Lecture 2

Question 1

what are 2 measures of dispersion?

how are they related to each other?

Answer 1

1. variance
2. standard deviation

standard deviation = sqrt (variance)

Question 2

what are the two different types of estimators?

how do they differ?

Answer 2

1. sample statistics - latin letters
2. population statistics - greek letter

> sample statistics are random variables, they vary from sample to sample

> population statistics are parameters, they have a fixed (but mostly unkown) value

Question 3

estimation of population variance

> when is estimator of population variance biased?

> when not?

Answer 3

population variance estimator

> is unbiased if population mean is known

> is biased if population mean is unkown, thus based on sample mean

> sample mean varies per sample, estimator of population variance mostly too small

Question 4

if population mean is unknown

> solution for systematic underestimation of population variance?

Answer 4

underestimation of population variance due to unkown population mean

> divide by n-1 instead of n

Question 5

what is the general principle behind the degrees of freedom?

Answer 5

whenever we use an estimated parameter, we lose a degree of freedom

Question 6

how big is the total area below the curve of a standard normal distribution?

Answer 6

1

Question 7

what are the one sided 5% cutoff values?

two sided 5% cutoff value?

Answer 7

one side cutoff 5%: 1.65

two sided cutoff 5%: 1.96

Question 8

what is the SEM

Answer 8

SEM: standard error of the mean

> indication of reliability of m as an estimator of mu

Question 9

what are the 3 assumptions of the central limit theorem

Answer 9

central limit theorem

1. the mean of the distribution equals the population mean
2. the standard deviation of the distribution of means equals SEM
3. n increases, the shape of the sampling distribution of means approaches that of the normal distribution, regardless the shape of the population distribution

Question 10

hypotheses always relate to …?

Answer 10

hypothese always relate to population statistics

Question 11

what are 3 influences on the t test statistic?

Answer 11

t is more extreme as

1. effect (m1-m2) is more extreme
2. spread (s1-s2) is smaller
3. n is greater

Question 12

when does the t distribution approximate the z distribution?

Answer 12

only for large sample sizes

solution: student t distribution (william gosset)

Question 13

how to treat matched pair designs with refard to analysis?

Answer 13

matched pair designs are classified along with repeated measure designs

> paired data