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Lecture 20

# STATS 13 Lecture Notes - Lecture 20: Null Hypothesis, Blind Experiment, Dependent And Independent Variables

Department
Statistics
Course Code
STATS 13
Professor
Tsiang, Mike
Lecture
20

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Bicycling to Work: Scope of Inference!
can we generalize to a larger population !
was the sample randomly obtained from a larger population!
no. it was on consecutive days which did not include all seasons!
data is only one person and two bikes, we cannot generalize beyond this particular person and his two
speciﬁc bikes!
can we draw a cause eect conclusion!
were the observational units randomly assigned to treatments !
yes!
if the p value was small (its not) we might be able to say its a cause eect conclusion but there's a ﬂaw in the
experimental design!
!
Bicycling to work: scope of inference!
a limitation is that this study is not double-blind!
researcher and subject were not blind to which treatment was being used!
knowing which bike he was on could inﬂuence his performance!
there could be other factors besides the bike type that could aect the dierence in mean commute times
between bikes!
double blind studies control for possible biases from the researcher or the subjects!
!
Section 6.3: Comparing Two Means: Theory-Based Approach !
!
Example 6.3: Breastfeeding and intelligence!
Study: Children who breastfeed during infancy dier from bottle fed!
Basics!
explanatory variable !
if the child was breastfed (categorical, binary)!
response variable !
the child's GCI at age 4 (quantitative)!
observational study: the researchers did not decide which children would be breast-fed !
cause and eects be drawn?!
no the study is not a randomized experiment!
!
Breastfeeding and Intelligence: Hypotheses!
null hypothesis!
there is no association between breastfeeding
during infancy and GCI at age 4!
the mean GCI value at age 4 for breastfed
children is the same as the mean GCI value at
age 4 for children who were not breastfed!
H : μbreastfed = μnot or μ breastfed - μ not =
0!
alternative hypothesis!
there is an association between breastfeeding
during infancy and GCI at age 4!
the mean GCI value at age 4 for breastfed
children in not the same as the mean GCI value
at age 4 for children who were not breastfed!
Ha: μbreastfed μ not to μbreastfed - μ not 0!
!
Breastfeeding and Intelligence: Possible Explanations!
the dierence in means was 4.4!
if breastfeeding is not associated with GDI at age 4!
is it possible or plausible that a dierence this large could happen by chance!
yes its always possible, but we need a test of signiﬁcance to assess the strength of evidence !
!
Two population means: New test statistic!
to test for a dierence in means, we need a test statistic that represents how far away our observed dierence in
means is from the dierence we would expect under the null hypothesis !