Samenvatting Statistics | English | KU Leuven | 2023/24

Statistiek samenvatting
Ginett e Lafi t – 2023-2024




Inhoudstafel




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, LES 1 – The data analysis workflow: an illustration

Boxplot: shows distribution of the dependent variable

 Median (not average!!)
 1st and 2th quartile
 Max score, min score
 Outliers (uitschieters) = a value that
is more than 1.5 times the
interquartile range (IQR) below the
first quartile or above the third
quartile
 Symmetric or skewed
 The larger the 2 tails, the bigger the standard deviation (= bad)  best = when both tails are
very short

Terminology

 H0 = null hypothesis
 H1 = alternative hypothesis
 α = significant level
 p = probability of exceedance (overschrijdingskans)
 Yij = score of person i in group j of the dependent variable, with j equal to 1 or 2
 nj = number of observations in group j = sample size
 Ȳj = sample mean (steekproefgemiddelde) in group j (for total group)
 µ = mean (for total population)
 σ² = variance
 σ = standard deviation
 df = degrees of freedom

Working model

1) Formulate model and hypothesis




2) Select the significant level α
3) Test statistics: choice and calculation




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,4) Derive sample distribution and determine the p-value
df = degrees of freedom (nodig voor tabel)

 The larger the p-value, the less evidence to reject the null hypothesis
 The smaller the p-value, the more evidence to reject the null hypothesis
 P-value: table D
5) Decision
 Is it a one-sided or two-sided test?
 Compare p-value with α: when p < α => reject H0
6) Determine effect size
 Confidence Interval (CI) (betrouwbaarheidsinterval – BI) for difference between two
averages



 CI = 100*(1- α) %
 CI is always by two-sided tests
 CI of 99% means that if we conduct this experiment over and over again, the score
will be in the interval 99% of the times
 Ȳ2 - Ȳ1 = center of CI = (lower limit of CI + upper limit of CI)/2
 t*(n1+n2-2) x SE(Ȳ2 - Ȳ1) = m = upper limit of CI - center of CI
7) Interpretation
 Formulate conclusion
o Answer research questions
o Use substantive terminology
 Summarize results using plots
o Not necessary when only 2 groups compared
o Useful with multiple groups
 State findings’ limitations of the study
o Randomization: causal inference possible
o Random samples: assumption questionable; strictly no inference to population
possible




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, LES 2 – Analysis of the variance with one factor (ANOVA)

When there are 1 or 2 groups => t-test is also possible

When there are more than 2 groups => use ANOVA

Terminology

 ANOVA = ANalysis Of VAriance
 IV = independent variable (most of the time: amount of groups)
 DV = dependent variable (most of the time: number of items)
 STOS = modality-specific speech and language development disorder
 Yij = score of person i in group j of the DV
 nj = number of observations in group j = sample size
 N = total number of observations
 a = number of groups
 Ȳj = sample mean in group j
 Ȳ = µ = overall sample mean = population mean
 S’ = standard deviation
 df = degrees of freedom
 CI / d / R² / ω² = effectgrootte
 MSeffect = tussengroepsvariabiliteit
 MSerror|full = binnengroepsvariabiliteit

Working model

1. Preparation
 N?
 a?
 ni?
2. Exploratory data analysis
 Ȳj for all groups?
 S’i for all groups?
 Ȳ?
 S’?
 Formulate presumption on research question
 View assumptions and conditions
 2 models:




 3 assumptions
 Normality
 Independence of the observations of the groups
 Equal population standard deviations within groups (=
homoscedasticity)
1) Violations of assumptions
 Robustness against violations of assumptions
 A statistical method is robust against a certain violation, if the
statistical inferences are valid, even if the assumption is violated
 A valid inference means that the stated uncertainty (e.g., p-value) is
the actual level of uncertainty


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