stats test 2

An inferential statistic z-score is used to determine

whether a specific sample is representative of the population the sample was taken from

Standard Deviation

- Measure of variability from the mean. - Larger score equals larger spread.

What is a standard error?

- the standard deviation of the distribution of sample means. - provides a measure of how much distance is expected on an average between a sample mean (M) and the population mean (u)

Explain a Related t-test

A parametric test for difference between two sets of scores. Data must be interval with a related design, i.e. repeated measures or matched pairs design.

Sample mean symbol

M

Sample standard deviation symbol

S

Sigma symbol

Sum up all the values of X

mode

The most frequently occurring category or score occurring in a distribution. Only measure of central tendency that works for nominal scale

alternative

assumes there is a relationship/difference/effect

null

assumes there is no relationship/difference/effect

μ

mean for a population

What does a z for a sample mean represent?

- The mean of the distribution of sample means is always equal to the population mean μ. - tells where sample mean is located - (+) z-score indicates a sample mean is greater than the pop mean - (-) z-score corresponds with a sample mean that is smaller than the pop mean. - descriptive statistics and inferential statistics

variability

- a way of summarizing how spread out the scores in a distribution are - how scores are scattered around the central point

mean

arithmetic average Calculating it requires numerical values measured on an interval or ration scale. It is obtained by adding up all the scores for the entire set of scores, then dividing this sum by the number of scores. (data: 1,2,2,3,5, thus _____= (1+2+2+3+5)/5

Alpha Level

ejection region. Alpha is .05 the rejection region is 5%

interval

equal intervals, categorize, rank order

interval estimation

error in point estimation, estimate that error within a range (ex. confidence intervals)

robust

even if you violate a t-test's assumption, it will usually still tell you the right answer

A descriptive statistic z-score describes

exactly where each individual is located

descriptive statistics

help us organize and summarize data

point estimation

infer from a sample statistic the corresponding population parameter (with one point) (s-hat)

If you change a score, add a score, or remove a score this will change the...

mean

x̄

mean for a sample

In a symmetrical distribution the...

mean, mode and median will always be equal

negative skew

mean<median (left)

positive skew

mean>median (right)

dependent variable

outcome of interest in an experiment, what we measure

correlational studies

participants come with their group membership (ex. # of pets, political affiliation, gender)

correlation

quantify the strength and direction of the relationship between two variables

type I error

rejecting a true null It was determined that there was a difference b/w groups when there actually is none

type II error

retaining a false null It was determined that there was no difference b/w groups when there actually is

repeated measures

same participants are tested twice

bar graph

set of NONadjoining rectangles whose heights represent frequency values, NOMINAL data

central tendency

single score representing the entire data set and it helps us interpret single scores (ex. mean, mode, range)

The mean doesn't work if you have ______________. Instead you can use ____________

skewed data or outliers. the median score

interpretation of r

small = .1 medium= .3 large= .5

Variability can be measured with

standard deviation/ variance and range

quantitative

tells about amount or degree of variable

main effect

the effect that one factor has on the DV regardless of the other factor

The smooth curve on a graph emphasises

the fact that the distribution is not showing the exact frequency for each category

expected value

the mean of a sampling distribution

rectangular distribution

the number of events are all equally likely

central limit theorem

the sampling distribution of the mean approaches a normal curve as N gets larger

theoretical

use mathematics to estimate distributions

independent variable

used to describe/explain DV differences or cause the DV changes

What happens to the standard error of the mean as n decreases?

As you increase your sample size, the standard error of the mean will become smaller. With bigger sample sizes, the sample mean becomes a more accurate estimate of the parametric mean, so the standard error of the mean becomes smaller.

random sample

subset of a population chosen so that all samples of size N have an equal opportunity of being selected

t-test singles sample

Data: Interval/Ratio # of Groups (1IV & 1DV): 1 Groups: Independent

t-test independent Samples

Data: Interval/Ratio # of Groups (1IV & 1DV): 2 Groups: Independent

median

Is the score that divides a distribution exactly in half. Also called the 50th percentile (50% of scores will be on wither side on the mid point)

How to calculate the median

Line up the scores in numerical order (rank order), hence they must measure on an ordinal, interval or ratio scale) then find the centre score

The sum of frequencies should equal

N, the total sample size

ordinal

NOT equal intervals (ex. educational level, place in a contest, standing in graduation class)

Beta

Probability of making a Type II error

How does standard error relate to a standard deviation?

SD, measures the amount of variability or dispersion for a subject set of data from the mean, while the standard error of the mean, or SEM, measures how far the sample mean of the data is likely to be from the true population mean. The SEM is always smaller than the SD.

histogram

Set of ADJOINING rectangles whose heights represent the frequency of their values; QUANTITATIVE data

What is the 'rule of r'?

Statistical tests with a letter 'R' in their name are those where the calculated value must be equal to or more than the critical value

How does a z differ from a t?

The Z score is scaled down by the population standard deviation. The T score is scaled down by the sample standard deviation. With a very large sample of means you can assume normality and use the Z score.

sample

subset of observations from the population of interest

range

Total distance covered by the distribution from the highest score to highest score to the lowest scores

Sampling Error

Untreated sample means are not frequently identical to pop. means

empirical

based on actual scores

nominal

categorize people/subjects into groups, groups usually have a title

ratio

categorize, ranks order, equal interval, true zero

parameter

characterizes a population

Cohen's interpretation of Effect Size

d=.2 (small) d=.5 (medium) d=.8 (large)

binomial distribution

distribution of the frequency of events that an have only 2 possible outcomes (ex. sex of a baby, flipping a coin, playing cards color)

inferential statistics

draw conclusions about populations based on sample data

Calculate Standard Error of the mean

1) total all samples divided by the # of samples 2) subtract the mean by the individual measurement 3) square each devotion from the mean 4) Add all the #'s from step 3 5) divide sum from step 4 by one less (n-1) 6) take square root of the number in step 5. = SD 7) divide SD by the square root of the sample size (n) = standard error 8) Subtract the Standard Error from the mean. Then add the SE to the mean

Calculating the standard deviation

1. Calculate each score's deviation (distance form the mean) 2. Square each deviation 3. Compute the mean for the squared deviations (this is the variance) 4. Take the square root of the variance (this is the standard deviation)

population

All participants

Standard Error of the Mean

Any spread or deviation in means (5 groups of 25 people assessed on IQ)

Z-scores

Correspond directly to SD Mean=0 SD-1 z-score of 2=2 SD above mean

A measure of central tendency and variability are __________ for a set of score

basic descriptive statistics

Frequency distribution

distribution of individual scores

Sampling distribution

distribution of sample statistics

What is the difference between σ and s?

σ : Population SD - gives amount of data for entire population - represents a parameter(every individual) S: Sample Standard Deviation - statistic that measures the distribution of data around the sample mean. - only examines some of the individuals in the population but has greater variability because it is more specific.