CM1005 Introduction to Statistical Analysis - Short summary
Including steps for SPSS output and hand calculations
General info
Nominal
● group classification
● no meaningful ranking possible
Ordinal
● meaningful ranking
● distances are not equal
Interval
● meaningful ranking
● distances are equal
Ratio
● all properties of interval
● true zero (absolute & meaningful zero point)
Sample Population
Mean M 𝜇
Variance s(squared) 𝜎(squared)
Standard deviation s 𝜎
Size n N
Measures of central tendency
Mean = average (interval/ ratio)
● sensitive to outliers
● sum of differences from mean is zero.
Median = middle value in a distribution of data listed in numeric order (ordinal/ interval/ ratio)
● not sensitive to outliers
Mode = value in a data set that occurs most often or most frequent (nominal/ ordinal/ interval/ ratio)
Measures of variability
Range = distance between highest and lowest score (ordinal/ interval/ ratio)
● always reported together with maximum & minimum
● sensitive to outliers
, The interquartile range (IQR) = describes the range of the middle part of the distribution (ordinal/
interval/ ratio)
● first order them, lowest to highest.
● split data into four groups with 3 values:
○ lower quartile Q1
○ median quartile Q2
○ upper quartile Q3
○ IQR = Q3 - Q1
● insensitive to outliers
Variance (interval/ ratio)
Low variance = low dispersion, everyone gets the same score → making comparisons
High variance = high dispersion, people got very different scores
● Based on the sum of squares, i.e. the squared distance from the mean
● Whenever you square, you should always end up with a positive number, so put ( )
Standard deviation = a measure of (approximately) the average distance to the mean (interval/ ratio)
● the square root of the variance
Type 1 error (alpha): Falsely rejecting a true H₀ hypothesis, rejecting H₀ while you shouldn’t.
Type 2 error (beta): Retaining a false H₀ hypothesis, assuming H₀ while you should have rejected it.
Alpha = 0.05!! (unless otherwise stated)
Always talk about ‘in the population’ with hypothesis
Hypothesis:
H₀: The population means has a certain value
- One sample t-test
H₀: The population mean of two groups are equal
- Two sample t-test
H₀: The population mean of more than two groups are equal
- Anova
H₀: The ordinal/nominal variable has a certain distribution in population
- Chi-square goodness of fit test
H₀: Two ordinal / nominal variables are not related to each other in the population
- Chi-square test for independence
H₀: In the population, R(squared) is zero; Y cannot be predicted by X
- Regression analysis - F-test for the model as a whole
(H₀: In the population, the effect of the given IV is zero)
- Regression analysis - one t-test for each individual IV
Crosstabs: Scatterplots
● Columns (IV’s) - vertical - X-axis = independent variable
● Rows (DV) - horizontal - Y-axis = dependent variable
Including steps for SPSS output and hand calculations
General info
Nominal
● group classification
● no meaningful ranking possible
Ordinal
● meaningful ranking
● distances are not equal
Interval
● meaningful ranking
● distances are equal
Ratio
● all properties of interval
● true zero (absolute & meaningful zero point)
Sample Population
Mean M 𝜇
Variance s(squared) 𝜎(squared)
Standard deviation s 𝜎
Size n N
Measures of central tendency
Mean = average (interval/ ratio)
● sensitive to outliers
● sum of differences from mean is zero.
Median = middle value in a distribution of data listed in numeric order (ordinal/ interval/ ratio)
● not sensitive to outliers
Mode = value in a data set that occurs most often or most frequent (nominal/ ordinal/ interval/ ratio)
Measures of variability
Range = distance between highest and lowest score (ordinal/ interval/ ratio)
● always reported together with maximum & minimum
● sensitive to outliers
, The interquartile range (IQR) = describes the range of the middle part of the distribution (ordinal/
interval/ ratio)
● first order them, lowest to highest.
● split data into four groups with 3 values:
○ lower quartile Q1
○ median quartile Q2
○ upper quartile Q3
○ IQR = Q3 - Q1
● insensitive to outliers
Variance (interval/ ratio)
Low variance = low dispersion, everyone gets the same score → making comparisons
High variance = high dispersion, people got very different scores
● Based on the sum of squares, i.e. the squared distance from the mean
● Whenever you square, you should always end up with a positive number, so put ( )
Standard deviation = a measure of (approximately) the average distance to the mean (interval/ ratio)
● the square root of the variance
Type 1 error (alpha): Falsely rejecting a true H₀ hypothesis, rejecting H₀ while you shouldn’t.
Type 2 error (beta): Retaining a false H₀ hypothesis, assuming H₀ while you should have rejected it.
Alpha = 0.05!! (unless otherwise stated)
Always talk about ‘in the population’ with hypothesis
Hypothesis:
H₀: The population means has a certain value
- One sample t-test
H₀: The population mean of two groups are equal
- Two sample t-test
H₀: The population mean of more than two groups are equal
- Anova
H₀: The ordinal/nominal variable has a certain distribution in population
- Chi-square goodness of fit test
H₀: Two ordinal / nominal variables are not related to each other in the population
- Chi-square test for independence
H₀: In the population, R(squared) is zero; Y cannot be predicted by X
- Regression analysis - F-test for the model as a whole
(H₀: In the population, the effect of the given IV is zero)
- Regression analysis - one t-test for each individual IV
Crosstabs: Scatterplots
● Columns (IV’s) - vertical - X-axis = independent variable
● Rows (DV) - horizontal - Y-axis = dependent variable
