Chapter 4

T/F 1. A sample systemically has less variability than a population. 2. The standard deviation is the distance from the mean to the farthest point on the distribution curve.

1. True; extreme scores affect variability, but less likely to be included in sample 2. False; standard deviation extends from mean about halfway to most extreme score

What are the two ways in computing SS?

Definitional Formula and Computational Formula

Range

Distance coved by scores in a distribution, from smallest to largest - For continuous data, real limits are:

Deviation

Distance from the mean

Variance

Equals the mean of the squared deviations ---> it's the average squared distance from the mean

What does low variability mean?

Existing patterns can be seen clearly

Does adding a constant to each score change the standard deviation?

No, but the mean is changed

What are the differences between population and sample variance?

Population Variance - mean is known - deviations are computed from a known mean Sample Variance - population mean is unknown - restricts variability

What is the formula for variance?

SS (sum of squares)= sum of squared deviations of scores from the mean

How does samples differ from population?

Samples have less variability

What is the most common and most important way in measuring variability?

Standard Deviation

The standard deviation measures....

Standard distance of a score from the mean

Does multiplying each score change the standard deviation?

Yes, both mean and standard deviation is changed Standard deviation is multiplied by the constant

What are 3 measures of variability?

range, variance, standard deviation

How to find Standard Deviation

the square root of the variance Variance is found as it equals the mean of the squared deviations

What is the purpose of measuring variability?

- Describe distribution of scores --> tells whether scores clustered close together or spread out over a large distance - Measure how well and individual score represents distribution

Sample variance and standard deviation

- Formula for variance has n-1 rather than N in the denominator - Used s instead of σ

Variability

- Quantitative distance measure based on differences between scores - Describes distance of spread of scores or distance of a score from mean

Population Variance and Standard Deviation

- Variance is average of squared deviations and represented as sigma squared: σ^2 - Standard deviation is square root of variance and represented as sigma: σ

T/F 1. A biased statistic has been influenced by researcher error. 2. On average, an unbiased sample statistic has the same value as the population parameter?

1. False; bias refers to systematic effect of using sample data to estimate population parameter 2. True; each sample's statistic differs from population parameter, but the average of all samples will equal the parameter

T/F 1. The computational and definitional formulas for SS sometimes give different results 2. If all the scores in a data set are the same, the Standard Deviation is equal to 1

1. False; results should be identical because computational formula is algebraic rearrangement of definitional formula 2. False; when all the scores are the same, they are all equal to the mean, their deviations=0 as well as their standard deviation

Definitional Formula

1. Find each deviation score 2. Square each deviation score 3. Sum squared deviations

Computational Formula

1. Square each score and sum squared scores 2. Find sum of scores, square it, divide by N 3. Subtract second part from first

How do you know if the sample statistics are unbiased or biased to population parameter?

If sample stats is UNBIASED, then the average value of the stats is equal to the population parameter If sample stats is BIASED, then the average value of the stats is underestimates/overestimated with the population parameter

What does standard deviation describe?

It describes variability by measuring distance from the mean

What does the vertical line in the "center" mean in a population and sample graph?

It is the location of the mean Horizontal line to right, left or both denotes distance of one standard deviation

What is the goal of inferential statistics?

It is used to detect meaningful and significant patterns in research results

What does high variability mean?

It means that it obscure any patterns that might have exist and be visible in low variability samples Variability also called error variance

Standard Deviation

Measure of the standard, or average, distance from the mean Describes whether scores are clustered closely around mean or widely scattered

Degrees of freedom

df= n-1