Experimental Designs Flashcards
determines the way sample is selected
experimental design/sampling plan
in an ___ study, the experimenter observes the data that already exists
observational
plan for collecting data in an observational study
sampling pl
in a ____ experiment, the experimenter imposes one or more experimental conditions on the experimental units and records the response
designed experiment
is the object on which a measurement or measurements) is taken.
experimental unit
is an independent variable whose values are controlled and varied by the experimenter.
factor
is the intensity setting of a factor.
level
is a specific combination of factor levels.
treatment
is the variable being measured by the experimenter.
response
A group of people is randomly divided into an experimental and a control group. The control group is given an aptitude test after having eaten a full breakfast. The experimental group is given the same test without having eaten any breakfast.
what is the experimental unit
person
A group of people is randomly divided into an experimental and a control group. The control group is given an aptitude test after having eaten a full breakfast. The experimental group is given the same test without having eaten any breakfast.
what is the response
score on test
A group of people is randomly divided into an experimental and a control group. The control group is given an aptitude test after having eaten a full breakfast. The experimental group is given the same test without having eaten any breakfast.
what is the treatment
breakfast or no breakfast
A group of people is randomly divided into an experimental and a control group. The control group is given an aptitude test after having eaten a full breakfast. The experimental group is given the same test without having eaten any breakfast.
what is the factor
meal
A group of people is randomly divided into an experimental and a control group. The control group is given an aptitude test after having eaten a full breakfast. The experimental group is given the same test without having eaten any breakfast.
what is the levels
breakfast or no breakfast
A group of people is randomly divided into an experimental and a control group. The control group is given an aptitude test after having eaten a full breakfast. The experimental group is given the same test without having eaten any breakfast.
The experimenter in the previous example also records the person’s gender. Describe the factors, levels and treatments.
what is the factor #1
meal
A group of people is randomly divided into an experimental and a control group. The control group is given an aptitude test after having eaten a full breakfast. The experimental group is given the same test without having eaten any breakfast.
The experimenter in the previous example also records the person’s gender. Describe the factors, levels and treatments.
what is factor #2
gender
A group of people is randomly divided into an experimental and a control group. The control group is given an aptitude test after having eaten a full breakfast. The experimental group is given the same test without having eaten any breakfast.
The experimenter in the previous example also records the person’s gender. Describe the factors, levels and treatments.
what is levels of factor #1
breakfast or no breakfast
A group of people is randomly divided into an experimental and a control group. The control group is given an aptitude test after having eaten a full breakfast. The experimental group is given the same test without having eaten any breakfast.
The experimenter in the previous example also records the person’s gender. Describe the factors, levels and treatments.
what is levels of factor #2
male or female
A group of people is randomly divided into an experimental and a control group. The control group is given an aptitude test after having eaten a full breakfast. The experimental group is given the same test without having eaten any breakfast.
The experimenter in the previous example also records the person’s gender. Describe the factors, levels and treatments.
what are the treatments
male and breakfast
female and breakfast
male and no breakfast
female and no breakfast
in ANOVA, All measurements exhibit ____
variability
The total variation in the response measurements is broken into portions that can be attributed to various factors.
ANOVA
assumption of ANOVA
The observations within each population are normally distributed with a common variance σ^2
Assumptions regarding the sampling procedures are specified for each design
procedures are fairly robust when sample sizes are equal and when the data are fairly mound-shaped.
analysis of variance
three designs of experimental
completely randomized design
randomized block design
axb factorial experiment
an extension of the two independent sample t-test.
completely randomized design
an extension of the paired difference test.
randomized block design
we study two experimental factors and their effect on the response.
axb factorial experiment
A one-way classification in which one factor is set at k different levels
completely randomized design
The k levels correspond to k different normal populations, which are the ___
treatments
Is the attention span of children
affected by whether or not they had a good breakfast? Twelve children were randomly divided into three groups and assigned to a different meal plan. The response was attention span in minutes during the morning reading time.
What is the null and alternative hypothesis
Ho: There is no significant difference between the average attention span based on breakfast type
Ha: There is a significant difference between the attention span based on breakfast type
why is it CRD
randomly assigned samples were placed into groups
total sum of squares is divided into two parts
sum of squares for treatments
sum of squares for errors
measures the variation among the k sample means.
sum of square for treatments
measures the variation within the k samples.
in such a way that:
sum of squares for error
F value is rejected when it is ___ than the f-critical value
greater
Is the attention span of children
affected by whether or not they had a good breakfast? Twelve children were randomly divided into three groups and assigned to a different meal plan. The response was attention span in minutes during the morning reading time.
F value is 5.00
F crit = 4.26
what is the decision
reject Ho
identify which of the three averages is the source of difference
Post-Hoc test
Designed to test all pairs of population means simultaneously, with an overall error rate of a.
Tukey’s Method for Paired Comparisons
Tukey’s Post Hoc test Assume that the sample sizes are ___and calculate a “ruler” that measures the distance required between any pair of means to declare a significant difference.
equal
Is the attention span of children
affected by whether or not they had a good breakfast? Twelve children were randomly divided into three groups and assigned to a different meal plan. The response was attention span in minutes during the morning reading time.
Tukey
Full Light = 0.693
Full No = 0.120
Light No = 0.033
interpret
Light breakfast has the significant difference between No breakfast
A direct extension of the paired difference or matched pairs design.
randomized block design
A two-way classification in which k treatment means are compared
randomized block design
The design uses blocks of k experimental units that are relatively similar or homogeneous, with one unit within each block randomly assigned to each treatment.
randomized block design
total number of observations in RBD
n = bk
two factors in rbd
treatments
blocks
if 3 treatments, and 3 locations are there (block) what is the total number of observations
9
we want to investigate the effect of 3 methods of soil preparation on the growth of seedlings. Each method is applied to seedlings growing at each of 4 locations and the average first year growth is located
what is the Ho and Ha
H0: No difference in average growth among soil preparation methods.
H1: There is a difference in average growth among soil preparation methods.
we want to investigate the effect of 3 methods of soil preparation on the growth of seedlings. Each method is applied to seedlings growing at each of 4 locations and the average first year growth is located
what is the treatment and block
soil prep - treatment
location - block
ANOVA for RBD is divided into three
sum of squares for treatments
sum of squares for blocks
sum of squares for error
A randomized block design should not be used when treatments and blocks ___ correspond to experimental factors of interest to the researcher
both
Remember that blocking may not always be ___.
beneficial
Remember that you cannot construct ___intervals for individual treatment means unless it is reasonable to assume that the b blocks have been randomly selected from a population of blocks.
confidence
A two-way classification in which involves two factors, both of which are of interest to the experimenter.
axb factorial experiment
The replications allow the experimenter to investigate the interaction between factors A and B
a x b factorial experiment
Interaction describes the effect of one factor on the behavior of the other. If there is no interaction, the two factors behave ___.
independently
A drug manufacturer has two
supervisors who work at each of three different shift times. Do outputs of the supervisors behave differently, depending on the particular shift they are working?
what is Ho and Ha
H0: There is no significant interaction between the supervisor and the shift
H1: There is no significant interaction between the supervisor and the shift
analysis of variance SS for axb is divided into four
sum of squares for factor a
sum of squares for factor b
sum of squares for interaction
sum of squares for error
Once Ho is rejected in interaction, is there a need to look at p values of factor a and b?
no
