Birth Weights Data Set 6 “Births” includes birth weights (g), hospitals, and the day of the week that mothers were admitted to the hospital. Using rows to represent the four hospitals (Albany Medical Center, Bellevue Hospital Center, Olean General Hospital, Strong Memorial Hospital), and using columns to represent the seven different days of the week, a two-way table has 28 individual cells. Using five birth weights for each of those 28 cells and using StatCrunch for two-way analysis of variance, we get the results displayed below. What do you conclude?

Verified step by step guidance

1. Step 1: Understand the setup of the two-way ANOVA. Here, we have two factors: Hospital (with 4 levels) and Day (with 7 levels), and their interaction. The goal is to determine if there are significant differences in birth weights based on these factors and their interaction.
2. Step 2: Examine the ANOVA table components. The table provides degrees of freedom (DF), sum of squares (SS), mean squares (MS), F-statistics, and p-values for each source of variation: Hospital, Day, Interaction, and Error.
3. Step 3: Interpret the p-values for each factor and their interaction. The p-value indicates the probability of observing the data if the null hypothesis (no effect) is true. Typically, a p-value less than 0.05 suggests a statistically significant effect.
4. Step 4: Compare the p-values for Hospital (0.7857), Day (0.5426), and Interaction (0.6413) to the significance level (usually 0.05). Since all p-values are greater than 0.05, we fail to reject the null hypotheses for all factors, indicating no significant differences in birth weights due to hospital, day, or their interaction.
5. Step 5: Conclude that based on this two-way ANOVA, there is no sufficient evidence to say that birth weights differ by hospital, day of the week, or the interaction between hospital and day.

Key Concepts

Two-Way ANOVA

Two-way ANOVA is a statistical method used to examine the effect of two categorical independent variables on a continuous dependent variable. It also tests for interaction effects between the two factors, helping to understand if the effect of one factor depends on the level of the other.

F-Statistic and P-Value

The F-statistic measures the ratio of variance explained by a factor to the unexplained variance (error). The p-value indicates the probability that the observed F-statistic would occur if the null hypothesis were true. A small p-value (typically < 0.05) suggests a significant effect.

Interaction Effect

An interaction effect occurs when the impact of one independent variable on the dependent variable changes depending on the level of the other independent variable. Detecting interaction is crucial because it indicates that the factors do not operate independently.