chpt 4

True or False: The Standard Deviation is the distance from the mean to the farthest point on the distribution curve

False! The standard deviation extends from the mean approximately halfway to the most extreme score.

True or False: A biased statistic has been influenced by researcher error

False. Bias refers to the systematic effect of using sample data to estimate a population parameter

True or False If all scores in a data set are the same, the Standard Deviation is equal to 1.00

False: When all the scores are the same, they are all equal to the mean. Their deviations = 0, as does their standard deviation.

Population Parameter

Mean: U=EX/N Variance: o~^2=ES/N=SS/N Standard Deviation:o~

Standard deviation

Most common and most important measure of variability is the standard deviation. -A measure of the standard/average, distance from the mean. -Describes if the scores are clustered closely around the mean or widely scattered.

Degrees of freedom:

Number of observations in a sample that are free to vary. df=n-1

True or False: On average, an unbiased sample statistic has the same value as the population parameter.

True. Each samples statistic differs from the population parameter, but the average of all samples will equal the parameter.

Population variance formula

Variance= sum of squared deviations/ number of scores SS= sum of squares

Interquartile range (IQR) is a...

a measure of variability that attempts to capture the range of the middle of the distribution. Range covered by the middle 50% of the distribution.

Standard Deviation

square root of variance because variance is standard deviation^2

Formula for the population variance is not the same as

the formula for the sample variance.

Average squared deviation is called

variance sum(X-mean)^2/N aka o~2

In an FINITE (small) sample we can figure-out the nth observation if

we know the mean M & we know the first (n-1) observations.

average deviation

what is the 'average deviation' across all scores?

Sum of deviation is always ____

zero.

Formula for the population mean is identical to

the formula of sample mean.

UNBAISED estimate of a population parameter

-Average value of statistic is equal to parameter -Average value uses all possible samples of a particular size 'n' -Corrected standard deviation formula (Dividing by n-1) produces an unbiased estimate of the population variance.

Goals for Inferential Statistics

-Draw general conclusions about population -based on limited information from a sample.

Samples differ from the population

-Samples have less variability -Computing the Variance and Standard Deviation in the same way as for a population would give a biased estimate of the population values.

Multiplying each score by a constant

-The mean is changed -Standard Deviation is also changed -The standard deviation is multiplied by that constant.

Adding a constant to each score

-The mean is changed -The standard deviation is unchanged

BIASED estimate of a population parameter

-systematically overestimates or underestimates the population parameter.

Quartiles

1st quartile(designated Q1) = lower quartile or the 25th %(Splits off the lowest 25% of data from the highest 75%) 2nd quartile(designated Q2) = median or the 50th % (cuts data in half) 3rd quartile(designated Q3) = upper quartile or the 75th% (splits off the highest 25% of data from the lowest 75%)

In a graph: Vertical line in the "center" denotes location of _____?

Mean

sample statistic

Mean: M=EX/n Variance: s^2=ES^2/N-1=SS/N-1 Standard Deviation: s

In a graph: Horizontal line to right, left or both denotes the distance of one _______ _________.

Standard deviation.

Defining the Standard Deviation

Step 1: Determine the Deviation(The distance from the mean.) Step 2:Find a "sum of deviations" to use as a basis of finding an "average deviation"(Deviations sum to zero so....) Step 2 Revised: Remove negative deviations.(1. FIRST sum the squared deviations.((SS)) 2. sum the squared deviations (SS)) Step 3: Average the squared deviations.(mean squared deviation is known as Variance and Variability is now measured in squared units.) Step 4:Goal to compute a measure of the standard (average) distance of the scores from the mean.

Range

The distance covered by the scores in a distribution. (highest score+.5)-(lowest score-.5)=range.

Variance is a necessary ______ _________ to standard deviation but NOT the same concept

companion concept

In an INFINITE sample we CANNOT

figure-out the infinitTH observation.(uncountable)

Sample variance

has (n-1) in the denominator -s^2=ES^2/n-1 = SS/N-1

population variance

has N in the denominator -o~^2=ES/N=SS/N

Deviation O~=(X - u)

how far away is an observation from the mean?

s^2 is popularly called SS because

it is sum of squares. or sum of squared deviation