1
Q
Statistical Origins
A
began 100-120 years ago with 4 guys in England
2
Q
Statistical Origins
- **4 guys (100-120 **years ago in England)
A
**Francis Galton **
Karl Pearson
Ronald Fisher
William “student” Gossett
3
Q
Francis Galton
A
interested in **quantifying human variation **
- money man *
- eugenics *
4
Q
Karl Pearson
A
wanted to show relationships between variables
- student of Galton** *
- fan of **Karl Marx ***
- enemy = **Ronald Fisher ***
5
Q
Ronald Fisher
A
wanted to **test if something caused something **
- statistics & genetics *
- studied causal relationships *
- enemy: Karl Pearson*
6
Q
William “student” Gossett
A
just wanted **everyone to get aloing **
*worked at brewery *
7
Q
Psychology & **Statistics **
- history/prevalence within psychology
*
A
When **Freudians & Behaviorists **ruled psych → no need for stats
**Personality, social, cognitive **psychologists created **demand **for statistics
8
Q
- stats became… when? (2)
- debate (2), when?
A
→ became language of psychology in 1950s
→ 1980s: stats became more complex (computer rev.)
21st Century - debate **(quantitative vs. qualitative) **
- bigger debate around how we use stats
9
Q
Definition of Statistics (2)
A
**Statistics **as:
- **collection **of **numerical facts **
- **methods **for dealing with **data **
10
Q
(2) Types of Statistics
A
1) Descriptive
2) **Inferential **
11
Q
**Inferential **statistics allow us to?
A
generalize from **samples **to **population **
12
Q
Population
A
complete set of **individuals, objects **or **measurements **having some common characteristic
13
Q
Parameter
A
any **characteristic **of a population that is measurable
14
Q
Sample
A
**subset **of a population
15
Q
Statistic
A
**number **resulting from **manipulation **of sample data
16
Q
Scales **(4) **
A
NOIR
Nominal
Ordinal
Interval
Ratio
17
Q
Nominal Scale
A
observation of **unordered variables **with **no ranking **to be inferred
18
Q
Ordinal Scale
A
classes differ & indicate rank
19
Q
Interval Scale
A
classes differ in **meaningful way **so arithmetic operations are possible
20
Q
Ratio Scale
A
interval scale but with **meaningful zero point **
21
Q
Grouping
A
**collapsing **scores into mutually exclusive classes defined by **grouping intervals **
22
Q
Grouping Data
**- pros (3) **
A
- difficult to deal w/ large # of cases spread over many scores
- some scores have low frequency counts
- less data leads to greater comprehension
23
Q
Grouping Data
- **cons (2) **
A
- info is lost when categories/data are combined
- categories can be **arbitrary **
24
Q
Ungrouped Frequency Distribution
A
frequency distribution (table that displays frequency of various outcomes in a sample) that does NOT group data into intervals
25
Grouped Frequency Distribution
groups data into intervals of size **i**
* mutually exclusive & exhaustive
**frequency** is equal to the number of values that fall within this interval
26
**Cumulative** Frequency Distribution
also include **cumulative frequency (*cf* ),** which indicates the number of values within the specified interval + # of values previously counted
**_ON GRAPH:_** highest point reached is total (**n**) # of values
27
**Cumulative Percentage** Distribution
also includes **c%,** which is ***cf/n*** **x 100%**
- shows the **cumulative frequency** as a percentage of the total (**n**) # of values
**_ON GRAPH:_** highest point reached is **100%**
28
IQ scores would be an example of data that are?
**Interval**
29
Percentile Ranks
form of **cumulative percentage** that **indicate where scores fall in a distribution**
30
How do **percentile ranks** work?
* i.e. **PR = 10%**
a score with a **PR = 10%** indicates that:
* its value is _**greater** than_ **10%** of all scores
* its value is _**less** than_ **90%** of all scores
31
Central Tendency
**index** of **central location** employed in the **description** of a **frequency distribution**
32
Mean
**average** taken by **summing scores** & **dividing** sum by **# of scores**
* **point in a distribution** about which **summed deviations** are equal to **zero → Σ(x-bar - x) = 0**
33
Mean **formula **
sample: **x-bar = Σx/n**
population: **µ = Σx/N**
34
Deviation score
score minus mean
**x - (x-bar)**
→ *summed deviations from the mean = 0*
35
Sum of Square Deviation Scores
* aka?
* size?
* positive/negative?
aka **SUM of SQUARES** **(SS)**
## Footnote
- **never** negative
- SS from the mean are **LESS** than SS from any other number
36
If data is from **population** rather than sample?
use **N** instead of **n → # of scores**
**μ** instead of **x-bar** → **mean**
37
Median
**score** that **divides distribution** so that same **# of scores** lie on each side
38
Median is a special case of?
percentile rank (**50th percentile**)
39
Mode
**score** that occurs with **greatest frequency**
40
\_\_\_\_ is associated with ___ data
a) **Mode**
b) **Median**
c) **Mean**
a) **nominal** data
b) **ordinal** data
c) **interval/ratio** data
41
If data distribution is normal...
**mean, median & mode** are...
**same** value
42
If distribution of scores is **NOT** normal...
**mean, median & mode**....
fall **alphabetically** from tail
1) mean
2) median
3) mode
43
Non-normal distributions may be..
skewed **positively** or **negatively**
44
Which distributions have **kurtosis?**
distributions that are too **light** or **heavy** in the tails have **_kurtosis._**
45
Do
* a) distributions with **kurtosis***
* b) **skewed** distribution*
affect central tendency?
a) **NO**
b) **YES**
46
A score at the median is at the ____ percentile
**50th**
assuming normal distribution
47
Variability
the **dispersion** of scores in a distribution
48
range
**crude measure** easily **influenced** by **outliers**
49
semi-interquartile range
less influenced by outliers but still crude
**(75th - 25th)** **/ 2**
50
Standard Deviation & Variance **(3)**
* reflect...
* basis for...
* exploits...
* reflect **dispersion** of scores
* **basis** for all **inferential statistics**
* **exploits mean** as **best measure** of central tendency
51
**Variance**
**quantitative measure** of **difference between scores** in a distribution that **describes degree** to which scores are **spread out/clustered together**
52
Variance **formula**
**S2 = SS/(n-1)**
= Σ(x-x̄)2 /(n-1)
53
Standard Deviation
square root of variance
provides **measure** of **standard/average distance** from mean
54
Standard Deviation **formula**
S=√S2
=√ [Σ(x-x̄)2 /(n-1)]
55
**Deviation** **Method **formula
if you have **many **scores
SS = ∑x2 - (∑x)2/n
56
Z score
**statistical** **measurement** of a **score's** **relationship** to the **mean** in a group of scores
57
Z score **formula**
Z = x-µ/σ
58
How are **Z scores **useful when given scores from different normal distributions?
can find the **z score **of the scores in order to facilitate **comparison**
59
Z formula is the ___ for many ___ \_\_\_
**foundation** for many **inferential** **statistics**
60
Z formula **numerator (x-µ) **reflects?
how score **deviates **from pop'n parameter (µ)
61
Z formula **denominator (σ) **reflects?
**variability **of scores in pop'n
62
the z formula **ratio **represents?
**score** **(z) **that can be compared to **theoretical distribution (normal distribution)**
63
When using **z scores **for a sample rather than individual score...
µx-bar = µ of popn
σx-bar ≠ σ
σx-bar = σ/√n
64
When variables are not normally distributed..
**Central Limit Theorem** to address these issues
* Zx-bar test
65
Central Limit Theorem
the **means **of a large # of **independant random samples** will be normally distributed regardless of underlying distribution
66
sampling distribution
t**heoretical distribution** of **possible values** of some sample statistic that would occur **if all possible samples of fixed size** were drawn from a given population
67
If the **sampling** **distribution** takes the form of a **normal distribution...**
we can use the known properties of the normal distribution to make inferences
68
Null hypothesis
a **general** **statement**/**default position** that there is **no relationship** between two measured phenomena
69
Alternative hypothesis
the hypothesis used in hypothesis testing that is **contrary to the null hypothesis.**
* usually taken to be that observations are result of a real effect
70
In psychology, outcome is **unremarkable **if **probability** of outcome **by chance alone **is?
**greater than **5 in 100
(\> 5 in 100)
71
**Remarkable** outcome if probability of occurance by chance alone is ...?
**equal to** or **less than** 5 in 100
(≤ 5 in 100)
72
Type **1 **error
α
## Footnote
when you **reject **null hypothesis that is **true**
73
Type **2 **error
**β**
**failing to reject **null hypothesis that is **false**
74
Statistical power
**capacity** to find something if its there
75
Logic of Testing
## Footnote
**(6) questions to ask**
1) what is the **appropriate statistic, **its **distribution &** its **assumptions**
2) **null & alternative hypotheses**
3) probability of making **type 1 error**
4) **obtained** value for test
5) **critical** value for test
6) **decision** regarding **obtained** value **relative** to **critical** value
PSYC 305
flashcards
Decks in class (3)
# Cards
