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.