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What is biometics?
study/observation of biological phenomena by means of statistical analysis; applied to life sciences.
What are descriptive statistics?
numbers or values that either describe and/or summarize date. Help of graphs, forms basis of every quantitative analysis of data. describes basic features of data found in study and provides simple summaries about sample and measure. simplified large amt for reducing data into simplier summaries.
2 attributes: Central Tendency and Dispersion
summarize attributes of data such as the 2 attributes mentioned
Purpose of inferential statistics?
conduct statistical produced to accept or reject a specific hypothesis based on experimental data.
why might a researcher consult a statistician to assist with the design of an experiment?
can help design an experiment that gets the maximum amt of info from the smallest reasonable sample size
an example of categorical data?
non-numeric characteristic (eg. smoker, nonsmoker, exsmoker); gender; marital status.
an example of ordinal data.
assume 90 doctors were asked to rank four sinus medications from most effective to least effective. the 90 ranks that each medication received
give an example of discrete numeric data.
involves observations where the numbers occur as discrete values. ex. number hospital stays a person has by age 40. number of students in a classroom.
an example of continuous numeric data.
amt of time a person sleeps at night, or systolic blood pressure of pt. in theory, data can take on infinite number of possible values within a finite interval
in a ecological study, a biologist gave predators access to three different prey items and noted which prey item was eaten first, second, and last. what type of data does this represent?
ordinal data because data are ranked values (first, second, and last)
an epidemiologist collected data from a group of patients on the number of migraine headaches per month. what type of data does this represent ?
discrete numeric data. number of headaches per month. observations on each individual
a herpetologist took measurements of body temperatures from lizards who were warming themselves in the sun. what type of data does this represent?
- continues numeric data. type of data is said to be changeable cuz numbers can take on infinite number of values for infinite interval
- eg. body temperature - can vary along continuous scale
a marine biologist noted the body color of randomly sampled sea stars. what type of data does this represent?
type of data is categorical. observations are sea star body colors (purple, orange, red) which form categories. data not numeric.
4 examples of measures of central tendency
arithmetic mean, geometric mean, harmonic mean, and median
what is the different between theoretical mean and sample same?
theoretical mean is the true mean of the population which can't calculate or know exactly, and the sample mean is average of a set of data and is estimate of theoretical mean.
3 types of means were computed, an arithmetic mean, a geometric mean, and harmonic mean. what can you say about the relative size of each of these descriptive statistics?
- x > G > H
- equality only holds if all data values are identical.
what restrictions are there on the data if one wishes to compute a geometric or harmonic mean?
data must be positive numeric values to compute a geometric or harmonic mean
what advantage does the median have over the arithmetic mean?
median is not affected by outliers whereas the arithmetic mean is sensitive to it.
4 examples of measures of dispersion.
variance, standard deviation, coefficient of variation, range, mean deviation.
what is the relationship between variance and the standard deviation?
standard deviation is the square root of the variance. also have same units of measurements as original data
how does one compute a coefficient of variation?
CV is equal to the standard deviation divided by the mean. is a dimensionless measure of dispersion (have no units)
when might we be likely to use a coefficient of variation?
- often used to compare diff populations or diff measurements since not dependent on unit of measurement (often presented as percentage and unitless)
- -comparing variety of measurements that are on different scales.
is the mean deviation a measure of central tendency or a measure of dispersion?
mean deviation is a measure of dispersion. mean deviation is sum of differences between each data and mean is divided by size of data. means that avg of differences between values of data and mean of data, indicates how far data is from mean.
-it measures avg absolute deviation of observations from mean
what is a disadvantage of using the range as a measure of dispersion?
range is computed as difference between largest and smallest data values, extremely sensitive to outliers
what are grouped data
is when data values are organized into groups to show frequency distribution. consist of set of unique numeric data values, X's, and their frequencies, f's. frequencies - number of times unique data values appeared in data set
a baby is born wit ha birth weight that is equal to the 75th percentile for newborns. explain this meaning?
means 75% of babies weigh the same or less than this baby. and 25% weigh more.
What is another name of the 50th percentile?
the median. 50% above and 50% below.
what is the different between an empirical percentile and a theoretical percentile?
empirical percentiles are based on a relative ranking of the data values themselves whereas a theoretical percentile uses the mean and standard deviation of the data to get percentiles based on a probability distribution, usually the normal distribution.
what does it mean to say that two outcomes of a trial are mutually exclusive?
cannot occur simultaneously
what does the addition rule for probabilities apply?
in general, if A and B are mutually exclusive outcomes of a trial, then addition rules says that Prob(a or B) = prob(A) + prob(B). if not mutually exclusive, then then Prob (AorB) = prob(A) + prob(B) -(probAandB)
what does it mean for two events to be independent?
the outcome of the first event does not affect the probability of the second event.
when does multiplication rule for probabilities for probabilities apply
if A and B are outcomes for two independent events, then Prob(A and B) = prob(A)*Prob(B)
an example where one would use the addition rule for probabilities.
if card is randomly chosen from deck of 52, probability of drawing an ace or a spade are not mutually exclusive outsomes, so one can not use the simple addition
an example where one would use multiplication rule for probabilities
applies when two events are independent. if man is a carrier of recessive gene OCA2 for albinism and recessive gene PKU1 for phenylketonuria, probability that he will pass both genes to his son is Prob(OCA2)*Prob(PKU1) = (1/2)*(1/2) = 1/4
genes on separate chromosomes
father learns that the probability of having three boys in a family of three is 1/8. since already have two children and both are boys, predicts that his next chlid have 7.8 change of being a girl. yes?
no, trial is completely independent from previous next event.
what is the difference between discrete and continuous probability distributions
- -discrete probability distribution consists of set discrete outcomes and their associated probabilities; involve integer values
- -cont. probability dist. involves cont. numeric random variable and associated probability density function; prob are def for intervals or ranges and are given by areas underneath pdf
when to use binomial prob dist?
- when have series of identical independent trials with two possible outcomes for each trial.
- trial have two possible outcomes: boy or girl
an example where probabilities of diff outcomes can be computed using binomial dist.
in an in-vitro fertilization procedure, four embryos are transferred to woman's uterus. if each embryo have 20% of implanting, then number of developing embryos could be predicted using binomial distribution
when to use Poisson prob dist?
when rare events are distributed randomly and independently over time and space.
EX of situation where probabilities outcomes can be computed using Poisson dist.
type of bacteria that's randomly distributed in lake.
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