Question

Data 4.1 introduces a study in mice showing that even low-level light at night can interfere with normal eating and sleeping cycles. In the full study, mice were randomly assigned to live in one of three light conditions: LD had a standard light/dark cycle, LL had bright light all the time, and DM had dim light when there normally would have been darkness. Exercises 8.28 to 8.34 in Section 8.1 show that the groups had significantly different weight gain and time of calorie consumption. In Exercises 8.55 and \(8.56,\) we revisit these significant differences. When Calories Are Consumed Researchers hypothesized that the increased weight gain seen in mice with light at night might be caused by when the mice are eating. Computer output for the percentage of food consumed during the day (when mice would normally be sleeping) for each of the three light conditions is shown, along with the relevant ANOVA output. Which light conditions give significantly different mean percentage of calories consumed during the day? \(\begin{array}{lrrr}\text { Level } & \text { N } & \text { Mean } & \text { StDev } \\ \text { DM } & 10 & 55.516 & 10.881 \\ \text { LD } & 9 & 36.485 & 7.978 \\ \text { LL } & 9 & 76.573 & 9.646\end{array}\) One-way ANOVA: Day/night consumption versus Light \(\begin{array}{lrrrrr}\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\ \text { Light } & 2 & 7238.4 & 3619.2 & 39.01 & 0.000 \\ \text { Error } & 25 & 2319.3 & 92.8 & & \\ \text { Total } & 27 & 9557.7 & & & \end{array}\)

Short answer

Based on the given ANOVA table, we can conclude that there are significant differences in the mean percentages of calories consumed during the day under the different light conditions.

Step-by-step solution

Understanding the Data

The data provides the mean percentage of calories consumed during the day by mice under three different light conditions. Each condition was conducted with a different number of mice (N) and the standard deviation (StDev) is provided for each condition. We will be looking at the Result of ANOVA test where the F-value and P-value play a crucial role in decision making.

Determine Significance with F value

In the one-way ANOVA table, look at the row labeled 'Light'. This row shows F = 39.01. This is the F-statistic, a test statistic for ANOVA. An F value significantly greater than 1 suggests there are significant differences in calorie consumption among the groups.

Verify Significance with P value

A significant F-statistic is not enough to establish significant differences among the groups. It must be performed along with the P-value, which in this case is 0.000, far less than the threshold level 0.05. This confirms that there are significant differences in calorie consumption among the groups.

Making Conclusion

As both the F-statistics value is significantly higher than 1 and P-value is lower than threshold value of 0.05, we can conclude that all the light conditions provide significantly different mean percentages of calories consumed during the day. It is important to note that this doesn't tell us which specific groups are significantly different, just that at least one group is different.

Key concepts

One-Way ANOVA

Understanding the one-way ANOVA is essential for analyzing experiments with three or more groups. It is a statistical method used to compare the means of three or more samples to find out if at least one sample mean is significantly different from the others. When studying the effect of different conditions—such as light exposure—on calorie consumption patterns in mice, the one-way ANOVA assists in determining whether the changes observed are due to the experimental manipulation or simply by chance.

It's computed by analyzing the variance (a measure of spread) within each group and comparing it to the variance between the groups. The F-statistic is calculated as a ratio of these variances and is used to generate a p-value. This p-value serves as a tool to assess whether observed differences in means across groups could plausibly have arisen by chance.

Calorie Consumption Patterns

A fundamental aspect of nutritional studies and related experiments is understanding calorie consumption patterns. These patterns can reveal how different environmental factors, such as light exposure, influence the eating behavior of organisms. When data reflects the percentage of calories consumed during typical rest periods (like daytime for nocturnal animals such as mice), it could suggest disruptions in normal behavioral patterns.

Investigating these patterns can help in assessing metabolic health or the effects of environmental disruptions on circadian rhythms. The light condition experiment with mice clearly demonstrates varying calorie consumption patterns, indicating potential alterations in their natural behavior.

Light Exposure Effects

Light plays a crucial role in regulating biological processes in many organisms, especially those with defined circadian rhythms. The effects of light exposure on behavior and physiology have been widely studied across species. For nocturnal creatures, such as the mice in the exercise, unexpected light exposure could lead to atypical behavior, such as increased calorie consumption during the day.

Understanding these effects is vital, not only for animal welfare but also for human health research, as it provides insights into possible disruptions of natural patterns due to artificial lighting.

Statistical Significance

Statistical significance is a determination used to decide if the results of a study are likely to be true and not due to random chance. This concept is central to hypothesis testing where researchers aim to ascertain whether a particular variable has a meaningful effect. In the context of the exercise, when the p-value obtained from the ANOVA is lower than the commonly accepted threshold (usually 0.05), it indicates a statistically significant result.

Statistical significance does not measure the magnitude of an effect but rather whether an effect is likely to be present at all. This distinction is critical when interpreting results and drawing conclusions from data.

F-Statistic

The F-statistic is the ratio of the variance calculated between the group means to the variance within the groups. A higher F-statistic implies that there is more variance between the groups than within them, which suggests that the group means are not all the same. In the given exercise, an F-value of 39.01 is significantly greater than 1, implying that the observed differences in calorie consumption are likely not due to random variations within groups but rather due to the different light conditions imposed on the groups.

However, it is worth noting that while an F-statistic provides evidence of differences, it does not pinpoint which specific means are different—that's a task for post-hoc testing (such as a Tukey test).

P-Value

The p-value is a probability that measures the evidence against the null hypothesis—the assumption that there's no effect or no difference. In essence, it answers the question 'If there were no actual difference, how likely would we be to observe data at least as extreme as what we've got?' The smaller the p-value, the stronger the evidence against the null hypothesis. A p-value of 0.000 in the exercise indicates that there is extremely strong evidence against the null hypothesis and that the differences in mean percentage of calories consumed are indeed statistically significant.