Often the basic assumptions of the ANOVA for an experimental design are not met or the statistical model is incorrectly specified. Randomization of treatments to experimental units is expected to protect against such shortcomings. This paper uses randomization theory to examine the impact on the expectations of mean squares, treatment means, and treatment differences for two model mis·specifications: Systematic response shifts and correlated experimental units. Systematic response shifts are presented in the context of the randomized complete block design (RCBD). In particular fixed shifts are added to the responses of experimental units in the initial and final positions of each block. The fixed shifts are called border shifts. It is shown that the RCBD is an unbiased design under randomization theory when border shifts are present. Treatment means are biased but treatment differences are unbiased. However the estimate of error is biased upwards and the power of the F test is reduced. Alternative designs to the RCBD under border shifts are the Latin square, semi-Latin square, and two-column designs. Randomization analysis demonstrates that the Latin square is an unbiased design with an unbiased estimate of error and of treatment differences. The semi-Latin square has each of the t treatments occurring only once per row and column, but t is a multiple of the number of rows or columns. Thus each row-column combination contains more than one experimental unit. The semi-Latin square is a biased design with a biased estimate of error even when no border shifts are present. Row-column interaction is responsible for the bias. Border shifts do not contaminate the expected mean squares or treatment differences, and thus the semi-Latin square is a viable alternative when the border shift overwhelms the row-column interaction. The two columns of the two-column design correspond to the border and interior experimental units respectively. Results similar to that for the semi-Latin square are obtained. Simulation studies for the RCBD and its alternatives indicate that the power of the F test is reduced for the RCBD when border shifts are present. When no row-column interaction is present, the semi-Latin square and two-column designs provide good alternatives to the RCBD. Similar results are found for the split plot design when border shifts occur in the sub plots. A main effects plan is presented for situations when the number of whole plot units equals the number of sub plot units per whole plot. The analysis of designs in which the experimental units occur in a sequence and exhibit correlation is considered next. The Williams Type Il(a) design is examined in conjunction with the usual ANOVA and with the method of first differencing. Expected mean squares, treatment means, and treatment differences are obtained under randomization theory for each analysis. When only adjacent experimental units have non negligible correlation, the Type Il(a) design provides an unbiased error estimate for the usual ANOVA. However the expectation of the treatment mean square is biased downwards for a positive correlation. First differencing results in a biased test and a biased error estimate. The test is approximately unbiased if the correlation between units is close to a half. / Ph. D.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Photometric techniques are often used to observe stars and it can be demonstrated that fundamental stellar properties can be observationally determined using calibrated sets of photometric data. Many of the most powerful techniques utilized to calibrate stellar photometry employ the use of stars in clusters since the individual stars are believed to have many common properties such as age, composition, and approximate distance. Broadband photometric Johnson/Cousins BVRI observations are presented for several nearby open clusters. The new photometry has been tested for consistency relative to archival work and shown to be both accurate and precise. The careful use of a regular routine when making photometric observations, along with the monitoring of instrumental systems and the use of various quality control techniques when making observations or performing data reductions, will enhance an observer's ability to produce high-quality photometric measurements. This work contains a condensed review of the history of photometry, along with a brief description of several popular photometric systems that are often utilized in the field of stellar astrophysics. Publications written by Taylor or produced during the early Taylor and Joner collaboration are deemed especially relevant to the current work. A synopsis of seven archival publications is offered, along with a review of notable reports of VRI photometric observations for the nearby Hyades open star cluster. The body of this present work consists of four publications that appeared between the years 2005 and 2008, along with a soon to be submitted manuscript for a fifth publication. Each of these papers deals specifically with high-quality broadband photometry of open clusters with new data being presented for the Hyades, Coma, NGC 752, Praesepe, and M67. It is concluded that the VRI photometry produced during the Taylor and Joner collaborative investigations forms a high-quality data set that has been: 1) stable for a period of more than 25 years; 2) monitored and tested several times for consistency relative to the broadband Cousins system, and 3) shown to have well-understood transformations to other versions of broadband photometric systems. Further work is suggested for: 1) the transformation relationships for the reddest stars available for use as standards; 2) the standardization of more fields for use with CCD detectors; 3) a further investigation of transformations of blue color indices for observations done using CCD detectors with enhanced UV sensitivity, and 4) a continuation of work on methods to produce high-quality observations of assorted star clusters (both open and globular) with CCD-based instrumentation and intermediate-band photometric systems.

In this work, the efficiency of the LUMBA UVES pipeline for processing of spectroscopic observations is tested by use on 23 high-resolution spectra of the open star cluster M67. An abundance trend discovered by Gavel et al. (2019) concerning iron abundances of giant and sub-giant stars of that cluster is examined. An initial run for a set of ”Gaia FGK benchmark stars”, as described in Blanco-Cuaresma et al. (2014) and Heiter et al. (2015) helps inspect the structure, method and output of the pipeline. Through Python language programming, processes are greatly automatized and the pipeline is run for a total of 460 weak and strong iron lines of our 23-star sample. The line fitting and efficiency of the pipeline is appreciated by statistically analyzing the results and looking into individual discrepant ones. The abundance trend is reproduced while using FeI lines, unlike runs using FeII lines. Trends in abundance over line strength plots also hint at bias through the Gaia-Eso Survey (GES) microturbulence relation. Using internal Data Release 6 (iDR6) and LUMBA-derived starting parameters, log(g) - Teff plots of our sample stars agree with a previously established 4.3 Gyr cluster age. An alternate run is performed for those stars, using LUMBA-derived starting parameters. The choice of starting parameters does impact abundance derivation, but is not the primary source of persistent systematic discrepancies.