Biostats chapter 1

what do you use to infer population mean?

sample mean

estimation

using a sample mean to infer population mean, calculate mean measurement in the sample, and take the sample from the population to measure each for the mean; approximation based on the sample

parameter

true value you want to know

sources of uncertainty or error

-sample may not be representative of the total population

-only subset of total population is measures

-measurements of individuals could have mistakes

quantifying uncertainty importance

in estimates, it is essential for drawing inferences about the populations

lower, more

the _______ the uncertainty, the _____- confidence we can place on estimates from

purpose of acorn experiment

illustrate the concept of generating estimates of population parameters from statistical samples

haphazard sample

close enough to truly random to be reasonably good

variable

measurements that can or will not be manipulated

-length

-width

sampling error

random or nonsystematic difference beween a sample estimate and the true population parameter

explanatory variable

explains or predicts variation in the response variable; causes variation is the direction of causation; independent

response variable

dependent

experimental

involves manipulation of the explanatory variable in a way that variation in the response variable can be attributed to causation

confounding variables

avoided by random assignment of treatments and helps infer causation

numerical:discrete

number of partners in a year

numerical:continuous

petal area of rose flowers

numerical:continuous

heartbeats per minute of a cyclist averaged over the duration of the race

numerical:continuous

birth weight

categorical:ordinal

stage of fruit ripeness

numerical:continuous

angle of flower orientation relative to the position of the sun

categorical:nominal

tree species

numerical:discrete

year of birth

categorical:nominal

gender

The population of interest is the pinion trees in the coastal range of CA. The researches took an average rather than combining into a single unit because it provides a better characterization of the population of interest because it is a random sample to minimize bias

The average age of pinion pine trees in the coast ranges of California was investigated by placing 500 10-hectare plots randomly on a distribution map of the species using a computer. Researchers then found the location of each random plot in the field, and they measured the age of every pinion pine tree within each of the 10-hectare plots. The average age within the plot was used as the unit measurement. These unit measurements were then used to estimate the average age of California pinion pines.

In reference to the pinion study, is the estimate of age based on 500 plots influenced by sampling error?

Yes, because they are only a subset of the total population, so the estimated age may differ from the true mean population age. If changes to 100 plots, the sampling error would increase.

explanatory:presence of vkorc1 mutation

response:survival

observational study

The anticoagulant warfarin is often used as a pesticide against house mice, Muss musculus. Some populations of the house mouse have acquired a mutation in the vkorc1 gene from hybridizing with the Algerian mouse, M. spretus (Song et al. 2011). In the Algerian mice, this gene confers resistance to warfarin. In a hypothetical follow-up study, researchers collected a sample of house mice to determine whether presence of the vkorc1 mutation is associated with warfarin resistance in house mice as well. They fed warfarin to all the mice in a sample and compared survival between the individuals possessing the mutation and those not possessing the mutation.

explanatory:care treatment

response:anxiety score

experimental study

Cooley et al. (2009) randomly assigned either of two treatments, naturopathic care (diet counseling, breathing techniques, vitamins, and an herbal medicine) or standardized psychotherapy (psychotherapy with breathing techniques and a placebo added), to 81 individuals having moderate to severe anxiety. Anxiety scores decreased an average of 57% in the naturopathic group and 31% in the psychotherapy group.

explanatory:reward sensitivity score

response:fMRI activity of fronto-striatal-amyglada-midbrain

observational study

Individuals highly sensitive to rewards tend to experience more food cravings and are

More likely to be overweight or develop eating disorders than other people. Beaver et al.(2006) recruited 14 healthy volunteers and scored their reward sensitivity using a questionnaire (they were asked to answer yes Or no to questions like “I’m always willing to try something new if I think it will be fun”). The subjects were then presented with images of appetizing foods (e.g., chocolate cake, pizza) while activity of their fronto-striatal-amygdala-midbrain was measured using functional magnetic resonance imaging (fMRI). Reward sensitivity of subjects was found to correlate with brain activity in response to the images.

explanatory:endostatin does

response:tumor growth

experimental study

Endostatin is a naturally occurring protein in humans and mice that inhibits the growth of blood vessels. O’Reilly et al. (1997) investigated its effects on growth of cancer tumors, whose growth and spread require blood vessel proliferation. Mice having lung carcinoma tumors were randomly divided into groups that were treated with doses of 0, 2.5, 10, or 20 mg/kg of endostatin injected once daily. They found that higher doses of endostatin led to inhibition of tumor growth.

random sample

the example with the ocean diving birds is not an example of this because the measurements are not statistically independent (some birds might have higher or lower heart rates).

explanatory:CCSVI

response:MS

observational study

hypothesis could have been used by stating the proportion of people possessing CCSVI who also have MS is higher than the proportion of people without CCSVI that have MS.

Garci et al. (2012) examined a sample of people with and without multiple sclerosis (MS) to test the controversial idea that the disease is caused by blood flow restriction resulting from a vein condition known as chronic cerebrospinal venous insufficiency (CCSVI). Of 39 randomly sampled patients with MS, 25 were found to have a CCSVI and 14 were not. Of 26 healthy control subjects, 14 were found to have CCSVI, and 12 were not. The researchers found an association between CCSVI and MS

hypothesis

tested in statistics that requires formulating a statement about a parameter that can then be tested with an estimate

random sample definition

-every individual in the population has an equal chance of being represented in the sample’

-the probability of an individual being representing in the sample is independent of the presence of other individuals in the sample

what is the value of taking a random sample for estimation?

help to ensure that the sample is representative of the population, which in turn helps to avoid systematic error or bias

number each acorn in the population and then use a random number generator to determine which acorns should be in the sample

for the acorn experiment, how can you take a random sample from the class population?

each student shakes the tub, closed eyes and selects an acorn

for the acorn experiment, how can you take a haphazard sample?

acorn experiment measurement errors with the variables

inconsistency in what proportion of the acorn is measured for length/width. subjectivity with assignment of color. Distortion in shape of acorn when case peels off. difficulty in seeing weevil holes when case peels. could minimize with coordination

length

numeric;continuous

width

numeric;continuous

number of bore holes

numeric;discrete

bore hole presence

binary

color

categorical;discrete

range representation

measures of variation among measurements of the individual acorns

histogram

depicts frequency distributions to show the number of observations that fall within ranges of values evenly divided across the entire data set

acorn length and width histograms

depict variation among acorn measurements. range and SD quantify the extent of variation and displays pattern of variation across the data set

What does mean of a variable represent?

typical or expected value

What does the mean bore hole presence represent?

proportion of acorns with bore holes

quantitatively summarize the qualitative acorn color measurement

calculate proportion of individuals in each volor category

What do the means calculated represent?

population parameters because the 100 acorns represent a population

what do the means calculated from only your acorns represent?

estimates because it is the sample

are the means identical

no because of sampling error. there is always some random deviation between the estimate and the parameter

what does the histogram of mean estimates represent?

variation in estimates taken from the repeated samples of the population. It conveys the uncertainty in our estimates due to sampling error (sampling distribution)

why do mean estimates differ?

sampling error and precision. more precision means less sampling error

bias

nonrandom or systematic error between the sample estimate and population parameter

how can haphazard sampling introduce bias?

some students could choose certain acorns as a group making a nonrepresentative of the population

biases if our acorns represent the population of interest

acorns being taken from the ground and then planted in a residential area in omaha with a different environment affecting how they grow and produce. Then being collected from the ground in a nonrepresentative way

hypothesis with class data

could be tested in what we come up with: the longer the acorn, the lighter the color with the explanatory being length and response being color.

bar graph

was made to test our own hypothesis which is not the best way to look at data but a good start. Can see whether it supports our hypothesis or not. Would need to quantify the uncertainty to avoid sampling error and consider biases

forming our own experiment

observational study of sending participants that are not aware of the hypothesis that choose only light acorns and then we measure to see if they are greater than or equal to 2.5 cm.

confounding variable

variable that could defer causes away

advantages of our experiment

minimizations of confounding variables by assigning experimental treatments and done randomly; needs manipulation to make experimental study