Captain Psychology

Statistics

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Statistics

Statistics

RStatistics is an area of mathematics, a collection of tools for analyzing data, and a way of thinking. As a subset of mathematics, statistics can be the study of multidimensional space, models of chance, or representational structure and change. For most people, statistics is more practical.

Most see statistics as a collection of procedures in a stat. program: you push the button and out comes the answer. Descriptive statistics helps summarize a variable by finding the most representative score (mode, median or mean). It also describes how diverse the scores are. Inferential statistics goes beyond describing. It uses patterns of numbers to infer the relationships between variables. Researchers predictions, forecasts and decisions based on these patterns.

But statistics is at its best as a way of thinking. We live in a world of freedom. Things are not set but can change. In a broad sense, this independence of events can be seen as uncertainty. We know the sun will come up tomorrow (certainty) but we don’t what our day will hold (uncertainty). This uncertainty doesn’t bother us because we believe we can handle the circumstances of life as they come.

In general, people are not good at handling uncertainty. So we generally ignore it, and assume that life is stable. We accept that we sometimes fall, run into things with our cars, and get sick. We accept, at least in ourselves, that these events are chance: they are not the result of goblins, dragons or unicorns.  But we’re less willing to accept that intelligence, running, and musical ability are randomly distributed. Statistical thinking is applying logic to life. It is using the scientific method to better understand life’s uncertainty.

Here is a catalog style description of the course:

Introductory course in descriptive and inferential statistics.  Special attention given to data description, probability and the normal curve. Topics include critical intervals, hypothesis testing, goodness of fit and factorial analysis. Technology is used to analyze data sets.

Here is what it really means:

This course is all about planning, thinking and interpreting. Number crunching isn’t as important as thinking.

Let’s start with some basic principles.

What Is Statistics

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Statistics1 by Nick Youngson CC BY-SA 3.0 Alpha Stock Images

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Critical Values of r

These critical values of the Pearson r are presented for training purposes. For real problems, your statistics book or stat software will provide more actual estimates. Also, these values are only for 2-tailed tests at .05 alpha.

df .05 alpha
1 0.997
2 0.950
3 0.878
4 0.811
5 0.755
6 0.707
7 0.666
8 0.632
9 0.602
10 0.576
11 0.553
12 0.532
13 0.514
14 0.497
15 0.482
16 0.468
17 0.456
18 0.444
19 0.433
20 0.423
25 0.381
30 0.349
35 0.325
40 0.304
45 0.288
50 0.273
60 0.250
70 0.232
80 0.217
90 0.205
100 0.195

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Critical Values of F

These critical values of F are presented for training purposes. For real problems, your statistics book or stat software will provide more actual estimates of F. Also, these values are only for .05 alpha.

df 1 2 3 4 5
1 161 200 216 225 230
2 18.51 19.00 19.16 19.25 19.3
3 10.13 9.55 9.28 9.12 9.01
4 7.71 6.94 6.59 6.39 6.26
5 6.61 5.79 5.41 5.19 5.05
6 5.99 5.14 4.76 4.53 4.39
7 5.59 4.47 4.35 4.12 3.97
8 5.32 4.46 4.07 3.84 3.69
9 5.12 4.26 3.86 3.63 3.48
10 4.96 4.10 3.71 3.48 3.33
11 4.84 3.98 3.59 3.36 3.20
12 4.75 3.88 3.49 3.26 3.11
13 4.67 3.80 3.41 3.18 3.02
14 4.60 3.74 3.34 3.11 2.96
15 4.54 3.68 3.29 3.06 2.90
16 4.49 3.63 3.24 3.01 2.85
17 4.45 3.59 3.20 2.96 2.81
18 4.41 3.55 3.16 2.93 2.77
19 4.38 3.52 3.13 2.90 2.74
20 4.35 3.49 3.10 2.87 2.71

 

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Critical Values of t

Critical Values of Student’s t

2-tailed t-tests

df

 .05 alpha

1

12.71

2

4.30

3

3.18

4

2.78

5

2.57

6

2.45

7

2.37

8

2.31

9

2.26

10

2.23

11

2.20

12

2.18

13

2.16

14

2.15

15

2.13

16

2.12

17

2.11

18

2.10

19

2.09

20

2.09

21

2.08

22

2.07

23

2.07

24

2.06

25

2.06

26

2.06

27

2.05

28

2.05

29

2.05

30

2.04

40

2.02

60

2.00

120

1.98
infinity

1.96

 

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Statistics Should Be Fun

Statistics should be fun. Well, maybe not as fun as a Ferris wheel but still…

Actually, a Ferris wheel might be a good analogy. It can be big, seem overwhelming, move rapidly and still be significantly enjoyable. So is statistics.

Statistics is a large field of study. It encompasses everything from political polls to rating scales to actuarial tables to business, education and scientific research. Many people use statistics as part of their job.

It also can seem overwhelming. Most people don’t spend a lot of time with formulas, numbers and data tables. Learning the vocabulary alone can be daunting. Then there’s the calculations. Fortunately, we have computers to do the heavy crunching, but getting used to working with numbers can take some doing.

Many classes in statistics move quickly. Even textbooks often only state a formula or theorem once. That’s one of the advantages of this site: we can take our time with the material. You can proceed at your own pace.

And, although you probably won’t become a researcher or professional statistician, I think you will gain an appreciation for how hard it is to get answers. If research was easy, it would already have been done. So it takes skill, creativity and luck to get some partial answers to the most difficult problems we face. But I think you’ll be pleased with your progress and success. And maybe the process will even be enjoyable. We’ll sure try to make it so.

 

 

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