Bstat CH 1-10 Conceptual

Science of collecting, organizing, analyzing and interpreting data to make more effective decisions

Methods of organizing, summarizing, and presenting data

Making inferences about a population based on a sample

Entire set of objects of interest

A portion of the population

Nonnumeric variables

Numeric variables (discrete = finite, continuous = infinite)

Determines how data should be summarized and presented and indicates the type of statistical analysis that can be performed (NOIR)

Data presented as labels/names, has no order, can only be classified or counted

Classified data that is either ranked or rated on a relative scale

The interval or distance between values is meaningful

The data has a meaningful interpretation of 0 on the scale

Ways to describe quantitative data in terms of centrality (mean, median, mode)

Ways to describe quantitative data in terms of variation (range, variance, standard deviation)

The average of a set of data
-atleast interval level
-unique
-sum of deviations of each value = 0
-affected by outliers

The middle value of a set of data
-atleast ordinal level
-not affected by outliers
-unique

The value that appears most frequently in a set of data
-atleast nominal level (all levels)
-not unique

The difference between the maximum and minimum values in a set of data
- (-): does not consider all values in a dataset

The variation around the mean (need to know mean to calculate)
-answer is in squared units
- = sum of (x-xbar)squared / n-1

The positive square root of the variance

For any set of observations, the proportion of values that lie within k standard deviations of the mean is at least 1-1/k^2 where k>1

Lists all the possible outcomes for an experiment and their probabilities
-probability of an outcome between 0 and 1
-outcomes are mutually exclusive
-list of outcomes are exhaustive (added = 1)

A variable measured as a result of an experiment
-discreet and continuous random variables

A probability distribution of a continuous random variable that is . . .
-bell-shaped
-asymptotic
-symmetrical around the mean
-total area under curve = 1

A unique distribution where the mean is 0 and the standard deviation is 1

How far away a value is from the mean in units of standard deviation
- = (x + mu) / standard deviation

If a random variable is normally distributed, approximately
-68% of observations will lie within +- 1 s.d. of the mean
-95% will lie within +- 2 s.d. of the mean
-99.7% will lie within +- 3 s.d. of the mean

All members of the population are known and have the same chance of being selected

A random starting point is selected, and then every kth member of the population is selected

The population is divided into strata, and a sample is randomly selected from each stratum

The population is divided into clusters using naturally occurring geographic or other boundaries, and then clusters are randomly selected, and a random sample is selected from the clusters

A probability distribution of sample statistics

The difference between a population parameter and a sample statistic

If the population follows a normal probability distribution or the sample size is >30, then the sampling distribution of the sample mean is approximately normal

A value computed from sample information used to estimate a population parameter (ex: sample mean or sample proportion)

Precision determined by:
1. level of confidence (larger CL, lower precision)
2. variability in population (greater variation, lower precision)
3. sample size (n) (greater sample size, higher precision)

An interval of values in which the parameter will fall under a certain level of predetermined confidence
- To compute a confidence interval, we must know whether the variance is known or unknown
- If the variance is known, we use the z-distribution
- If the variance is unknown, we use the t-distribution

A distribution used when the variance is unknown and the sample size is small (also with quantitative data)
-continuous
-bell shaped
-mean = 0, s.d. depends on n
-more spread out (more variability)
-uses degrees of freedom

A distribution used when the variance is known and n is large
-also with qualitative data
-continuous
-bell shaped
mean = 0, s.d. = 1
narrower than t-dist
does not use degrees of freedom

The number of independent variables that can be estimated in a statistical analysis

The fractionatio/percent indicating the part of the sample having a particular trait/attribute

1. binomial conditions
2. n(p) and n(1-p) >= 5

1. Margin of error (E) the researcher will tolerate
2. level of confidence desired
3. variation of population being studied

if sampled population is finite then adjustments to the margin of error need to be made to compute the CI for a sample proportion or mean
*when sample is large compared to the population you need to adjust margin of error

A procedure based on sample evidence and probability to determine whether a hypothesis is reasonable

The hypothesis being tested, states the 'status quo' about the population parameter

The hypothesis being researched, states the 'expectation' about the population parameter

Rejecting the null hypothesis when it is actually true

Accepting the null hypothesis when it is actually false

A sample value used to reject or accept the null hypothesis (t or z)

The dividing point between where the null hypothesis is rejected and where it is not
-# from chart to create the RR
-reject the null if the test statistic falls in RR set by critical value

The probability of observing a sample value as more extreme than the one currently being observed
-reject null if p-value < alpha level