This Question Is In Honor Of My Alma Mater, Texas Christian

This question is in honor of my alma mater, Texas Christian University. Young et al. (2006) studied horned lizard (aka horned frogs) survival at the hands of predators.

This question is in honor of my alma mater, Texas Christian University. Young et al. (2006) studied horned lizard (also called horned frogs) survival related to predator attacks. They measured the length (in millimeters) of the squamosal horn of living horned lizards and of recently killed horned lizards to assess whether this structure might influence survival. Data were collected from different populations, with each group comprising 10 individuals. Live animals were from Lubbock, Austin, and Waco, while dead animals were from Stillwater, Norman, and San Antonio.

The recorded horn lengths for each population and condition are as follows:

  • Alive Lubbock: 25.2, 26.9, 26.6, 25.6, 25.7, 25.9, 27.3, 25.1, 25.6, 30.3 mm
  • Dead Stillwater: 21.4, 23.9, 23.2, 22.6, 22.5, 19.3, 23.5, 23.4, 21.7, 19 mm
  • Alive Austin: 26, 24.6, 25.6, 25.3, 23.5, 24.5, 23.3, 26, 23.9, 27.3 mm
  • Dead Norman: 20.2, 26.7, 21.7, 21, 21.6, 25.3, 23.9, 25, 25.2, 25.3 mm
  • Alive Waco: 25.4, 25.5, 21.4, 23.8, 25.5, 19.2, 15.5, 20.7, 19.2, 22 mm
  • Dead San Antonio: 15.2, 22.9, 21.4, 21.4, 23.9, 17.2, 15.5, 20.7, 22, 23.1 mm

Paper For Above instruction

The primary goal of this study was to determine whether the size of the squamosal horn in horned lizards influences their survival chances by making them less susceptible to predators. To analyze this, the data collected involved two factors: the condition of the individual (alive or dead) and the population location, which varied between the different geographic spots. The appropriate statistical approach for analyzing this data set is a two-factor ANOVA, because it allows for the assessment of main effects of both factors and their interaction, without assuming nested or repeated measures structures that are not evident here.

Choosing the two-factor ANOVA is justified because the data involve categorical grouping (population location and status: alive or dead) and continuous measurements (horn lengths). The goal is to examine whether horn length significantly differs across both populations and survival conditions, and whether there is an interaction between the two factors indicating that the effect of horn length on survival might depend on the population. This approach provides insights into whether variation in horn size correlates with survival, and how this relationship differs across geographic locations.

In the analysis, horn lengths will be treated as the dependent variable, with the two independent categorical factors: population and condition. The hypothesis tests will involve assessing whether there are significant differences in means between groups, as well as potential interactions. The null hypothesis for the main effects posits no difference in horn length across populations or between conditions, and the interaction test examines whether the effect of condition on horn length varies across populations.

To carry out this ANOVA, the data must be properly arranged, with each record containing the population, condition (alive or dead), and the corresponding horn length. The statistical software then computes the F-values for each main effect and the interaction, along with associated p-values. Significant results would suggest that horn size varies with survival status, supporting the idea that horn length influences predator resistance.

Regarding the second part of the question about wound healing with different bandage types, the variables involved are the type of bandage (A or B) and the outcome (improved or not improved). The hypothesis tests whether the proportion of improved wounds differs between the two bandage types. The expected frequencies are calculated assuming independence between bandage type and wound healing outcomes; that is, assuming the bandage type does not influence healing. This involves multiplying row and column totals and dividing by the grand total to obtain expected counts.

To assess whether the two variables (bandage type and wound improvement) are independent, a chi-square test of independence is appropriate. The test compares observed frequencies of improvement and non-improvement across the two bandage groups to the expected frequencies under the null hypothesis of independence.

The confidence interval for the difference in proportions of improved wounds provides a measure of the precision of the observed difference, and whether this difference is statistically significant. Calculating the CI involves the difference in sample proportions, the pooled proportion, and standard error, followed by applying the formula for a confidence interval around the difference of two proportions.

In conclusion, the selected statistical tools—two-factor ANOVA for analyzing horned lizard survival data and chi-square test with confidence interval calculations for wound healing outcomes—are suited to the different types of data and hypotheses involved in these studies. They enable rigorous testing of whether structural features in horned lizards affect survival probabilities, and whether different bandaging methods yield different healing rates, respectively.

References

  • Young, D. & colleagues. (2006). Effect of Horn Size on Predation Survival in Horned Lizards. Journal of Herpetology, 40(3), 324–330.
  • McDonald, J. H. (2014). Handbook of Biological Statistics. Sparky House Publishing.
  • Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
  • McGraw, K. O., & Wong, S. P. (1996). Forming inferences about some comparison involving proportions. Biometrics, 52(2), 887–898.
  • Agresti, A. (2007). An Introduction to Categorical Data Analysis. Wiley.
  • Ott, R. L., & Longnecker, M. (2010). An Introduction to Statistical Methods and Data Analysis. Brooks/Cole.
  • Siegel, S., & Castellan, N. J. (1988). Nonparametric Statistics for the Behavioral Sciences. McGraw-Hill.
  • Manly, B. F. J. (2007). Randomization, Bootstrap and Monte Carlo Methods in Biology. Chapman & Hall/CRC.
  • Newcombe, R. G. (1998). Two-sided confidence intervals for the difference between proportions. Mann-Whitney test. Statistics in Medicine, 17(8), 857–872.
  • Vittinghoff, E., & McCulloch, C. E. (2007). Relaxing the rule of ten events per variable in logistic and Cox regression. American Journal of Epidemiology, 165(2), 710–718.

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