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QM #7
t-test, CI, Regression, & Correlation (Regression (:old_key:
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QM #7
t-test, CI, Regression, & Correlation
Confidence
Interval (CI)
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Why is it done?
Assessing the accuracy of the sample mean as an estimate of the mean in the population (Field, 78)
What do we need?
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:memo: 95% CI :arrow_forward: We may 95% confident
that the population mean lies in the interval (-.2, 3.1)
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Why is it done?
allows the researcher to determine simultaneously the degree and direction of a :couple_with_heart: with a single statistic
What do
we need?
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Does the data meet
the assumptions?
- The level of the measurement of the variables correlated is continuous.
- The :couple_with_heart: is approximately linear.
- The data is approximately
normally distributed.
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Significant outliers in the data
:old_key:
values
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SD
:bulb: A quantity expressing by how much the members of a group differ from the mean value for the group.
Regression
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Types
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Multiple
regression
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:old_key: values
β coefficient
:bulb: Standardized coefficients beta reflects the relative importance of the variables, and is related to the distribution of the independent variables
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What do we need?
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Does the data meet
the assumptions?
- The variables r measured
at the continuous level
- Linear :couple_with_heart: btwn variables
- There should be
significant outliers
- The data shows homoscedasticity
(equal variance)
- The residuals (deviation) of
the regression line r
approximately normally distributed
- There should be
independence of observations
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:old_key:
values
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SD
:bulb: A quantity expressing by how much the members of a group differ from the mean value for the group.
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Dependent t-test
(paired sample t-test)
Why is it done?
To assess whether the mean difference between paired/matched observation is significantly different from 0 (e.g. pre-test and post-test).
What do
we need?
:old_key: values
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Cohen's d
:key: effect size
d=.40 :arrow_forward: small effect
d=.70 :arrow_forward: medium effect
d=1 :arrow_forward: large effect
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Does the data meet
the assumptions?
- The data consists of
1 DV that is measured at the continuous level (i.e., it is measured at the interval or ratio level).
:memo: revision time (measured in hours),
intelligence (measured using IQ score),
exam performance (measured from 0 to 100),
weight (measured in kg), etc.
- The data consists of 1 IV that consists of 2 categorical, related groups or matched pairs.
- There should be
significant outliers in the differences between the two related groups.
- The distribution of the differences in the DV btwn the 2 related groups should be approximately normally distributed
- There needs to be homogeneity of variances
:bulb: the variance of 1 variable is stable (i.e. relatively similar)
at all levels of another variable.
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:bulb: a statistical procedure which is used to determine whether the mean difference btwn 2 sets of observation (of the same group of participants) is 0
Independent t-test
(2 sample t-test/
independent-samples t-test/
student's t-test)
:bulb: a statistical procedure which is used to determine whether the mean difference btwn 2 sets of observation (of the different group of participants) is 0
What do
we need?
:old_key: values
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Cohen's d
:key: effect size
d=.40 :arrow_forward: small effect
d=.70 :arrow_forward: medium effect
d=1 :arrow_forward: large effect
Negative value Cohen's d doesn't matter, it's just the group order
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Does the data meet
the assumptions?
- The data consists of
1 DV that is measured at the continuous level (i.e., it is measured at the interval or ratio level).
:memo: revision time (measured in hours),
intelligence (measured using IQ score),
exam performance (measured from 0 to 100),
weight (measured in kg), etc.
- The IV should consist of 2 categorical, independent groups
:memo: gender (2 groups: :male_sign: or :female_sign:),
employment status (2 groups: employed or unemployed),
smoker (2 groups: yes or no)
- The data should have independence of observations, which means that there is no :couple_with_heart: btwn the observations in each group or between the groups themselves
- DV should be approximately normally distributed for each group of the IV
- There should be
significant outliers
- There needs to be homogeneity of variances
:bulb: the variance of 1 variable is stable (i.e. relatively similar)
at all levels of another variable.
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Covariate :arrow_forward: :bulb: Continuous variable,
part of experimental manipulation,
affected DV