Descriptive Statistics
Nominal Data
Chi Square
Professor McGonagall is curious about the
distribution of students from different
Hogwarts houses in her Transfiguration class.
She surveys 100 students and records the
number from each house (Gryffindor,
Hufflepuff, Ravenclaw, and Slytherin). She
wants to test if the distribution is significantly
different from the expected equal
distribution.
Multiple
Chi Square
Professor Flitwick is conducting a study on
students' preferences and affiliations. He
surveys 150 students to gather information
on their favorite pets (Cat, Owl, Rat) and
the type of wand they use (Dragon
Heartstring, Phoenix Feather, Unicorn
Hair). Professor Flitwick is interested in
understanding whether there is a significant
association or independence among
students' preferences for magical creatures
and their chosen wand types.
How many IVs are there?
1 (Hogwarts houses)
How many groups are in each IV?
Multiple groups: 4 (each house)
Are the groups correlated?
No
DV Type: Nominal (houses)
How many IVs are there?
2 (animals & wands)
How many groups are in each IV?
3: animals (3) wands (3)
Are the groups correlated?
No
DV Type: Nominal (pets/wands)
McNemar
Madam Pomfrey is conducting a study to
evaluate the effectiveness of a new healing
potion on students' injuries. She assesses 50
students with injuries after a field trip to the
Forbidden Forest. For each student, she
records the condition of their injuries
before administering the potion and after
administering the potion. The study aims to
determine if there's a significant
improvement in the students with injuries
before and after the potion.
How many IVs are there?
1 (time in relation to treatment)
How many groups are in each IV?
2 (injuries before and after potion)
Are the groups correlated?
Yes (before and after)
DV Type: Nominal (improved or not)
Descriptive Statistics
t-test
1 IV and 1 DV
single sample
Madam Hooch, the Quidditch instructor at
Hogwarts, is considering allowing teams to
participate in upcoming matches based on
their average practice hours. She wonders if
the average practice hours for Ravenclaw
Quidditch players are significantly different
from the required standard of 20 hours.
Which statistical test should she conduct to
make this determination?
How many IVs are there?
1 (number of practice hours)
How many groups are in each IV?
1 (hours)
Are the groups correlated?
N/A
DV Type: Interval (hours practiced)
t-test
independent samples
How many IVs are there?
1 (house teams)
Madam Hooch, the Quidditch instructor at
Hogwarts, wants to compare the average
practice hours between the Gryffindor and
Ravenclaw Quidditch teams. She wonders if
there is a significant difference in their
practice hours. Which statistical test should
she conduct to make this determination?
How many groups are in each IV?
2 (Gryffindor and Hufflepuff)
Are the groups correlated?
No
DV Type: Interval (hours practiced)
t-test
paired samples
Madam Hooch, the Quidditch instructor at
Hogwarts, is interested in determining if
there is a significant difference in the
practice hours before and after a specific
training session (time) for Gryffindor
Quidditch players. She wants to know if the
training session has a measurable impact on
their practice hours and will measure their
hours before the training and after to
determine this.
How many IVs are there?
1 (time in relation to training)
How many groups are in each IV?
Multiple groups: 2 (before and after)
Are the groups correlated?
Yes (before and after)
DV Type: Interval (hours practiced)
Descriptive Statistics
1-way
ANOVA
Madam Hooch, the Quidditch instructor at
Hogwarts, is curious about the average
practice hours among Quidditch players
from the house teams of Gryffindor,
Ravenclaw, and Hufflepuff. She wants to
determine if there is a significant difference
in practice hours among the three houses.
1 IV and 1 DV
How many IVs are there?
1 (house Quidditch teams)
How many groups are in each IV?
3 (Gryffindor, Ravenclaw, Hufflepuff)
Are the groups correlated?
No
DV Type: Interval (hours practiced)
1-way
repeated measures
ANOVA
Madam Hooch, the Quidditch instructor at
Hogwarts, is investigating the effects of a
magical potion on the practice hours of
Gryffindor Quidditch players. She
administers three different versions of the
potion and measures the practice hours of
Gryffindor players after each administration.
She wants to determine if there is a
significant difference in practice hours
across the three potion types. Which
statistical test should she conduct to make
this determination?
How many IVs are there?
1 (potion type)
How many groups are in each IV?
3 (potion types)
Are the groups correlated?
Yes (before and after)
DV Type: Interval (hours practiced)
Descriptive Statistics
2-way ANOVA
(factorial)
Professor Snape is conducting an experiment to examine
factors affecting the brewing time of magical potions. He
considers two independent variables: potion ingredient
(Mandrake Root, Dragon Scale) and cauldron type
(Brass, Copper). Professor Snape wants to determine if
there are significant differences in brewing time based
on both the potion ingredient and the cauldron type.
2+ IVs and 1 DV
How many IVs are there?
2 (ingredients and cauldrons)
How many groups are in each IV?
Multiple: ingredients (2) cauldrons (2)
Are the groups correlated?
No
DV Type: Interval (brewing time)
mixed ANOVA
(split plot)
Professor Snape is conducting a long-term experiment to
investigate the effects of two different potion
ingredients (Mandrake Root, Dragon Scale) and a
treatment (Heat Charm or no Heat Charm) on the
brewing time for potions. He measures brewing time at
various points using two different cauldron types
(Brass, Copper). Snape wants to determine if there are
significant differences in brewing time based on the
potion ingredient, the treatment, and how brewing time
changes over time with different cauldron types.
repeated
measures
ANOVA
Professor Snape is conducting a comprehensive
experiment to investigate the effects of potion
ingredients (Mandrake Root, Dragon Scale), a
treatment (Heat Charm), and cauldron types (Brass,
Copper) on the brewing time of magical potions. Instead
of applying the Heat Charm treatment to different
groups, he administers the treatment to the same
group over multiple time points. Professor Snape wants
to determine if there are significant differences in
brewing time based on the potion ingredient, the
treatment over time, and how brewing time changes with
different cauldron types.
How many IVs are there?
4 (ingredients, charm, cauldron, time)
How many groups are in each IV?
Multiple: ingredients (2) charm (2)
cauldrons (2) time (2+)
Are the groups correlated?
No
DV Type: Interval (brewing time)
How many IVs are there?
4 (ingredients, charm, cauldron, time)
How many groups are in each IV?
Multiple: ingredients (2) charm (2)
cauldrons (2) time (2+)
Are the groups correlated?
There are repeated measures
DV Type: Interval (multiple brewing time)
Descriptive Statistics
2+ IVs and 1+ groups each
ANCOVA
Professor Snape is conducting a comprehensive
experiment to investigate the effects of potion
ingredients (Mandrake Root, Dragon Scale), a
treatment (Heat Charm), and cauldron types
(Brass, Copper) on the brewing time of magical
potions. Additionally, he wants to examine how
magical expertise influences brewing time and
whether the observed effects of potion
ingredients, treatment, and cauldron types are
confounded by participants' magical
expertise. Professor Snape measures magical
expertise as a continuous covariate.
How many IVs are there?
2 (ingredients and cauldrons)
How many groups are in each IV?
Multiple: ingredients (2) cauldrons (2)
Are there continuous variables?
Yes
DV Type: Interval (brewing time)
MANOVA
How many IVs are there?
4 (ingredients, charm, cauldron, time)
Professor Snape is conducting a comprehensive
experiment to investigate the effects of potion
ingredients (Mandrake Root, Dragon Scale), a
treatment (Heat Charm), and cauldron types
(Brass, Copper) on multiple potion brewing
characteristics. The potion brewing
characteristics include brewing time, potion
color intensity, and potion viscosity. Snape is
interested in understanding how these
characteristics are influenced by potion
ingredients and cauldron types.
How many groups are in each IV?
Multiple: ingredients (2) charm (2)
cauldrons (2) time (2+)
DV Type: (interval)
Brewing time
Potion color intensity
Potion color viscosity
Tests of Relationship and Prediction
Bivariate Correlation Coefficients
Pearson’s R
What type of data is X?
Interval: Study time
Hermione Granger is conducting a study to examine the
relationship between the amount of time Hogwarts
students spend studying spells and their proficiency in
casting those spells. She collects data on the number of
hours students dedicate to studying (X) and their
corresponding spell proficiency scores (Y). Hermione
wants to determine if there is a linear relationship
between study time and spell proficiency.
What type of data is Y?
Interval: Spell proficiency
What is the purpose of the study?
Study the relationship between interval variables (study
time and spell proficiency)
Is there interest in a linear relationship?
Yes
Spearman’s
Rho
Professor Snape is curious about the relationship
between the complexity of potion recipes he assigns
and the rankings of students in his Advanced PotionMaking class. Snape ranks his students based on their
overall performance in brewing complex potions, and
he also rates the difficulty of each assigned potion
recipe. Snape wants to determine if there is a
monotonic relationship between potion complexity
and student rankings.
What type of data is X?
Ordinal: Potion complexity
What type of data is Y?
Ordinal: Student ranking
What is the purpose of the study?
Study the relationship between ordinal variables (potion
complexity and student rankings)
Is there interest in a linear relationship?
Yes
Point-Biserial
What type of data is X?
Dichotomous: Team member or not
Madam Hooch is interested in understanding the
relationship between students' Quidditch engagement
(X: dichotomous variable indicating whether a student is
on the Quidditch team or not) and their magical ability
(Y: a continuous variable representing the scores from a
standardized magical ability test). She wants to assess
whether being on the Quidditch team correlates with
higher magical ability scores.
What type of data is Y?
Continuous: Magic ability
What is the purpose of the study?
Study the relationship between a dichotomous variable
and a continuous variable (Quidditch involvement and
Magical ability scores)
Is there interest in a linear relationship?
Yes