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Mammograms A 9 -year study in Sweden compared 21,088 women who had mammograms with 21,195 who did not. Of the women who underwent screening, 63 died of breast cancer, compared to 66 deaths among the control group. (The New York Times, Dec 9, 2001) a) Do these results support the effectiveness of regular mammograms in preventing deaths from breast cancer? b) If your conclusion is incorrect, what kind of error have you committed?

Short Answer

Expert verified
The results don't strongly support the effectiveness of mammograms in reducing breast cancer deaths. A Type II error (false negative) might have been committed.

Step by step solution

01

Analyze the Data

We are given two groups: one with 21,088 women who had mammograms and another with 21,195 women who did not. In the mammogram group, 63 women died from breast cancer, and in the non-mammogram group, 66 women died.
02

Calculate Death Rates

Calculate the breast cancer death rate for both groups. For the mammogram group, the death rate is \( \frac{63}{21088} \approx 0.2989\% \). For the non-mammogram group, the death rate is \( \frac{66}{21195} \approx 0.3114\% \).
03

Compare Death Rates

Compare the calculated death rates. The death rate in the mammogram group (0.2989%) is slightly lower than the non-mammogram group (0.3114%).
04

Statistical Significance and Effectiveness

Determine if the difference in death rates is statistically significant. A slight difference, such as 0.0125%, is not likely to be statistically significant in such large groups. Since significant statistical evidence would be needed to assert effectiveness, these results may not support the claim that mammograms are effective at reducing breast cancer mortality.
05

Assess Possible Error

If the conclusion that mammograms don't significantly reduce breast cancer deaths is incorrect, it might be a Type II error (failing to reject a false null hypothesis). This means we might conclude that mammograms are not effective when they actually are.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mammogram Effectiveness
Mammograms are screening tools used to detect breast cancer early. The goal is to identify the disease before symptoms develop.
This allows for earlier treatment, which can potentially improve outcomes.
In the study from Sweden, 21,088 women had regular mammograms, and 63 of them died from breast cancer. In the control group of 21,195 women without mammograms, 66 died. Despite the smaller number of deaths in the mammogram group, the effectiveness of mammograms in significantly reducing breast cancer mortality is called into question.
The difference in mortality (0.2989% vs. 0.3114%) is very slight. Understanding mammogram effectiveness requires looking beyond just death rates. Consider:
  • Detection rates, early diagnosis, and treatment outcomes
  • Reduction in breast cancer stages at diagnosis
  • Cost-effectiveness and accessibility of mammogram programs
The question of effectiveness isn't straightforward and often requires more comprehensive analysis and studies.
Statistical Significance
In studies like this, researchers determine if results are statistically significant.
This means checking whether the observed difference is likely due to chance or reflects a true difference.
In the Swedish study, the difference in death rates was 0.0125%.
Generally, for large groups, such a tiny difference would not be considered statistically significant. Here's what to consider regarding statistical significance:
  • A p-value is commonly used to assess significance: a p-value less than 0.05 is often considered significant.
  • The larger the sample size, the easier it becomes to find statistical significance with small differences, though practical significance might still be low.
  • Statistical tests like Chi-square or T-tests may be used to calculate significance.
When performing statistical tests, the key is to ensure the assessment of whether the observed effect could happen just by random chance is accurately determined.
Type II Error
A Type II error occurs when a study fails to reject a false null hypothesis.
In simple terms, it's when the study suggests there is no effect when there actually is one.
In the case of mammograms, if we conclude they do not significantly reduce breast cancer mortality and we're wrong, that's a Type II error. Key features:
  • Type II errors are impacted by sample size, variability, and effect size.
  • The probability of a Type II error is referred to as beta (β).
  • Reducing Type II errors often requires larger sample sizes or more sensitive measures.
Both Type I errors (false positives) and Type II errors (false negatives) are important to consider when designing an experimental study and interpreting its results.
Breast Cancer Mortality Rates
Breast cancer mortality rates refer to the number of deaths from breast cancer per a certain number of people (usually per 100,000).
These rates help gauge the severity of breast cancer and the effectiveness of treatments and prevention methods, like mammograms.
The Swedish study gives an insight into how these rates differ between women who have regular mammograms and those who do not.
However, slight differences in mortality rates may not always reflect true effectiveness. Aspects that impact breast cancer mortality rates include:
  • Early detection through screening methods such as mammograms
  • Advancements in treatment options and cancer therapies
  • Overall health initiatives and awareness campaigns
Understanding breast cancer mortality rates is crucial for formulating public health policies and improving screening programs.

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Most popular questions from this chapter

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