These data come from a case-controlled study to examine the potential relationship between age at first pregnancy and cervical cancer. In a case-control study a random sample of cases (i.e. people with the disease in question) and controls (i.e. people similar to those in the case group, except they do not have the disease) and the proportion of people with some potential risk factor are compared across the two groups. In this study we will be comparing the proportion of women who had their first pregnancy at or before the ages of 25, because researchers suspected that an early age at first pregnancy leads to increased risk of developing cervical cancer. The data is presented in the table below: Age at First Pregnancy 25 Cervical Cancer 42 7 Control 203 114 What is the appropriate null hypothesis to determine if there is an association between age at first pregnancy and later development of cervical cancer?

Question

These data come from a case-controlled study to examine the potential relationship between age at first pregnancy and cervical cancer.  In a case-control study a random sample of cases (i.e. people with the disease in question) and controls (i.e. people similar to those in the case group, except they do not have the disease) and the proportion of people with some potential risk factor are compared across the two groups.  In this study we will be comparing the proportion of women who had their first pregnancy at or before the ages of 25, because researchers suspected that an early age at first pregnancy leads to increased risk of developing cervical cancer.  The data is presented in the table below:

Age at First Pregnancy <=25	Age at First Pregnancy>25
Cervical Cancer	42	7
Control	203	114

What is the appropriate null hypothesis to determine if there is an association between age at first pregnancy and later development of cervical cancer?

BlackTom AI · Accepted Answer

In a case-control study, the null hypothesis typically states that there is no association between the exposure (age at first pregnancy, here defined as <=25) and the outcome (cervical cancer). Option under consideration: 'Ho: There is no association between age at first pregnancy and if a woman gets cervical cancer or not.' Why this is appropriate: The research question aims to determine whether early age at first pregnancy is related to later development of cervical cancer. The null hypothesis corresponds to independence between the exposure category (<=25 vs >25) and disease status (cervical cancer vs control). If the null is true, the proportion of cases and controls with exposure <=25 should be similar, and any observed difference would be due to random variation. Why the null is not about causation or direction: The null should not assert a causal claim or specify a direction of effect; it merely asserts no association, leaving open the possibility that an association exists in either direction if data support it. Potential misunderstandings to avoid: - Stating the null as 'no difference in risk' or 'no difference in proportions' is conceptually similar, but phrasing as 'no association between exposure and disease' is the standard epidemiological formulation for independence between exposure and outcome. - Saying 'the age at first pregnancy causes cervical cancer' would be an alternative hypothesis, not the null. - Framing the null as applicable only to cases or only to controls would be incorrect; the null concerns the relationship across both groups. In summary, the provided null hypothesis correctly reflects the goal of testing for an association between age at first pregnancy (<=25 vs >25) and cervical cancer status in this case-control design.

STAT_3615_20055_202501 Mod 9 HW Chi Squared Tests

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