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## Elang 273: Statistics

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### 1. Descriptive Statistics ... 1. Descriptive Statistics. Three ... 1. Descriptive Statistics. How could you depict the data for each of these types? Nominal ... – PowerPoint PPT presentation

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Title: Elang 273: Statistics

1
Elang 273 Statistics
• September 15, 2008

2
Statistics
• The scientific method is defined by
• 1. The research question is empirical
• 2. The data we collect is public
• 3. The data is falsifiable

? But also with this
? Statistics helps most with this
3
Statistics
• Research question Is the word glistening used
more often in one register (as shown in COCA)
than another?

SECTION SPOKEN FICTION MAGAZINE NEWSPAPER ACADEMIC

PER MIL 0.4 12.0 2.8 2.1 0.6
SIZE (MW) 76.6 69.6 78.1 73.4 73.0
FREQ 32 833 219 156 43
How much different do these frequencies have to
be before we can say they are different?
4
Statistics
• Researchers have agreed that if the chance that
the difference between two groups is greater than
a certain percentage, then we will consider the
difference to be statistically significant.
• A significant difference is better than one in
twenty of happening by chance (p lt .05). The
opposite of significance is random chance.

5
Two types of statistics
• 1. Descriptive
• a. nominal (categorical)
• b. ordinal (rank order)
• c. continuous
• 2. Inferential
• a. chi-square
• b. t-tests/ANOVA
• c. correlations
• d. varbrul

6
1. Descriptive Statistics
• These are the types of statistics you are
familiar withshowing means, percentages,
quartiles, usually through bars, pie charts, and
graphs

7
1. Descriptive Statistics
• Three types of data
• Nominal (Categorical) sex, race, national
origin, native speaker, how often you choose one
thing over another, how often a word occurs in
one register versus another
• Continuous height, weight, age, scores on a
language test, IQ, working memory span
• Ordinal (Rank Order) No fixed interval (first,
second, third place in a race)what order people
choose their favorite dialect

8
1. Descriptive Statistics
• How could you depict the data for each of these
types?
• Nominal
• Continuous
• Ordinal (rank order)

9
1. Nominal (Categorical)
Answers to Where is this speaker from? (native
listeners)
10
1. Nominal (Categorical)
correct dialect identification by American
English speakers
11
2. Continuous
12
Native listeners status vs. solidarity
Status RP Birmingham Network NYC West
Yorkshire Alabama
Solidarity RP Birmingham Network New York West
Yorkshire Alabama
13
3. Ordinal (Rank Order)
Coupland Bishop, 2007
14
2. Inferential Statistics
• Chi square
• ANOVA/t-test
• Correlations (rank order correlations)
• Logical regression
• Varbrul

15
2. Inferential Statistics
• For each type of statistics we need to know
• Statistical value (chi value, F statistic, t
statistic)
• Probability value (p value)
• Degrees of Freedom (df)

16
2. Inferential Statistics
• Research question Is the word glistening used
more often in one register (as shown in COCA)
than another?

SECTION SPOKEN FICTION MAGAZINE NEWSPAPER ACADEMIC

PER MIL 0.4 12.0 2.8 2.1 0.6
SIZE (MW) 76.6 69.6 78.1 73.4 73.0
FREQ 32 833 219 156 43
17
2. Inferential Statistics
• Research question Is the word glistening used
more often in one register (as shown in COCA)
than another?
• What kind of data is this?
• Nominal (categorical)
• For this kind of data we use a chi square

18
a. Chi-square
• Tells us whether something happened more often
than chance would predict
• http//www-user.uni-bremen.de/anatol/qnt/qnt_chi.
html
• Use with multiple choice questions, percentage of
time respondents choose specific choice, more
corpora or frequency data

19
a. Chi-square
• Is the distribution into categories random or
not? (Uses counts of nominal data)
• For example, multiple choice questions.
• Jill loves the taste of coffee.
• A-cæfi-186 B-cfi-113 C-cafi-70
• Is 186, 113, 70 really different from what random
choice would give?

20
a. Chi square
• To compute chi square, you need to know what is
observed (the responses you got from your survey,
corpus) and the expected frequencies.
• To calculate expected frequencies, you add up all
the observed frequencies and divide by the number
of data points

Data point 1
Data point 2

Observed
Expected
21
a. Chi-square
• (Invented) frequency of use of dude in four
million word spoken corpora
• US NZ AU UK
• 15 9 11 5
• Random distribution would be

Observed (what the actually did)
US NZ AU UK

US NZ AU UK 10 10 10 10
Expected (what you would expect by random chance)
22
a. Chi Square
• http//www.physics.csbsju.edu/stats/contingency_NR
OW_NCOLUMN_form.html

chi-square 2.77 degrees of freedom
3 probability 0.429
The larger the chi value and the smaller the p
value the more likely that the difference between
the observed and the expected did not occur by
chance
23
a. Chi square
• Practice Is the word glistening used more often
in one register (as shown in COCA) than another?

SECTION SPOKEN FICTION MAGAZINE NEWSPAPER ACADEMIC

PER MIL 0.4 12.0 2.8 2.1 0.6
SIZE (MW) 76.6 69.6 78.1 73.4 73.0
FREQ 32 833 219 156 43
To do this, you need to times each number by 10
and use only whole numbers
24
a. Chi Square
• Results
• chi-square 97.2 degrees of freedom
4 probability 0.000

25
a. Chi square
• More practice
• 1. Multiple choice question Jill loves the taste
of coffee.
• A-cæfi-186 B-cfi-113 C-cafi-70
• did respondents choose number A more often than
the other two choices?
• 2. Identification American Listeners choose the
following choices when asked where is this
speaker from (he was from Birmingham UK)
• London 45 England 25 Scotland 25
Ireland 5

26
Chi-square Homework