Statistic at Maastricht University | Flashcards & Summaries

Lernmaterialien für Statistic an der Maastricht University

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Quantitative Variable

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takes numerical values for which arithemetic operations such as adding and averaging make sense

- interval scale
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Cases

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objects described by a set of data (customers, companies, subjects in study, …)

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residuals

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- difference between an observed value of the response variable and the value predicted by the regression line. That is, residual = observed y−predicted y =y−yˆ

- the mean of the least-squares residuals is always zero


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Intercept

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the value of y when x = 0

b0= y¯-b1*x¯

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Inter-rater reliability/ Cohen’s Kappa (K oder  Ψ)




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-  provides a measure of agreement between two observers coding on a nominal scale
- observed level of agreement relative to the level of agreement that would be expected by chance
- To what extent are the judgements similar?
Kappa (К) = (Ao–Ae) / (N -Ae)
Ao= Agreement observed
Ae= Agreement expected
0.70 or higher considered‘good’ (0.40 ≤ К≤ 0.70 ‘reasonable’, К< 0.40 ‘bad’)


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Outliers in regression

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- outliers in the y direction of a scatterplot have large regression residuals, but other outliers need not have large residuals

- Points that are out-liers in the x direction of a scatterplot are often influential for the least-squares regression line

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Facts about least-squares regression

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1. 

There is a close connection between correlation and the slope of the least-squares line.     

  • change of one standard deviation in x corresponds to change of r standard deviations in y
  • correlation=0, slope= 0
2.
The least-squares regression line always passes through the point (x¯,y¯)
3.
The distinction between explanatory and response variables is essential in regression
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Correlation

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r
- measure direction& strength of linear relationship between 2 quantitative variables

- positive correlation when the association is positive and vice versa

- variables has to be quantitative

- because you use the z- score r does not change when you make a linear transformation

- always a number between 1 & -1


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Histiogram

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  • Stemplots are not suitable for large data sets
  • displays only the count or percent of the observations that fall into each class
  • large sets of data are usually presented in a frequency table
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Categorical Variable(qualititativ)

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places a case into one of several groups or categories(e.g. gender)
- nominal, ordinal

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Inferential statistics
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conclusions about population based on limited number of elements (= sample) from that population

 

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Quartils
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- describe spread by giving several percentiles
  • median is the 50th percentile
  • upper quartile is the median of the upper half of the data
  • lower quartile is the median of the lower half of the data
  • The first quartile Q1 is the median of one half of the distribution
    The third quartile Q3 is the median of the other half of the distribution
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Q:

Quantitative Variable

A:

takes numerical values for which arithemetic operations such as adding and averaging make sense

- interval scale
Q:

Cases

A:

objects described by a set of data (customers, companies, subjects in study, …)

Q:

residuals

A:

- difference between an observed value of the response variable and the value predicted by the regression line. That is, residual = observed y−predicted y =y−yˆ

- the mean of the least-squares residuals is always zero


Q:

Intercept

A:

the value of y when x = 0

b0= y¯-b1*x¯

Q:

Inter-rater reliability/ Cohen’s Kappa (K oder  Ψ)




A:

-  provides a measure of agreement between two observers coding on a nominal scale
- observed level of agreement relative to the level of agreement that would be expected by chance
- To what extent are the judgements similar?
Kappa (К) = (Ao–Ae) / (N -Ae)
Ao= Agreement observed
Ae= Agreement expected
0.70 or higher considered‘good’ (0.40 ≤ К≤ 0.70 ‘reasonable’, К< 0.40 ‘bad’)


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Q:

Outliers in regression

A:

- outliers in the y direction of a scatterplot have large regression residuals, but other outliers need not have large residuals

- Points that are out-liers in the x direction of a scatterplot are often influential for the least-squares regression line

Q:

Facts about least-squares regression

A:

1. 

There is a close connection between correlation and the slope of the least-squares line.     

  • change of one standard deviation in x corresponds to change of r standard deviations in y
  • correlation=0, slope= 0
2.
The least-squares regression line always passes through the point (x¯,y¯)
3.
The distinction between explanatory and response variables is essential in regression
Q:

Correlation

A:
r
- measure direction& strength of linear relationship between 2 quantitative variables

- positive correlation when the association is positive and vice versa

- variables has to be quantitative

- because you use the z- score r does not change when you make a linear transformation

- always a number between 1 & -1


Q:

Histiogram

A:
  • Stemplots are not suitable for large data sets
  • displays only the count or percent of the observations that fall into each class
  • large sets of data are usually presented in a frequency table
Q:

Categorical Variable(qualititativ)

A:

places a case into one of several groups or categories(e.g. gender)
- nominal, ordinal

Q:
Inferential statistics
A:

conclusions about population based on limited number of elements (= sample) from that population

 

Q:
Quartils
A:
- describe spread by giving several percentiles
  • median is the 50th percentile
  • upper quartile is the median of the upper half of the data
  • lower quartile is the median of the lower half of the data
  • The first quartile Q1 is the median of one half of the distribution
    The third quartile Q3 is the median of the other half of the distribution
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