Summary How to do Linguistics with R - Natalia Levshina, Chap. 6, 7, 8, 12, 13
32 views 2 purchases
Course
Statistics 2 (LIX002X05)
Institution
Rijksuniversiteit Groningen (RuG)
Book
How to Do Linguistics with R
Summary of the book How to do Linguistics with R from author Natalia Levshina. Summary contains chapters 6, 7, 8, 12, 13, and a small summary of Baayen Chapter 7.1. Note: this summary is created for the course Statistics II from the bachelor Communication and Information Science and Informatiekunde...
summary statistics ii communication and information science
Connected book
Book Title:
Author(s):
Edition:
ISBN:
Edition:
More summaries for
Summary How to do linguistics with R, Natalia Levshina (LCX046B05)
Statistics 2 Notes
short overview statistics
All for this textbook (6)
Written for
Rijksuniversiteit Groningen (RuG)
Communicatie- En Informatiewetenschappen
Statistics 2 (LIX002X05)
All documents for this subject (3)
Seller
Follow
aesther30
Reviews received
Content preview
CHAPTER 6
MEASURING RELATIONSHIPS BETWEEN TWO QUANTITATIVE VARIABLES
6.1 WHAT IS CORRELATION?
Positive correlation = when the values of variable X and variable Y decrease or increase
together → X increases, Y increases
Negative correlation = when the values of variable X and variable Y change in opposite
directions → X increases, Y decreases
De strength of this relationship is measured by means of a correlation coefficient → ranges
from -1 (perfect negative correlation) to 1 (perfect positive correlation)
Interval- and ratio-scaled variables: Pearson’s product-moment coefficient r
Ordinal data, interval- and ratio-scaled data transformed into ranks: Spearman’s ρ
and Kendall’s τ
6.2 THE PEARSON PRODUCT-MOMENT CORRELATION COEFFICIENT
You can create a scatterplot to visualize the relationship, including a regression line (= line
that shows the general trend in the data)
> plot(variable1 ~ variable2, main = “name of scatterplot”
> m <- lm(variable1 ~ variable2)
> abline(m)
Pearson’s product-moment coefficient r is the most common used correlation coefficient
→ is used for interval- and ratio-scaled data (requirement: normally distributed data)
> cor.test(variabele1, variabele2)
De strength of the r-value is determined as follows:
- Similar to or greater than 0.7 or smaller than -0.7 = strong
- Between 0.3 and 0.7 or between -0.3 and -0.7 = moderate
- Between 0 and 0.3 or between 0 and -0.3 = weak
- Merely 0 = no correlation
→ the closer to 0, the more points deviate from the correlation line in the plot and the
weaker the correlation
Note: a steep slope does not mean that the correlation is strong, it only shows the number of
units by which y will change if x changes.
Fitted value = a value that presents the expected location of a certain x-value on the
correlation line
Observed value = a value that presents the actual/observed value of a particular x-value on
the correlation line
Residuals = difference between the observed values and the fitted values → the smaller the
residuals, the stronger the correlation
1
,REMARKS ON THE PEARSON CORRELATION TEST
1. The relationship between variables should be monotonic and linear
→ a relationship between variables is monotonic when a decrease/increase of X results in a
decrease/increase of Y
→ a relationship between variables is linear when Y decreases/increases to the same extent
as X decreases/increases
A linear relationship is always monotonic, but a monotonic relationship is not always linear!
2. It is very sensitive towards outliers
→ outliers may result in a false correlation because of one or multiple extremely high values
→ these are called leverage points, as they draw the regression line into a particular
direction
Outliers can be excluded from the data:
> variable1_1 <- variable1(variable1 < critical point)
> length(variable1_1)
ASSUMPTIONS OF PEARSON CORRELATION
1. The sample is randomly selected from the population it represents
2. Both variables are at least interval-scaled
3. Both variables come from a bivariate normal distribution (= for any given value of X, the
scores on Y are normally distributed) and/or the sample size is large (>30)
> mvnorm.etest(cbind(variable1_1, variable2_1), R = 999)
(H0 = normality)
4. The residual (error) variance is homoscedastic (= the relationship between variables
should be of equal strength across the entire range of both variables)
> ncvTest(lm(variable1_1 ~ variable1_2))
(H0 = error variance is homoscedastic)
5. The residuals are independent, there is no autocorrelation (= when the value of a variable
depends on its previous or next value)
> durbinWatsonTest(lm(variable1_1 ~ variable1_2))
(H0 = no autocorrelation)
SPEARMAN AND KENDALL
When the relationship is not linear but monotonic, one should use non-parametric
correlation statistics, such as Spearman’s ρ and Kendall’s τ
Spearman’s ρ is identical to Pearson’s r, with ranked scores
> cor.test(variable1, variable2, method = “spearman”)
Kendall’s τ works with differences in the ranks of each pair of observations (x1, y1). A pair of
ranks is concordant if two coordinates x2, y2 are both higher/lower than coordinates x1, y1. A
pair is discordant if one of the two coordinates x2, y2 differs positively, whereas the other
differs negatively regarding coordinates x1, y1 (and vice versa).
2
, This method is preferred when the dataset is small and has tied ranks (when two or more
observations have identical scores and therefore identical ranks)
> cor.test(variable1, variable2, method = “kendall”)
Two assumptions:
1. The sample is randomly drawn from the population
2. Both variables are on the ordinal scale of measurement (they will be transformed to ranks
by R automatically)
CHAPTER 7
MORE ON FREQUENCIES AND REACTION TIMES: LINEAR REGRESSION
7.1 THE BASIC PRINCIPLES OR LINEAR REGRESSION ANALYSIS
Regression explains and models the relationship between the response (dependent) variable,
and one or more explanatory (independent) variables
- one explanatory variable: simple linear regression
- more than one explanatory variable: multiple linear regression
Explanatory variables can be categorical to ratio-scaled, but the response variable should be
on interval or ratio scale
Regression is the same as correlation, but with directionality:
- correlation: the degree to which x and y are related
- regression: how variable x is related to variable y by means of a formula
REGRESSION LINE
A regression line visualizes the relationship between x and y. Its position and orientation can
be described by a formula:
ŷ = b0 + bx
ŷ = the fitted (expected) values of the response variable y
b0 = the intercept, i.e. the predicted value of y when x is equal to zero → when x increases by
one unit, y increases by the intercept
b = the coefficient the determines the slope of the regression line
x = the explanatory variable
The difference between ŷ and the actual value of y are the residuals.
The actual values of y can be described by the following formula:
y=ŷ+ε
So, the observed value of y for a given observation is the sum of its fitted value and the
residual.
3
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller aesther30. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $3.80. You're not tied to anything after your purchase.
