PPT 1: Descriptive Statistics

PPT 1: Descriptive Statistics

Intro to Biostats

• Why do we use statistics in biology?

  • Most things are probabilistic (data based on probabilities) rather than deterministic (data based on know facts)

Definitions

• What is the difference between observational and experimental populations?

  • Observational- A finite population, but is difficult to count

  • Experimental- An infinite amount in the population

• What is a sample survey (or an observational study)

  • A study of the individuals actually present in a population (under what the investigator can control)

• What is the difference between an experiment and an observation?

  • Observations are descriptions of patterns

  • Experiments are designed to collect observations according to a plan

• What is a sample?

  • The amount of a population actually measured

• What is a sample unit?

  • An individual thing drawn from the population (e.g. an organism or a measurement)

• What is inference?

  • A generalization of an observation (as samples do not always contain all of the population)

• What is random sampling?

  • Truly random, all members of a population have a chance to be chosen

• What is simple random sampling?

  • A random sample within the whole population

• What is a stratified random sample?

  • A random sample within a group (males v females, age 1 age 2, etc)

Biological Variables

• What is continuous measurement of variables?

  • Any value between two extremes can be selected

• What are discrete measurements of variables?

  • Fixed values are chosen between extremes (whole numbers)

• What are rank variables?

  • Indicate more or less of variables based on their rank (e.g. smallest to greatest)

• What are qualitative variables

  • Categorical variables (e.g. male/female, living/dead)

• What is a rate?

  • The quantity per unit (eg. time, mass, births per year)

• What are indices (or index)?

  • Complex derived variables (e.g. condition index: condition of body)

• What is the difference between accuracy an precision?

  • Accuracy- How close a value is to the true value

  • Precision- How close repeated variables are

• What is bias?

  • Departure from the true value

Frequency Distribution

• What can frequency distribution show?

  • Location, dispersion, and symmetry

• What are examples of frequency distributions?

  • Symmetrical unimodal:

• Asymmetrical bimodal:

• Symmetrical uniform:

• Asymmetrical (skewed) unimodal:

• Symmetrical bimodal:

• Extremely skewed:

• What is the difference between absolute and relative frequencies?

  • Absolute- The vertical axis represents the real number of observations

  • Relative- The axis represents a percentage of observations

• What does ∑ represent?

  • The sum of all of the variables

• What is the statistics of location (or mean)?

  • The position of a sample oolong a given dimension representing a variable

• What is the difference between an arithmetic mean and a weighted mean?

  • Arithmetic- The balance point of a distribution. All numbers are treated equally and have equal weight. Most commonly used

  • Weighted- The averages of the values are taken to find the mean (may be based on prevalence or the overall percentage of some variables)

• Why do we transform our results?

  • We want to be able to shift the data to get a normal distribution

• What is the geometric mean (GM)?

  • The back-transformed mean of a log transformed variable (Y becomes logY, and then is changed back to Y)

• What is a harmonic mean?

  • 1/Y

  • When we take a (highly) skewed distribution and make it normal.

• What is the median?

  • M or Y

  • It is the middle value of the distribution

• What is mode?

  • The most frequent value. Can be bimodal or multimodal.

• Where are the mode, median, and means in an asymmetric distribution?

  • Mode- Farthest from the tail

  • Median- in between

  • Mean- Closest to the tail

• What is the mean deviation?

  • A measure of the average deviation from the mean

• What is standard deviation?

  • A measure of the amount of variation from the variables around the mean

  • The square root of the variance

  • σ

• What is variance?

  • The overall deviation of the observations from their mean

• What is a parameter?

  • The true number value of a population (this number is the goal of an estimate)

• What is a sample statistic?

  • The estimate of a parameter based on a sample

• What is μ?

  • The population mean or expected value

• What is ȳ?

  • The unbiased estimate of μ (the mean)

• What is σ?

  • The standard deviation

• If the means and standard deviations are the same, how do we measure interdependence (how variables are related)?

  • We use covariance. It describes the extent and direction of two numerical variables with numbers. You take the product of two deviations.

• What happens if there is a positive covariance?

  • Large Y1, and large Y2

  • Small Y1, and small Y2

  • (left in figure)

• What happens if there is a negative covariance?

  • Large Y1, small Y2

  • Small Y1, large Y2

  • (right in figure)

• What happens if the covariance is 0?

  • (middle of figure)

  • This means that knowing one variable tells you nothing about the other

• What is standardized covariance?

  • The correlation coefficient

  • It scales the variance between -1 and 1

PPT 2: 2 prob and distributions

• What is n?

  • Equally likely outcomes

  • The number of possible events

• What is s?

  • Successful outcomes

• What is the probability of success?

  • s/n

• What is a simple event?

  • Any 1 element in a sample space

  • Only one can occur in a trial

• What is an event?

  • When more successes happen (depending on what is the desired outcome)

• What is an intersection?

  • An “and” relationship among common elements (eg. (A,B) = A⋂B)

• What is a union?

  • An “either/or” relationship among all elements in both sets (e.g. A⋃B)

• What is independence?

  • Among two events, when probability of one occurring does not affect the other

• What is replacement? 

  • P(D)2

  • When you remove one individual and there is a chance of getting another (the sample space is unchanged)

• What happens to the chance of an event (2 draws) happening as the population size increases?

  • Your chance of an event occurring increases

  • A smaller population results in less chances of an event

• Can we multiply two probabilities of the two events we want to get the probability of both events?

  • No

• What is π?

  • The probability of a success

• What is 1-π?

  • The probability of a failure

• What is n and r in C(n,r)?

  • The number of combinations of n things taken r at a time (r successes)

• What is the equation for the mean of the distribution?

  • wi= frequencies (graph)

  • ri= # of successes

• What is the equation for the expected mean (or the absolute frequency of success)?

  • μ (mean) = n (number of equally likely outcomes) π (probability of success)

• What is the equation for the s (standard deviation)  of the distribution?

• What happens to σ with changes in n?

  • σ increases, with an increase of n

  • σ decreases, with a decrease of n

• What is the distribution expected if π (probability of success) is 0.5?

• What is a repulsed distribution?

  • s (success) < σ (SD)

  • When there is excess in the center and too few at the tails

• What is a clumped distribution?

  • s (success) > σ (SD)

  • When there is an excess in tails

• What is skewness?

  • When data has a tail to one side (left or right)

  • Can be measured with g1

• What is kurtosis?

  • The shape and height of a distribution

  • E.g. leptokurtic (high peaked)

  • E.g. platykurtic (rounded)

• What happens to the standard error of the mean with changes of n?

  • As n increases, the SD decreases

• What is a confidence interval?

  • The percent of the results that are expected to include the μ (mean)

• What is the central limit theory?

  • As the sample size n increases, the distribution of the sample mean ( ȳ) approaches a normal distribution, even if the original population is not normally distributed

• What is Pr?

  • 95% of the data is between the two extremes

  • The confidence interval

• 95% probability the true mean is between sample mean +- std error

• 95% of intervals calculated from samples will contain the sample mean

• Changing in the 1.96→ changes the % confidence interval 

  • 1.96 is the Z value

• There is no 100% confidence interval