included in the study\u2022 Never assume that a causation exists just because there is an association
between two variables – always be on the lookout for lurking variables
Q: Causation
Answer:
A change in one variable creates a change in the other variable.o
Can only be determined from an experiment
Q: Association
Answer:
means there is a relationship between two variables.Association does not necessarily imply
causation.
o We can use scatterplots to visualize the data and determine if there is at least an association, but
we cannot determine causation from a scatterplot alone.o<\/li>\n<\/ul>\n\n\n\n
Can establish association through an observational study.
Q: Observational Study
Answer:
There are no treatment or control groups because the participants self-select their groups.
Researchers observe if there is an association between variables.
Q: Experimental Study
Answer:<\/p>\n\n\n\n
- \n
- Researchers randomly assign participants to two or more groups. One group is designated as a
control group where no treatment (placebo) is given while all other groups are given treatments
to determine if there is causation between variables.
Q: Graphical Displays:
Answer:
Just C – Pie chart or bar chart\u2022 Just Q – Histogram, stem plot, boxplot, or dot plot\u2022
C \u2019 C – Two-way table with Conditional Percentages\u2022
C \u2019 Q – Side-by-side boxplot with 5-number summary\u2022 Q \u2019 Q – Scatterplot with correlation
coefficient
Q: Correlation Coefficient (Q \u2019 Q)
Answer:
Strength: On a scatterplot, the closer the points are laid out in a line,the stronger the correlation.
measures the direction and strength of the linear relationship between the variables The closer r
is to +1, the stronger the positive correlation. The closer r is to -1, the stronger the negative
correlation. The closer r is to 0, the weaker the correlation.
Q: Positive Correlation<\/li>\n<\/ul>\n\n\n\nAnswer:
scatterplot reveals an “uphill trend.” as the explanatory variable increases, the response variable
increases.
Q: Negative Correlation
Answer:
scatterplot reveals a “downhill trend.”As the explanatory variable increases, the response
variable decreases.
Q: No CorrelationAnswer:
scatterplot reveals no trend between the variables
Q: Variable Type Q \u2019 Q
Answer:
Graphical Display: Scatterplot
Numerical Measure: Correlation Coefficient (r value)
Q: Variable Type C \u2019 Q
Answer:
Graphical Display: Side by Side Boxplots
Numerical Measure: Five Number Summary
Q: Variable Type C \u2019 C
Answer:
Graphical Display: Two Way Table
Numerical Measure: Conditional Percentages<\/p>\n\n\n\nQ: Explanatory Variable
Answer:
Influences the response variable.
Q: Response Variable
Answer:
Is affected by the explanatory variable.
Q: Standard Deviation Rule
Answer:
68% of the data is within 1 standard deviation of the mean.\u2022
95% of the data is within 2 standard deviations of the mean.\u2022
99.7% of the data is within 3 standard deviations of the mean
Q: Mode –
Answer:
value that occurs most often in a data set
Q: Median
Answer:
halfway point, equal number of data points above the median as below, always order the data
from smallest to largest first
Q: Mean
Powered by https:\/\/learnexams.com\/search\/study?query=<\/a><\/p>\n\n\n\n![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2023\/12\/wgu-c955-formulas-and-terms-latest-2023-2024-update-applied-probability-and-statistics-questions-and-ver-725x1024.png\")
<\/a><\/figure>\n\n\n\nOpen Circle
value is not included<\/p>\n\n\n\nClosed Circle
Value is included<\/p>\n\n\n\n1 Tbsp
3 tsp<\/p>\n\n\n\n1 fl oz
2 tbsp<\/p>\n\n\n\n1 L
1000 mL<\/p>\n\n\n\n1 kg
1000 g<\/p>\n\n\n\n1 g
1000 mg<\/p>\n\n\n\nm
slope<\/p>\n\n\n\nb
y-intercept<\/p>\n\n\n\nPositive slope
uphill line<\/p>\n\n\n\nNegative slope
downhill line<\/p>\n\n\n\nQuantitative (numerical) data
consists of data values that are numerical,
quantities that can be counted or measured (additions\/subtractions make
sense)
Examples: Height, Salary, Chance of rain, Weigh<\/p>\n\n\n\nCategorical (qualitative) data
consist of data that are groups or labels,
and are not necessarily numerical (additions\/subtractions do not make
sense)
Examples: Hair Color, Country of Origin, Blood Type, Zip Codes<\/p>\n\n\n\nPie Chart
Displays parts of the whole, percentages<\/p>\n\n\n\nBar Chart
Displays counts or frequencies of each category<\/p>\n\n\n\nHistogram
displays the shape and spread of data<\/p>\n\n\n\nBox Plot
displays center, spread and outliers. Each section covers 25%
of the data regardless of length. Can be horizontal or vertical<\/p>\n\n\n\nDot Plot
displays clusters, gaps, and outliers for smaller data sets. Each
data value is seen in a dot plot<\/p>\n\n\n\nStem Plot
Display shape according to place values. Each data value if
seen in a stem plot<\/p>\n\n\n\nSymmetric Normal
Mean, Median, and Mode are approximately equal.<\/p>\n\n\n\nSkewed Right (positively skewed)
Mode < Median < Mean.<\/p>\n\n\n\nSkewed left (negatively skewed)
Mean < Median < Mode.<\/p>\n\n\n\nMedian
halfway point, equal number of data points above the
median as below, always order the data from smallest to largest firs<\/p>\n\n\n\nExplanatory Variable
Influences the response variable<\/p>\n\n\n\nResponse Variable
Is affected by the explanatory variable<\/p>\n\n\n\nExperimental Study
Researchers randomly assign participants to
two or more groups. One group is designated as a control group
where no treatment (placebo) is given while all other groups are given
treatments to determine if there is causation between variables.<\/p>\n\n\n\nObservational Study
There are no treatment or control groups
because the participants self-select their groups. Researchers
observe if there is an association between variables<\/p>\n\n\n\nAssociation
means there is a relationship between two variables.
Association does not necessarily imply causation.<\/p>\n\n\n\no We can use scatterplots to visualize the data and determine if
there is at least an association, but we cannot determine
causation from a scatterplot alone.
o Can establish association through an observational study<\/p>\n\n\n\nCausation
A change in one variable creates a change in the other
variable.<\/p>\n\n\n\no Can only be determined from an experiment.<\/p>\n\n\n\n
Lurking variable
A variable not included in the study, but affects
the variables that were included in the study. Never assume that a causation exists just because there is an
association between two variables – always be on the lookout for
lurking variables<\/p>\n\n\n\nSimpson’s Paradox
A counterintuitive situation that occurs when a result that appears in
individual groups of data disappears or reverses when the groups are
combined. Can only occur when the sizes of the groups are inconsistent.<\/p>\n\n\n\nSimple linear equation (regression line or line of best fit)
models
the data on a scatter plot with a line<\/p>\n\n\n\no x is the explanatory variable, and y is the response variable
o Equation is given by y = mx + b where m is the slope and b is
the y-intercept<\/p>\n\n\n\nSample Space
set of all possible outcomes.<\/p>\n\n\n\nTheoretical Probability =
Number of outcomes with the desired event\/
Total number of outcomes<\/p>\n\n\n\nTree Diagram
Used to determine the sample space<\/p>\n\n\n\nComplementary events
events that do not have any common
outcomes and when combined they comprise the sample space.
o P(not A) = 1 – P(A<\/p>\n\n\n\nP(A or B)
represents the probability that event A will occur, or
event B will occur, or both A and B will occur<\/p>\n\n\n\nP(A and B)
represents the probability that events A and B will
occur at the same time<\/p>\n\n\n\nP(A|B)
represents the probability that event A will occur, given
that event B has already occurred<\/p>\n\n\n\nDisjoint Events
cannot occur at the same time.
P(A and B) = 0
Example:<\/p>\n\n\n\n- \n
- A = Randomly selecting a person with type B blood.<\/li>\n\n\n\n
- B = Randomly selecting a person with type O blood.<\/li>\n<\/ul>\n\n\n\n
Independent Events
We say events A and B are
independent if the occurrence of one of them does not affect
the probability that the other will occur.
P(A|B) = P(A) and P(B|A) = P(B)<\/p>\n\n\n\n- \n
- “probability of A will be the same whether or not B
has already occurred. Also, probability of B will be
the same whether or not A has already occurred.”
Example:<\/li>\n\n\n\n - A = Flipping a coin and landing on tails<\/li>\n\n\n\n
- B = Rolling a die and landing on 3<\/li>\n<\/ul>\n\n\n\n
OR Rule (General Addition)
P(A or B) = P(A) + P(B) – P(A and B)
Simplifies to P(A or B) = P(A) + P(B) for disjoint events<\/p>\n\n\n\nAND Rule (General Multiplication)
P(A and B) = P(A) x P(B|A)
Simplifies to P(A and B) = P(A) x P(B) for independent
events<\/p>\n\n\n\nConditional Probability
P(B|A) = P(A and B)\/
P(A)<\/p>\n","protected":false},"excerpt":{"rendered":"WGU C955 Formulas and Terms (Latest 2023\/ 2024 Update) Applied Probability and Statistics | Questions and Verified Answers| 100% Correct WGU C955 Formulas and Terms (Latest2023\/ 2024 Update) Applied Probability andStatistics | Questions and Verified Answers|100% CorrectQ: Simpsons ParadoxAnswer:A counterintuitive situation that occurs when a result that appears in individual groups of datadisappears or reverses […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-130854","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/130854","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=130854"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/130854\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=130854"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=130854"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=130854"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- “probability of A will be the same whether or not B