Unit 4 Flashcards
What are univariate descriptive statistics?
They describe single Variables
-> e.g.: how many people scored higher than 15
What are bivariate descriptive statistics?
They evaluate the relation between two variables
-> e.g.: Is the level of self-esteem related to academic performance?
What is Causality?
One variable is responsible for the change in another
What is Relation?
Two variables vary jointly, at the same time
-> can be positive and negative
What is association between categoric variables?
comparison between the relation of nominal and ordinal variables
-> does having the air conditioning on correlate with better grades?
What are joint frequencies?
the frequency shared by some values and others
What are marginal distributions?
absolute frequencies for each category in each variable
What are contingency tables and how are they used?
Contingency tables display the relationship between categorical variables and can be created for all measurement scales. They are most commonly used with categorical variables.
What can contingency tables, similar to frequency distributions include?
relative frequencies (fi)
percentages
What do we use frequency distributions for?
a single variable
What kind of graphical representation do we use for categorical variables?
grouped bars diagram
What does the Chi-Square Correlation Index quantify? What can it be used for?
the degree of relationship between two variables
Can be used for:
Nominal-Nominal
Nominal-Ordinal
Ordinal-Ordinal
How does the Chi-Square Index work?
it compares observed frequencies (fo) with expected frequencies (fe)
-> observed frequencies are the actual data
-> expected frequencies are what we’d expect if there were no association between the variables
What are expected frequencies in the Chi-Square test?
Expected frequencies (fe) are the values we would expect if there were no association between the variables. In this case, the frequencies would be equally distributed
How is the strength of the association measured in the Chi-Square test?
The greater the difference between observed (fo) and expected (fe) frequencies, the higher the Chi-Square value (x²), indicating a stronger association between the variables
What is the formula of the Chi-Square?
x² = ∑ (fo - fe)² : fe
How do we calculate the expected frequencies?
Marginal distribution in variable X, multiplied by the marginal distribution in variable Y, divided by the sample size
(Ergebnis unten x Ergebnis rechts geteilt durch n)
How do we evaluate the association in Chi-Square?
0 = no association
the higher the value is the stronger the association
What are the steps of calculating the Chi-Square?
- Build the contingencies table (joint frequencies of both variables) = table of observed frequencies
What does it mean when two variables are linearly related?
Two variables are linearly related when they covary together, meaning that as one variable changes, the other variable tends to change in a consistent, predictable way.
What is a positive (direct) correlation?
A positive or direct correlation occurs when values are high in one variable and also high in the other. As one variable increases, the other variable increases as well
What is a negative (inverse) correlation?
A negative or inverse correlation occurs when values are high in one variable and low in the other. As one variable increases, the other variable decreases
What is linear correlation?
Linear correlation refers to the relationship between two variables where changes in one variable correspond to predictable changes in the other. This can be either positive or negative, depending on the direction of the relationship
What does the covariance index measure in linear correlation?
measures the degree of linear relationship between two variables
-> allows us to know the direction of the relationship
-> In chi-squared we could not know in which direction they were related.
What is the covariance?
the average of the products of the deviation scores of the two variables
-> ‘average of the distances from the mean of the two variables’. ‘How the deviations of each variable are connected’
what do the different associations mean?
0 = No association
Negative value = Negative/Inverse association
Positive value = Positive/Direct association.
What is the formula of Linear correlation?
Sxy = ∑(xi-x_) x (yi - y_) : n - 1
What range of values does the covariance index have?
does not have a limited range of values
-> - infinity to + infinity (we don’t know whether the ratio is large/strong or small/weak
What is Pearson’s correlation index and what is its range?
Pearson’s correlation index measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1
How do you interpret the Pearson correlation index?
The Pearson correlation index provides two key pieces of information:
Direction: Positive or negative correlation.
Magnitude/Strength: How strong the relationship is.
Strong negative: -1
Strong positive: +1
No association: 0
What is the formula for Pearson’s correlation coefficient (r)?
rxy = Sxy : sx x sy
Sxy = Covariance index
sx = Standard deviation (variable x)
sy = Standard deviation (variable y)
What does the magnitude of Pearson’s r indicate?
The magnitude of Pearson’s r indicates the strength of the linear relationship:
High negative: r ≤ -0.500
Moderate negative: r between -0.500 and -0.290
Low negative: r between -0.290 and -0.100
No association: r around 0
Low positive: r between 0.100 and 0.290
Moderate positive: r between 0.290 and 0.490
High positive: r ≥ 0.500
