Inhoudsopgave
Week 1.......................................................................................................................................................... 2
Types of variables (nominal, ordinal, interval, ratio)...........................................................................................2
Histogram, bar chart............................................................................................................................................2
Measures of central tendency (mean, mode and median)..................................................................................3
Measures of variability (variance, standard deviation, interquartile range).......................................................3
Boxplots...............................................................................................................................................................4
Theoretic distribution: skewed, symmetric..........................................................................................................4
Z-score..................................................................................................................................................................5
Measure of association (Pearson correlation).....................................................................................................5
Association and simple linear regression.............................................................................................................5
Dependent/independent variables......................................................................................................................6
R-square...............................................................................................................................................................6
Week 2.......................................................................................................................................................... 7
Association for qualitative variables (OR, RR, chi-square)...................................................................................7
Population, sample and Sampling distribution....................................................................................................8
Central Limit Theorem..........................................................................................................................................8
Confidence interval...............................................................................................................................................9
One sample problem............................................................................................................................................9
Week 3.......................................................................................................................................................... 9
Null/alternative hypothesis (H0 /Ha)...................................................................................................................9
P-value................................................................................................................................................................10
Z-test, t-test (one sample)..................................................................................................................................10
Type I - and type II error (α and β resp.), power................................................................................................11
t-test (two samples)...........................................................................................................................................12
The pooled-variance t procedure.......................................................................................................................13
The unpooled-variance t procedure (Welch)......................................................................................................14
t-test (paired samples).......................................................................................................................................15
Week 4........................................................................................................................................................ 15
Testing regression coefficients for simple linear regression..............................................................................15
Chi-square test...................................................................................................................................................16
,Week 1
Types of variables (nominal, ordinal, interval, ratio)
Variable: is a recorderd piece of information/ characteristic (age,weight, BMI)
Different type of variables:
- categorical/qualitative variable: place or people are put into groups or categorized
(nominal= no order based on magnitude or size)
(ordinal= rank or order)
- numeric/quantitative variable: recorded numerical quantities
(discreet= integer only e.g 1, 2, 3, 4)- subdivided in RATIO, which is a meaningful “0”
value or ratio and INTERVAL, which is a non-meaningful “0” value or ratio.
(continuous= measured on continuous scale) )- subdivided in RATIO, which is a
meaningful “0” value or ratio and INTERVAL, which is a non-meaningful “0” value or
ratio.
Identifiers: are not variables but are used for identification such as ID or student number.
Can always convert numerical variables categorical variables e.g age is divided into
child/adult/senior.
Categorical variables are recorded using numbers.
Histogram, bar chart
Summarizing categorical variable
Frequency table/distribution shows the distribution and
contains:
Frequency: in numbers
Proportion/ relative frequency: in decimal proportions
Percentages: in percentages
Bar chart (visual representation of distribution): A bar chart plots numeric values for levels
of a categorical feature as bars. Levels are plotted on one chart axis, and values are plotted
on the other axis. Each categorical value claims one bar, and the length of each bar
corresponds to the bar's value.
Pie chart (visual representation of distribution): A pie chart,
sometimes called a circle chart, is a way of summarizing a set
of nominal data or displaying the different values of a given
variable (e.g. percentage distribution). This type of chart is a
circle divided into a series of segments. Each segment
represents a particular category or percentage.
Histogram:
- Uses quantitave data
- No gaps
- Bar width is the bin size or class size
- Y-axis corresponds to the frequency
, Measures of central tendency (mean, mode and
median)
The concept of average in descriptive statistics can be defined as
searching for a typical or middle number central tendency
- Arithmitic mean: is the sum of all the numbers divided by the
amount of numbers
- Median: the middle number when the number set is ordered
(uneven amount of numbers: take the middle one, even
amount of numbers: take the mean of the two middle
numbers). The median is not sensitive to outliers. (The
median is a non-parametric measure).
- Mode: the most frequent number in a data set.
Mean and median are roughly equal to each other when there is a symmetrical
distribution, but when there is a skew distribution the mean is ‘pulled’ towards the
skewness.
Sample mean: The sample mean is a statistic
obtained by calculating the arithmetic average
of the values of a variable in a sample. The
sample mean is sensitive to outliers.
(parametric measure)
Population sample: The population mean is an
average of a group characteristic. The group
could be a person, item, or thing.
Trimmed mean: the mean after removing top
and bottom α %
Measures of variability (variance, standard deviation, interquartile
range)
Range: the largest occurring number – the smallest occurring number
Variance: The variance is a measure of variability. It is calculated by
taking the average of squared deviations from the mean. Variance
tells you the degree of spread in your data set. The more spread the
data, the larger the variance is in relation to the mean. (sensitive to
outliers)
Sample variance: S2
Population variance: σ 2
Standard deviation: A standard deviation (or σ) is a measure
of how dispersed the data is in relation to the mean. Low
standard deviation means data are clustered around the
mean, and high standard deviation indicates data are more
spread out. (sensitive to outliers)
Interquartile range: the range in the middle of the data. It is the difference between the
upper and lower quartiles inn a data set. (not sensitive to outliers)
- Quartiles: the values that divide a list of numbers into quarters
- Lower quartile: the median of the lower half of a set of data
- Upper quartile: the median of the upper half of a set of data
Week 1.......................................................................................................................................................... 2
Types of variables (nominal, ordinal, interval, ratio)...........................................................................................2
Histogram, bar chart............................................................................................................................................2
Measures of central tendency (mean, mode and median)..................................................................................3
Measures of variability (variance, standard deviation, interquartile range).......................................................3
Boxplots...............................................................................................................................................................4
Theoretic distribution: skewed, symmetric..........................................................................................................4
Z-score..................................................................................................................................................................5
Measure of association (Pearson correlation).....................................................................................................5
Association and simple linear regression.............................................................................................................5
Dependent/independent variables......................................................................................................................6
R-square...............................................................................................................................................................6
Week 2.......................................................................................................................................................... 7
Association for qualitative variables (OR, RR, chi-square)...................................................................................7
Population, sample and Sampling distribution....................................................................................................8
Central Limit Theorem..........................................................................................................................................8
Confidence interval...............................................................................................................................................9
One sample problem............................................................................................................................................9
Week 3.......................................................................................................................................................... 9
Null/alternative hypothesis (H0 /Ha)...................................................................................................................9
P-value................................................................................................................................................................10
Z-test, t-test (one sample)..................................................................................................................................10
Type I - and type II error (α and β resp.), power................................................................................................11
t-test (two samples)...........................................................................................................................................12
The pooled-variance t procedure.......................................................................................................................13
The unpooled-variance t procedure (Welch)......................................................................................................14
t-test (paired samples).......................................................................................................................................15
Week 4........................................................................................................................................................ 15
Testing regression coefficients for simple linear regression..............................................................................15
Chi-square test...................................................................................................................................................16
,Week 1
Types of variables (nominal, ordinal, interval, ratio)
Variable: is a recorderd piece of information/ characteristic (age,weight, BMI)
Different type of variables:
- categorical/qualitative variable: place or people are put into groups or categorized
(nominal= no order based on magnitude or size)
(ordinal= rank or order)
- numeric/quantitative variable: recorded numerical quantities
(discreet= integer only e.g 1, 2, 3, 4)- subdivided in RATIO, which is a meaningful “0”
value or ratio and INTERVAL, which is a non-meaningful “0” value or ratio.
(continuous= measured on continuous scale) )- subdivided in RATIO, which is a
meaningful “0” value or ratio and INTERVAL, which is a non-meaningful “0” value or
ratio.
Identifiers: are not variables but are used for identification such as ID or student number.
Can always convert numerical variables categorical variables e.g age is divided into
child/adult/senior.
Categorical variables are recorded using numbers.
Histogram, bar chart
Summarizing categorical variable
Frequency table/distribution shows the distribution and
contains:
Frequency: in numbers
Proportion/ relative frequency: in decimal proportions
Percentages: in percentages
Bar chart (visual representation of distribution): A bar chart plots numeric values for levels
of a categorical feature as bars. Levels are plotted on one chart axis, and values are plotted
on the other axis. Each categorical value claims one bar, and the length of each bar
corresponds to the bar's value.
Pie chart (visual representation of distribution): A pie chart,
sometimes called a circle chart, is a way of summarizing a set
of nominal data or displaying the different values of a given
variable (e.g. percentage distribution). This type of chart is a
circle divided into a series of segments. Each segment
represents a particular category or percentage.
Histogram:
- Uses quantitave data
- No gaps
- Bar width is the bin size or class size
- Y-axis corresponds to the frequency
, Measures of central tendency (mean, mode and
median)
The concept of average in descriptive statistics can be defined as
searching for a typical or middle number central tendency
- Arithmitic mean: is the sum of all the numbers divided by the
amount of numbers
- Median: the middle number when the number set is ordered
(uneven amount of numbers: take the middle one, even
amount of numbers: take the mean of the two middle
numbers). The median is not sensitive to outliers. (The
median is a non-parametric measure).
- Mode: the most frequent number in a data set.
Mean and median are roughly equal to each other when there is a symmetrical
distribution, but when there is a skew distribution the mean is ‘pulled’ towards the
skewness.
Sample mean: The sample mean is a statistic
obtained by calculating the arithmetic average
of the values of a variable in a sample. The
sample mean is sensitive to outliers.
(parametric measure)
Population sample: The population mean is an
average of a group characteristic. The group
could be a person, item, or thing.
Trimmed mean: the mean after removing top
and bottom α %
Measures of variability (variance, standard deviation, interquartile
range)
Range: the largest occurring number – the smallest occurring number
Variance: The variance is a measure of variability. It is calculated by
taking the average of squared deviations from the mean. Variance
tells you the degree of spread in your data set. The more spread the
data, the larger the variance is in relation to the mean. (sensitive to
outliers)
Sample variance: S2
Population variance: σ 2
Standard deviation: A standard deviation (or σ) is a measure
of how dispersed the data is in relation to the mean. Low
standard deviation means data are clustered around the
mean, and high standard deviation indicates data are more
spread out. (sensitive to outliers)
Interquartile range: the range in the middle of the data. It is the difference between the
upper and lower quartiles inn a data set. (not sensitive to outliers)
- Quartiles: the values that divide a list of numbers into quarters
- Lower quartile: the median of the lower half of a set of data
- Upper quartile: the median of the upper half of a set of data
