Statistics Lecture 6: Treatment Means Comparison

Comparing specific treatments to each other in a pre-planned manner.

Comparing all possible pairs of treatment means.

Declaring a significant difference when one doesn't exist.

Appropriate for planned comparisons, but risk of experiment-wise error increases with more comparisons.

LSD computed only if null hypothesis (Ho) is rejected.

A formula used to calculate the statistical significance of differences between treatment groups in an experiment.

A type of contrast where the sum of the products of the corresponding coefficients of any two comparisons is zero. This ensures that the contrasts are independent of each other.

A comparison of the effectiveness of fungicides containing mercury (Hg) against those without mercury.

A measure of the statistical significance of a contrast test, indicating the probability of observing the difference between groups by chance alone.

Deciding that the observed differences between groups are statistically significant and not likely due to chance.

The number of degrees of freedom associated with a specific comparison between two groups, usually 1 for a simple contrast.

A type of contrast that examines the overall trend or pattern in the data across multiple treatment levels.

A desirable property of contrasts where the information gained from one comparison is independent of the others.

When contrasts are not orthogonal, meaning they provide overlapping information.

The number of possible orthogonal contrasts is equal to the number of treatment levels minus one.

They ensure that the information obtained from each contrast is independent and does not overlap with other contrasts.

They allow researchers to examine the overall trend or pattern in the data across multiple treatment levels, providing insights into the response curve.

Equations that represent relationships between independent variables and their powers (linear, quadratic, cubic, etc.).

A straight line relationship between variables. Change in one variable directly affects the other.

A curved relationship between variables. The effect of one variable on another is not constant.

A relationship between variables that creates an S-shaped curve. One variable changes at an increasing rate, then slows down.

An analysis of variance (ANOVA) used to test different powers of a variable's effect on another variable.

A test comparing the effect of the independent variable's linear component on the dependent variable

A test comparing the effect of the independent variable's quadratic component on the dependent variable

A test comparing the effect of the independent variable's cubic component on the dependent variable

The influence of different row spacing distances on the yield of a crop, like soybeans.

A way to analyze the relationship between row spacing and yield using a mathematical equation.

A statistical test used to determine if there are significant differences in yield between different row spacing treatments.

An experimental design that helps control for variability in the field by dividing it into blocks.

The first step in analyzing the row spacing experiment is to perform ANOVA to identify any significant differences in yield between the different row spacings.

Based on the ANOVA results, we can then determine if the yield differences between the row spacings are statistically significant.

Investigate whether wider row spacing leads to higher or lower yield compared to narrower row spacing.

Predicting the yield of soybeans given the row spacing treatments.

A measure of variability explained by a particular contrast, representing the amount of variation in response attributable to the specific trend captured by the contrast.

An analysis of variance (ANOVA) table that incorporates polynomial contrasts, allowing for a more detailed understanding of treatment effects beyond just significance testing. It provides information about the nature of treatment effects and their specific trends.

A comparison of the linear and quadratic components of treatment effects, allowing for a deeper understanding of how the response variable changes with increasing treatment level. It helps identify if the trend is primarily linear, curved, or a combination of both.