stat exam 1

Statistics

statistical procedures and the answers obtained from those procedures.

statistical procedures are used to:

organize, summarize, and communicate data, and then conclude what the data indicate

empirical

•knowledge obtained through observation of events. Empirical research involves measurement.

data

The scores obtained in research

statistical notation

the standardized code for symbolizing the mathematical operations performed in the formulas and the answers we obtain

rounding

the final answer after rounding needs two more decimal places than the original score

transformation

mathematical procedure for systematically converting a set of scores into a different set of scores.

proportion

•a decimal number between 0 and 1 that indicates a  fraction of the total

percent

a proportion multiplied by 100

x-axis

the horizontal line across the bottom of a graph

y axis

the vertical line at the left hand side

population

The entire group to which a law applies

sample

a relatively small subset of a population that is intended to represent, or stand for, the population

participants or subjects

The individuals measured in a sample

representative sample

the characteristics of the sample accurately reflect the characteristics of the population.

random sampling

method of selecting a sample in which the individuals are randomly selected from the population.

stratified random sample

proportionate across a variable.

cluster sample

a common group taken together

quantitative variable

indicates the amount of a variable that is present

qualitative variable

classifies an individual on the basis of some characteristic

variable

anything that, when measured, can produce two or more different values

descriptive statistics

uprocedures used for organizing and summarizing data.

inferential statistics

procedures for deciding whether sample data accurately represent a particular relationship in the population, they allow us to make inferences about the score and relationship found in the population

studys design

the way the study is laid out

2 major types of designs

experiments, correlational studies

experiment

the researcher actively changes or manipulates one variable and then measures participants’ scores on another variable to see if a relationship is produced

independent variable

uthe variable that is changed or manipulated by the experimenter.

condition

uis a specific amount or category of the independent variable that creates the specific situation under which participants’ scores on another variable are measured.

The dependent variable

uthe variable that is measured under each condition of the independent variable.

correlational study

measure participants’ scores on two variables and then determine whether a relationship is present

What determines the statistic that can be used?

research hypothesis and how data is measured (scaling)

4 types of measurment scaled

nominal, ordinal, interval, ratio

nominal sclae

does not indicate an amount; rather, it is used for identification, as a name

ordinal scale

indicates rank order. There is not an equal unit of measurement separating each score.

interval scale

uscale indicates an actual quantity and there is an equal unit of measurement separating adjacent scores. Interval scales do not have a “true” 0.

ratio scale

reflects the true amount of the variable that is present because the scores measure an actual amount, there is an equal unit of measurement, and 0 truly means that zero amount of the variable is present.

continuous scale

allows for fractional amounts and so decimals make sense

discrete scale

only whole-number amounts can be measured

frequency

The number of times a score occurs, symbolized by f

distribution

the general name for any organized set of data

N

the sample size indicating the number of scores

simple frequency distribution

shows the number of times each score occurs in a set of data

a simple frequency bar graph is used for what kind of data

nominal and ordinal

a histogram is used for what kind of data

interval or ratio

a frequency polygon is used for what kind of data

large range of differnt scores

normal distribution

bell shaped curve (normal curve), the far left and right portions are called the tails

tails of normal distribution

The far left and right portions containing the low-frequency extreme scores

skewed distributions

not symmetrical as it has only one pronounced tail, positive or negative skew

negative skew

contains extreme low scores that have a low frequency, but does not contain low frequency extreme high scores

positive skew

contains extreme high scores that have a low frequency, but does not contain low frequency extreme low scores

bimodal distribution

symmetrical distribution containing two distinct humps

rectangular distribution

a symmetrical distribution shaped like a rectangle

relative frequency

the proportion of time the score occurs

cumulative frequency

the frequency of all scores at or below a particular score

percentile

is the percent of all scores in the data that are at or below the score

measure of central tendency

•a score that summarizes the location of a distribution on a variable

•It is a score that indicates where the center of the distribution tends to be located

mode

most frequently occurring score

unimodal

When a polygon has one hump

bimodal

When a distribution has two scores that are tied for the most frequently occurring score

median

the score at the 50th percentile

When data are normally distributed

the median is the same score as the mode

the mean

the score located at the mathematical center of a distribution

deviation

is the distance separate the score from the mean

positive skew graph where is everything located (mean, median, mode)

mode is far left, median middle, mean far right

negative skew graph where is everything located

mean is left, median middle, mode right

Measures of variability

the extent to which scores in a distribution differ from each other.

The variance and standard deviation

two measures of variability that indicate how much the scores are spread out around the mean

sample variance

the average of the squared deviations of scores around the sample mean

sample standard deviation

the square root of the sample variance

standard deviation

the “average deviation” from the mean, the consistency in the scores, and how far scores are spread out around the mean

population variance

the true or actual variance of the population of scores.

population standard deviation

is the true or actual standard deviation of the population of scores.

z scores

is a location on the distribution. A z-score also automatically communicates the raw score’s distance from the mean

describes a raw score’s location in terms of how far above or below the mean it is when measured in standard deviations

original raw score

when a z score and the associated Ox and mu are known, you can caluclate this

z-distribution

the distribution produced by transforming all raw scores in the data into z-scores.

standard normal curve

perfect normal z-distribution that serves as our model of the z-distribution that would result from any approximately normal raw score distribution

sampling distribution of means.

A distribution which shows all possible sample means that occur when an infinite number of samples of the same size N are randomly selected from one raw score population

central limit theorem

tells us the sampling distribution of means

standard error of the mean

The standard deviation of the sampling distribution of means

After exploring the literature on topic

hypotheses are developed

Hypotheses are predictions

often about how one variable (IV) impacts another (DV).

hypotheses are

operationally defined

a clear hypothesis dictates

the research design

prediction of hypothesis is tested against

alpha (.05)

testing involves three competing hypotheses:

null

confounding

alternate hypothesis

null

no difference/effect, either accept or reject null.

confounding

even if statistical significance is found, must rule out other variables, extraneous variables.  Can control for before and after study, some are never known.

alternate hypothesis

predicted hypothesis, determined statistically by ruling out previous two.  Decision is made based on acceptance or rejection of Null. 

if a number (p) is greater than 0.05 then what

not statistically signifigant and fail to reject null hypothesis

if a number (p) is less than 0.05 then what

is statistically signifigant and you reject null hypothesis

type 1 error

false positive, which means there is no effect (null is true), a researcher does something and it really doesnt work but their results say it works (basically out of luck) You think you found something, but you didn't. (Alarm goes off, but there is no fire).

type 2 error

false negative, a test tells you something is negative (no result, no effect, no disease) when the true reality is positive (there is a result, effect, or disease).