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QM #2 - #4 The normal distribution & null hypothesis-testing…
QM #2 - #4
The normal distribution &
null hypothesis-testing
Populations & Samples
Populations
:bulb:
The collection of units
to which we want to generalize a set of findings or a statistical model
:memo: people, plankton, plants, cities, suicidal authors, etc.
Samples
:bulb:
A smaller
(but hopefully
representative
)
collection of units from
a population used to determine truths about that population
Calculating "error"
Standard
deviation (SD)
:bulb: A quantity expressing by how much the members of a group differ from the mean value for the group.
Sum of Squared
Errors (SS)
:bulb: The sum of different deviations
SS, variance, & SD represent the same thing
Error :confounded:
How well the mean represents the observed data :ok_woman::skin-tone-2:
The
variability
in the data
The ‘fit’ of the mean
to the data
Variance
:bulb:
Standard
error (SE)
:bulb: the standard deviation
of the sample means
Mean
:bulb: a simple statistical model of the centre of a distribution of scores
Test Statistic
:bulb: A statistic for which the frequency of particular values is known
Probability
:bulb: A quantitative statement of the likelihood of occurrence of an event
Statistic &
lang. research
Descriptive
statistic
:bulb: used to display, summarise & describe data
:old_key: Mean, standard
deviation, & range
Inferential
statistic
:bulb: used to
interpret the data
:old_key: a statistical test that tests a prediction
:memo: statistical test
χ2 (“chi-square”)
t-test
Dependent
Independent
Analysis of Variance (ANOVA)
correlation
Data
patterns
Distribution
:bulb: the
pattern
of values in a set of observation
Measures of
central tendency
:bulb: measure representing the centre or middle of a distribution
Mode
:bulb: Most frequently occurring scores
:memo: bi/trimodal
Mean
:bulb: Arithmetic
average of score
Measures of dispersion
:bulb: reflect spread of values (scores, measures, etc.) in a distribution
Normal distribution
:bulb: A symmetric, :bell:
-shaped probability distribution
, used as the theoretical model for the distribution of physical and psychological variables
Involved many observations
Percentage &
percentiles
:bulb:
Percentiles
indicates the location of a score
in a distribution (in %) >
where
:loudspeaker: % of the data that is
below
the amount in :question:
:loudspeaker: % of the data that is
at
or
below
the amount in :question:
:memo:
https://www.youtube.com/watch
?v=mDJvDRvvDXo
Standard scores
(z scores)
:bulb: how many SD away from the mean
:memo:
Calculating Z score
Formula: test score - mean / SD
:hammer_and_wrench: Function
Comparing an individual score in relation to the group
Locating a
data in a distribution
:couple_with_heart: among
observations :eyeglasses:
possible
sources
Systematic
factors
Chance
Systematic factors
:heavy_plus_sign: Chance
Logic of experimental research
Cause and Effect
:bulb: contiguity
Confounding
variable
:bulb: The
3rd factor
that cause
confusion
on the result of a research
:memo: The :couple_with_heart: between breast implants & :skull: is confounded by self esteem
Null hypothesis-testing
:bulb: An attempt to reject a purely chance explanation
Rejecting a NH supporting our research
No theory can
be
proved
Confirm / support a theory
Dis-confirm