Samenvatting Descriptive and Inferential Statistics
12 views 1 purchase
Course
Descriptive and Inferential Statistics (P0X82A)
Institution
Katholieke Universiteit Leuven (KU Leuven)
Summary of all powerpoints and lessons. Created for the master's programme in Psychology for the course Descriptive and Inferential Statistics for the January 2025 exam period. See the tags for the various topics.
The document has 38 pages and is made in my usual template (using color and mostly...
VARIABLES
= the values we want to measure, e.g. time in seconds, score on a test, gender
- Random variables are variables whose values are unknown and are realizations of a random process
INDEPENDENT VS DEPENDENT VARIABLES
Independent variables Dependent variables
= variable that is not dependent on any other = variable that depends on other factors, the output,
variable, the input, the predictor, the explanation the criteria, the response
- Commonly represented as X1, …, Xj, …, Xk - Commonly represented as Y1, …, Yj, …, Yk
- E.g. the amount of time spent studying - E.g. the exam result
DISCRETE VS CONTINUOUS VARIABLES
Discrete variables Continuous variables
= a variable that only assumes a limited number of = numeric variable that has an infinite number of
values possibilities between two values
- E.g. someone speaks 3 languages, yes/no - E.g. someone looked at a picture for 1,3828 sec
- A discrete variable that - A variable is considered continuous when
• Only assumes two values is a dichotomous • The variable takes on a wide range of values
variable • The variable is a manifestation of an
• Only assumes three values is a underlying continuous variable
trichotomous variable
• Assumes three or more values is a
polytomous variable
QUALITATIVE VS QUANTITATIVE VARIABLES
Qualitative variables Quantitative variables
= numbers only refer to equalities and inequalities = numbers are assigned so that differences between
between the research elements (regarding the numbers correspond with distances between
measured characteristics) research elements (regarding the measured
The number is only a name or label characteristics)
Calculating is not meaningful Number is a real number
Calculating is meaningful
- Nominal variable, e.g. Dutch (1), English (2)
- Ordinal variable, e.g. not satisfied (1) → very - Interval variable, e.g. temperature in °C, Likert-
satisfied (5) scale in numbers
• ! the numbers must be compared by - Ratio variable, e.g. temperature in °K, time
size/order but are not meaningful to
calculate with
There is a hierarchy within the different types of variables:
- While all quantitative variables can be ordinal variables
(seeing as they are numbers and can be ordened), not all
ordinal variables are quantitative variables
- Ordinal variables can be thought of as qualitative variables
where order matters but numerical measurement or
distance between categories doesn’t really matter
,DIS – januari 2025 2
DESCRIBING 1 VARIABLE
TABLES
- Variables are represented by capital letters in
italics in the columns, e.g. X4
- Research elements are located in the rows and
are represented with a Xij formula, with i
referring to the research element and j to the
variable, e.g. X14 = 3
FREQUENCY TABLES
The (absolute) frequency distribution of X is denoted as f(X), e.g. f(X=77) = 3 because the score 77 occurs 3
times
Cumulative frequency of a specific score on X is the total number of scores lower than or equal to that specific
score and its distribution is denoted as F(X), e.g. F(X=77) = 14
- This is not meaningful for qualitative data as the categories are not ordered
Relative frequencies or proportions of scores on X are the frequencies divided by the number of observations
and its distribution is denoted as p(X), e.g. p(X=77) = 3/30 = 0.1
Relative cumulative frequencies or cumulative proportions of a specific score on X equals the cumulative
frequency divided by the total number of observations and its distribution is denoted as P(X), e.g. P(X=77) =
14/30 = 0.47
STEM-AND-LEAF PLOTS
- Read scores by stem.leaf*101, e.g. 8.4*101 = 84
- When looking for a certain percentile and the n is even,
take then average of the two scores, e.g. P50 of n = 30 is
the 15th score, so (78+78)/2 = 78
- When looking for a percentile and matching score is not
in there (e.g. P25 when n = 10), look at the score above
,DIS – januari 2025 3
KEY STATISTICS
PERCENTILES
= score on X under which at least (so lower or equal) a specific % of scores is situated, e.g. 10th percentile
corresponds to score 8 so at least 10% of scores ≤ 8 → P10 = 8
- To calculate, simply find the corresponding score to the % given in the relative cumulative frequency table
• Is the % not literally in the table? Find the smallest higher percentile and take that score
• Is the % literally in the table and n is an even number? Take the median between that one and the one
above
- Special percentiles:
• Quartiles (in 4), with Q1 = P25, Q2 = P50 and Q3 = P75
• Deciles (in 10), with D1 = Pc10, D2 = P20, …
These are all special forms of quantiles or fractiles: a score under which a specific proportion of scores is
situated
Example with Stem-and-leaf plot
CENTER
MODE
= score or category with highest frequency, e.g. 2, 3, 3, 4, 6 → mode = 3
- Can be used for both quantitative and qualitative variables
- Uniqueness?
• Unimodal distribution: mode is uniquely defined
• Bimodal or multimodal distribution: two (or more) scores or categories have the maximum frequency,
e.g. 2, 3, 3, 4, 4, 6 → bimodal: mode = 3 and 4
MEDIAN
= the middle value, so (at least) half of the scores are above it and (at least) half are below it
= Q2 = P50
- Calculate by ordering all observed scores, then taking the middle score or averaging the two middle scores
THE (ARITHMETIC) AVERAGE
1 1
𝑋̅ = 𝑛 ∑𝑛𝑖=1 𝑋𝑖 with ∑𝑛𝑖=1 𝑋𝑖 as the sum of all observed values and 𝑛 as this sum divided by the number of
observed values, e.g. 2, 3, 3, 4, 4, 5 → 𝑋̅ = (2+3+3+4+4+5)/6 = 21/6 = 3.5
, DIS – januari 2025 4
Different formulas for frequency table with k scores with examples:
1
- Using absolute frequencies: 𝑋̅ = 𝑛 ∑𝑘𝑖=1 𝑋𝑖 × 𝑓𝑖 , waarbij ∑𝑘𝑖=1 𝑓𝑖 =
𝑛
e.g. 2, 3, 3, 4, 4, 5 → 𝑋̅ = (2+3x2+4x2+5)/6 = 21/6 = 3.5
- Using relative frequencies: 𝑋̅ = ∑𝑘𝑖=1 𝑋𝑖 × 𝑝𝑖 , waarbij ∑𝑘𝑖=1 𝑝𝑖 = 1
e.g. = 2*.17 + 3*.33 + 4*.33 + 5*.17 = 3.5
SPREAD
If a distribution needs to be described by a single number, one usually chooses a measure of central tendency
(mean, median …). However, two distributions can have the same mean/median yet look completely different!
RANGE
= difference between max and min score
- 𝐵 = 𝑋[𝑚𝑎𝑥] − 𝑋[𝑚𝑖𝑛]
- This is extremely sensitive to outliers!
INTERQUARTILE RANGE
= difference between third and first quartile
- 𝐼𝑄𝑅 = 𝑄3 − 𝑄1
- This is a more robust measure of spread for quantitative variables
VARIANCE
= average quadratic deviation from the arithmetic average
1
- 𝑆𝑋2 = 𝑛 ∑𝑛𝑖=1(𝑋𝑖 − 𝑋̅ )2
- Can never be negative!
Calculate by
1) Sum to n
2) Calculate 𝑋̅
3) Calculate the deviations (𝑋 − 𝑋̅)
4) Square the deviations
5) Sum these squares
6) Divide by n
STANDARD DEVIATION
= corrects the “squaredness” from the variance to ensure it is expressed in the original unit of measurement
- 𝑆𝑋 = √𝑆𝑋2
- Can never be negative!
STANDARDIZING AND Z-SCORES
= transforming a variable such that the average becomes 0 and the standard deviation becomes 1
- Scores on standardized variables are called standard scores or z-scores, which indicate how many standard
deviations you score above or below the average
𝑋𝑖 −𝑋̅
- 𝑧𝑖 = 𝑆𝑋
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller Mellowerillish. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.39. You're not tied to anything after your purchase.
