Stats 1

statistics

statistics are mathematical techniques used by social scientists to analyze data in order to answer questions and test theories

variable

any trait that can change values from case to caseand can be measured or categorized.

hypothesis

a statement about the relationship between variables that is specific and exact

a variable is said to be discrete if…plus example

it has a basic unit of measurement that cannot be subdivided…example—number of people per household

a variable is said to be continuous if….plus example

it has scores that can be subdivided infinitely (at least theoretically), suc has time

examples of nominal levels of measurement:

zip code, political party affiliation, and relgiiosu preference, gender

examples of ordinal levels of measurement

socioeconomic class, pain scale, satisfaction level—the scores have no absolute or objective meaning and the distance between scores cannot be described in precise terms

interval-ratio level

actual numbers that can be analyzed with all possible statistical techniques—add or multiply scores, they have equal intervals and true zero points—number of children, life expectancy, years married, number of siblings, years of education, income

measures of association

statistics that summarize the strength and direction of the relationship between varialbles

descriptive statistics

the branch of statistics concerned with summarizing the distribution of a single variable or measuring hte relationship between two or more varialbegsd

discrete variable

a variable with a basic unit of measurement that cannot be subdivided

continuous variable

a variable with a unit of measurement that can be subdivided infinitely

inferential statistics

the branch of statistics concerned with making generalizations from samples to populations

theory

a generalized explanation of the relationship between two or more variables

cumulative frequency

an optional column in a frequency distribution that displays the number of cases within an interval and all preceding intervalsfr

frequency distribution

a table that displays the number of cases in each category of a variable

inference

conclusion based on a data point

statistic

data point derived from evidence

nominal and ordinal levels of measurement are also known as…

grouped/discrete levels of measurement

interval/ratio levels of measurement are also known as

continuous

sex, race, religion, are examples of ____ levels of measurement (classify not order)

nominal

social class, attitude, and opinion are examples of _____ level of measurement

ordinal—classify into categories and rank them

age, number of children, income are all examples of ____ level of measurement

interval-ratio, spacing between numbers if quantifiable, equal units

three commonly used measures of central tendency:

mode (most common score), median (the score of the middle case), mean (average score)

what is the formula to calculate the mean?

summation of scores/the number of cases

measures of variation describe…

the variety, diversity, or heterogeneity of a distribution of scores

interquartile range (Q) is

the range of the middle 50% of cases in a distribution; the difference between the third and first quartile

deviation

the difference between the score and the mean

standard deviation

a statistic that quantifies the amount of variation around the mean

variance

the square of the standard deviation

variation

the amount of variety, or heterogeneity, in a distribution of scores

characteristiscs of the mean

all scores cancel out around the mean (sum of deviations from the mean is zero), the mean is the point of minimized variance (least squares principle), the mean uses all the scores (the mean is affected by extreme values—outliers)

strength and weaknesses of the mean:

strength: the mean uses all the availabl einformation from the variable. weaknesses: the mean is affected by every score. If there are some very high or low scores, the mean may be misleading.

for a positive skew, the mean will be ____ than the median

greater than

for a negative skew, the mean will be ___ than the median

less than

the range

high score-low score. quick and easy indication fo variability. limitations based on only two scores: distorted by atypically high or low scores. No information about variation between high and low scores.

percentiles

let you know where you lie in relation to others; statistics that indicate where observation lies, relative to otherst

the median is the ___ percentile

50% percentile

Interquartile range (Q)

avoids some problems of R by focusing on the middle 50 percent of scores

normal curve

a theoretical distribution of scores that is symmetrical, unimodal, and bell-shaped. The standard normal curve always ahs a mean of 0 and a standard deviation of 1.

normal curve table

a detailed description of the area between a Z score and the mean of any standardized normal distribution

Z scores

standard scores; the way scores are expressed after they have been standardized to the theoretical normal curve

What are characteristics of the normal curve?

bell-shaped, unimodal, symmetrical, unskewed, mode+mean+mean, follows the empirical rule

the empirical rule

68-95-99 rule (typically rounded up at 0.5, but you susaully don’t round a probability up to 1

z=

(x-x̄)/s or (raw-mean)/standard deviation

Central Limit Theorem

a theorem that specifics the mean, standard deviation, and the shape of the sampling distribution, given that the sample is large

Cluster sampling

a method of sampling by which geographical units are randomly selected and all cases within each selected unit are tested

EPSEM

the equal probability of selection method for selecting samples. Every element or case in the population must have an equal probability of selection for the sample.

nonprobability sample

any sample that does not mean the EPSEM criterion

nonprobability sample

any sample that does not meet the EPSEM criterion

parameter

a characteristic of apopulationrep

representative sample

a sample that reproduces the major characteristics of the population from which it was drawn

sampling distribution

the distribution of a statistic for all possible sample outcomes of a certain size. Under conditions specified in two theorems, the sample distribution will be normal in shape, with a mean equal to the population value and a standard deviation equal to the population standard deviation divided by the square root of N

sampling frame

a list of all the cases in a population. The list can be numbered and used to draw a simple random sample, a systematic random sample, or a stratified random sample

simple random sample

a method for choosing cases from a population by which every case and every combination of cases has an equal chance of being includedst

standard error of the mean

the standard deviation of a sampling distribution of sample meansst

stratified sample

a method of sampling by which cases are selected from sublists of hte populations

systematic sampling

a method of sampling by which the first case from a list of the population is randomly selected. Thereafter, every kth case is selected

the central problem of statistics

We want to know about a population. All we’ve got is one sample. We must use that sample to make inferences about the population.

Point estimate

Use the sample statistic to make your best guess about the (most) likely value of the population parameter—the sample statistic

Interval estimate/confidence interval

use the sample statistic and other information from the sample and some choices to make an educated guess about the likely range of values of a population parameter

alpha level

alpha levels reflect your willingness to be wrong—ie to have the interval “miss” the true population value, or to have the true population value fall outside the interval. every alpha level has a corresponding z-score, sometimes call a critical value.

smaller alpha level

more likely to be right, but interval is wider, so your estimate is less informative

larger alpha level

less likely to be right but interval is narrower, so your estimate is more informative