Why 1) do we use samples?
Samples are used by researchers who are interested in finding results that apply to an entire population of
people or things. A population can be very general or very narrow. we cant collect all the data about a
research because of the number of these data, so we choose part of the data to represent things about the
data as a whole. This part of data is sample.
2) What is the mean and how do we tell if its a representative of the data?
A mean is a statistical model of the data. If the standard deviation is large, then one can know that mean
will not actually represent data, but if the standard deviation is small, one can know that the mean can
easily represent the data. The mean will determine the sum of squares, variance and standard deviation.
3) What is the difference between standard deviation and standard error?
Standard deviation is the average error between the mean and the observations made, while standard error
is the error between the mean of a sample set of population and the mean of the whole population.
4) In Chapter 1 we used an example of the time taken for 21 heavy smokers to fall off a treadmill at the
fastest setting (18, 16, 18, 24, 23, 22, 22, 23, 26, 29, 32, 34, 34, 36, 36, 43, 42, 49, 46, 46, 57). Calculate
the sums of squares, variance, standard deviation, standard error and 95% confidence interval of these
data.
Value
Mean
Deviance
18
32.19
-14.19
16
32.19
-16.19
18
32.19
-14.19
24
32.19
-8.19
23
22
22
32.19
32.19
32.19
-9.19
-10.19
-10.19
23
32.19
-9.19
26
29
32.19
32.19
-6.19
-3.19
Deviance
Squared
201.369614
5
262.131519
3
201.369614
5
67.0839002
3
84.4648526
1
103.845805
103.845805
84.4648526
1
38.3219954
6
10.1791383
32
-0.19
34
32.19
1.81
34
32.19
1.81
36
32.19
3.81
36
43
32.19
32.19
3.81
10.81
42
32.19
9.81
49
32.19
16.81
46
32.19
13.81
46
32.19
13.81
57
Total
32.19
32.19
24.81
676
2
0.03628117
9
3.27437641
7
3.27437641
7
14.5124716
6
14.5124716
6
116.845805
96.2267573
7
282.560090
7
190.702947
8
190.702947
8
615.512471
7
2685.23809
5
5) What do the sum of squares, variance and standard deviation represent? How do they differ?
Sum of squares represents each deviance squared to try and obtain a better measure for accuracy of
model. Variance is average error between the mean and observations made. Variance is a squared number.
Standard deviation is calculated by taking square root of variance. Standard deviation would be
considered the number to use when talking about the fit.
6) What is a test statistic and what does it tell us?
A test statistic is a ratio of effect to error , for which we know how different values occur frequently. The
observed value of such a statistic is typically used to test hypotheses, or to establish whether a model is a
reasonable representation of whats happening in the population.
7) What are Type I and Type II errors?
Type I error is when we believe there is a genuine effect in our population. Type 2 error occurs when we
believe that there is no effect in the population when in fact there is. And is the opposite of Type I error
8 What is an effect size and how is it measured?
An effect size is an objective and standardized measure of the magnitude of an observed effect. The most
common way to measure the effect is with Cohens d Pearsons correlation coefficient of r and odds ratio.
9 What is statistical power?
Statistical power is the ability of a test to detect an effect of that size.