Question

Suppose you want to find out if reading speed is any different between a print book and an e-book. (a) Clearly describe how you might set up an experiment to test this. Give details. (b) Why is a hypothesis test valuable here? What additional information does a hypothesis test give us beyond the descriptive statistics we discuss in Chapter \(2 ?\) (c) Why is a confidence interval valuable here? What additional information does a confidence interval give us beyond the descriptive statistics of Chapter 2 and the results of a hypothesis test described in part (b)? (d) A similar study \(^{53}\) has been conducted, and reports that "the difference between Kindle and the book was significant at the \(p<.01\) level, and the difference between the iPad and the book was marginally significant at \(p=.06 . "\) The report also stated that "the iPad measured at \(6.2 \%\) slower reading speed than the printed book, whereas the Kindle measured at \(10.7 \%\) slower than print. However, the difference between the two devices [iPad and Kindle] was not statistically significant because of the data's fairly high variability." Can you tell from the first quotation which method of reading (print or e-book) was faster in the sample or do you need the second quotation for that? Explain the results in your own words.

Short answer

An experiment could be designed where two groups of people read the same content from a print book and an e-book, and their reading speeds are compared. Hypothesis tests and confidence intervals are valuable tools that give us insights into the statistical significance and reliability of observed differences. A similar study found that e-books (both Kindle and iPad) result in slower reading speeds than print books, but there was no statistical difference between the two e-book platforms.

Step-by-step solution

Designing the Experiment

An experiment can be set up by selecting two groups of individuals. One group would read a print book and another group would read an e-book. Ensure that both groups read the same content and are comprised of individuals with similar reading habits. The reading speed of each individual could then be measured.

Value of Hypothesis Test

A hypothesis test is valuable here to statistically determine if there is a significant difference in reading speed between the two groups. It provides value beyond basic descriptive statistics by allowing judgments to be made on population parameters, based on sample data. A null hypothesis suggesting no difference in reading speed between the two groups, and an alternative hypothesis suggesting a difference exists, could be tested.

Importance of Confidence Intervals

A confidence interval provides a range of values, derived from sample data, which is likely to contain the value of an unknown population parameter. This helps in assessing the precision and reliability of estimates of the population parameter. It gives us more information above the simple result of the hypothesis test by quantifying the uncertainty in the estimate.

Interpretation of Study Results

The first statement from a similar study is about the statistical significance of the differences. It means that the difference in reading speeds between Kindle, iPad and the printed book is not due to random chance. The second statement reveals that the iPad and Kindle were slower than the print book and there was no statistically significant difference between the iPad and Kindle due to high variability in data. So, both the quotations are necessary to fully understand the results.

Key concepts

Hypothesis Testing

When conducting research, such as determining if there is a difference in reading speeds between print books and e-books, hypothesis testing serves as a critical tool. The process begins with the formulation of two hypotheses: the null hypothesis (\(H_0\)) which asserts that there is no difference in reading speeds, and the alternative hypothesis (\(H_1\)) which posits that a difference does indeed exist. Hypothesis testing uses sample data to make inferences about the population from which the sample was drawn.

Statistical tests are then applied to determine whether the observed data can lead to the rejection of the null hypothesis with a certain degree of confidence, which ties into the concept of statistical significance. If the null hypothesis can be rejected, it suggests that the findings are not the result of random variation, but instead may reflect a genuine effect or difference in the population.

Hypothesis tests value lies in their capacity to move beyond mere descriptive statistics by testing assumptions about population parameters, allowing us to make more confident decisions based on our data.

Confidence Intervals

While hypothesis testing lets us know whether or not there is a statistically significant difference, confidence intervals provide additional insight by quantifying the uncertainty around our estimate of the population parameter. A confidence interval is a range of values, typically centered around a sample statistic, that is believed with a certain level of confidence—often 95%—to contain the true population parameter.

Returning to our reading speeds example, a confidence interval around the mean difference in reading speed between print and e-books not only shows the estimated difference but also provides an upper and lower bound for that estimate. This range reflects the precision of the estimate: narrower confidence intervals represent more precise estimates. Confidence intervals are especially valuable when comparing two means; they can indicate whether the difference is substantial or whether it may be so small that it's not practically significant, even if it is statistically significant.

Descriptive Statistics

Descriptive statistics are the foundation of any data analysis. They provide a snapshot of our data, summarizing its main features through measures such as the mean (average), median (middle value), mode (most frequent value), variance (measure of variability), and standard deviation (average distance from the mean).

In our reading speed study, descriptive statistics would include the average reading speed for each group, as well as the spread and distribution of reading speeds among participants. While these statistics describe the sample, they don't by themselves allow us to make inferences about the population or determine the reliability of the results. Descriptive statistics are a first step in data analysis, providing a clear, concise summary before we move on to more complex inferences through hypothesis testing and confidence intervals.

Statistical Significance

The findings of a study become compelling when they achieve statistical significance. This concept indicates that the observed effects are unlikely to have occurred by chance alone. Statistical significance is often conveyed through a p-value, which quantifies the probability of observing results at least as extreme as those found if the null hypothesis were true. A commonly used threshold to denote significance is a p-value less than 0.05.

In our example, a p-value of less than 0.01 means there is less than a 1% probability that the observed difference in reading speed between print and Kindle is due to random chance. The term 'marginally significant' associated with a p-value of 0.06 means that while the results are suggestive, they do not reach the conventional threshold for statistical significance, and thus, are not as reliable. It's important to note that statistical significance does not imply practical importance and should be interpreted within the context of the study.