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

by OC2550403

Department

StatisticsCourse Code

STATS 13Professor

Tsiang, MikeLecture

20This

**preview**shows half of the first page. to view the full**3 pages of the document.**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 eﬀect 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 eﬀect 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 aﬀect the diﬀerence 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 diﬀer 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 eﬀects 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 ₀: 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 diﬀerence in means was 4.4!•

if breastfeeding is not associated with GDI at age 4!•

is it possible or plausible that a diﬀerence 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 diﬀerence in means, we need a test statistic that represents how far away our observed diﬀerence in •

means is from the diﬀerence we would expect under the null hypothesis !

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