu)

what is σ

population standard deviation (sigma)

what is σ^2

population variance (sigma squared)

what is X

sample mean (X bar)

what is s

sample standard deviation

what is s^2

sample variance

properties of sampling distribution

1. the mean of all samples is always equal to the population mean

2. selection of observational units is unbiased and independemt,

3. under random sampling, increasing size reduces variability, more precise estimation

as sampling size increases, sampling variability______

decreases, yielding a more precise estimate

what is Y

the sampling distribution of sample means

sampling error

how much a statistic calculated from a sample differs from the true population value due to random variation

criteria of a random sample

every observational unit in the population have an equal chance of being included, the selection is independent

does random sampling ensure accuracy or precision

accuracy, ensures precision as sample size increases

what is a confidence interval

A range of values that is likely to contain the population parameter with a specified level of confidence. reflects the uncertainty of the mean estimate

what is the margin of error

the maximum typical deviation we expect between a sample estimate and the true population due to sampling variability at a chosen confidence level

what does a larger confidence level (95% or 99%) tell us

provides a more plausible range for the parameter. values inside the interval are more plausible, those that lie outside are considered less plausible based on sample data

what does a 95% confidence interval tell us

we are 95% confident the true population mean lies between the lower and upper limits of the interval (NOT 95% probability)

higher confidence =

wider interval, less precision

lower confidence =

narrower interval, more precision

what is normal distribution

bell curve

what is a t-distribution

It is bell-shaped and has a mean of zero, but has a larger standard deviation than the standard normal distribution, and therefore, has thicker tails than the standard normal distribution.

what is the t-statistic

measures the deviation of the sample mean from the true population mean, it is unit free and comparable across populations. It is universal and only varies as a function of sample size

when do we use the t-distribution

when sample size and population standard deviation is unknown

what is the square-root transformation

it compresses variation, stabilizing variance and skewedness, primarily used to normalize right skewed data

What is Jensen's inequality?

a mathematical rule used to compare the average of a function to the function of an average, used to calculate risk and inequality in curved functions. used for small sample sizes

is variance biased or unbiased when divided by n instead of n-1

BIASED due to degrees of freedom

what is scientific evidence

information, facts, or data that support or challenge a claim, prediction, assumption, or hypothesis

statistical hypothesis framework

a quantitative method of statistical inference that allows to generate evidence for or against a hypothesis

Null Hypothesis (H0)

nothing systematic is going on

Alternative hypothesis (HA)

Hypothesis in which there are nonzero effects and there are differences between treatments

The frequentist hypothesis testing framework

evaluates how compatible the data are within an assumed model (H0) measured by P-values

what does a small p value mean (<0.05)

strong evidence against the null hypothesis, reject null

what does a large p value mean (>0.05)

strong evidence supporting null hypothesis, reject HA

what does the significance level alpha represent

the probability of rejecting the null hypothesis when it is actually true (a Type I error or "false positive")

Type I Error

H0 is true, we reject H0 (false positive)

Type II Error

H0 is false, we accept H0 (false negative)

if p

reject the null hypothesis

if p>a

accept null hypothesis

1-B

propability of correctly rejecting the null hypothesis when it is truly false

what is a one sample t test

testing a hypothesis based on a single sample

assumptions of one sample t test

the sample is random and independent, the variable of interest is assumed to follow normal distribution for small sample sizes

two sample t test

a statistical method used to compare the means of 2 groups of subjects

two sample t test assumptions

random and independent

what is a paired design

both treatments are applied to every sampled unit, minimized the impact of variability thus increasing precision

what is the F test

Variance among group means/variance within groups, large value indicates significance

Welch's t-test

compares the means of two groups and can be used even when the variances of the two groups are not equal

Welches t test assumptions

normal distribution, independent + random, does not assume equal variance, degrees of freedom can be non-whole numbers to provide more accurate results accounting for unequal variances

ANOVA

One continuous response variable and one categorical predictor variable, uses F statistic

what does ANOVA assume

independent, random, normally distributed, equal variance

tukeys honest test

post hoc test (after ANOVA), determines which group means differ