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Final Exam Study Set (Ch. 9-15)
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Terms in this set (71)
sampling distribution of means
drawing a sample from a population and calculating the sample mean (x-bar), it will, on average be the same as the population mean (mew).
Central Limit Theorem
The theory that, as sample size increases, the distribution of sample means of size n, randomly selected, approaches a normal distribution.
standard error of the mean
the standard deviation of the sampling distribution of the mean
degrees of freedom
the number of values in a set of scores that are free to vary after certain restrictions are placed on the data
estimated standard error of the mean
an estimate of the standard deviation of the sampling distribution
t distribution
probability distribution of t scores, which are estimated z scores
confidence interval
the range of values within which a population parameter is estimated to lie
null hypothesis
the hypothesis that assumes a particular value for a population parameter
alternative hypothesis
the hypothesis that the value of a population parameter is something other that what we have assumed it to be
nondirectional hypothesis
states that the population parameter is not equal to the value specified by the null hypothesis
directional hypothesis
states that the direction of the difference between a population parameter and the value assumed by the null hypothesis
significant
indicating rejection of the null hypothesis
type 1 or alpha error
rejecting a true null hypothesis
type 2 error
failing to reject a false null hypothesis
power
probability that the inferential test will detect a false null hypothesis
effect size
difference between the null hypothesis and alternative hypothesis in standardized units
meta-analysis
procedure for analyzing research results from large numbers of studies using effect size
control group
in an experiment, the group not exposed to the treatment; contrasts with the experimental group and serves as a comparison for evaluating the effect of the treatment
independent samples
samples in which behavior of the members of one sample is not related to the behavior of the members of the other
sampling distribution of the mean differences
distribution whose scores are differences between pairs of sample means
standard error of the difference between means
standard deviation of the sampling distribution of the means differences
estimated standard error of the mean
estimated standard deviation of the sampling distribution of the differences
two-tailed test
significance test that considers both ends of the distribution
one-tailed test
significance test that considers only one end of the distribution
homogeneity of variance
condition in which population variances are the same
robustness
property of a statistical test to give valid conclusions even when assumptions of the test are violated
matched pairs
dependent samples in which subject pairs are as closely matched as possible on some characteristics relevant to the dependent variable
within-subjects comparisons
the same individuals are subjected to each of two treatment conditions; each subject is his or her own control
repeated measures design
experimental design in which each subject experiences all levels of the independent variable
counterbalancing
method to control for order effects in a repeated measures design by including all orders of treatment presentation
double-blind
referring to an experimental design in which neither that participant nor the treatment administrator knows the participant's group designation
Analysis of Variance (ANOVA)
parametric inferential technique designed to test for significant differences among two or more different groups
additivity
the property of variance that, for individual samples, the variance of a sum of parts is equal to the sum of the variances of the parts
total variability
variability in data based on the deviation between each score and the overall, or total, mean
within group variability
part of the ANOVA test based on the deviation between each score in a group and the group mean
individual differences
differences between participants in an experiment because of different participant backgrounds experiences, abilities, motives, and so on
experimental error
source of variability in data cause by such things as imprecise measuring equipment, momentary changes in experimenter and subject attention, and slight changes in background conditions during data collection
between-group variability
part of the ANOVA test based on the deviation between each group mean and the total mean
treatment effect
variability in data based on the deviation between each score and the overall, or total mean
total sum of squares
sum of the squared deviation of each score from the total mean in the analysis of variance
between groups sum of squares
based on the deviation between each group mean and the total mean
ANOVA summary table
the table used to summarize the results of an ANOVA test
mean square
the analyzed variance in the ANOVA test, found by dividing each sum of squares by the appropriate df
F ratio
ratio of the variability between groups to the variability within-groups, test statistic for the ANOVA test
post hoc test
"a posteriori tests" unplanned comparisons following a significant F-ratio
a priori tests
tests designed to look at specific hypotheses before the experiment is done
Fisher LSD (least significant difference) test
powerful post-ANOVA test that compares pairwise differences in means with a computed least significant difference (also called a protected t test)
two-way ANOVA
ANOVA technique used for analyzing data resulting from the administration of two or more levels of two independent variables
factors
designation for variables when there are two or more
factorial design
experimental design in which there are two or more variables
main effect
in a factorial experiment, the effect of each independent variable, considered by itself
interaction
joint effect of two independent variables
correlation
the degree of relationship between two or more variables
linear correlation
the degree to which a straight line best describes the relationship between two variables
positive correlation
A direct relationship between two variables in which an increase in one is related to an increase in the other, and a decrease in one is related to a decrease in the other.
scatterplot
a graph that plots pairs of scores, with the scores on one of the variables plotted on the x-axis and the scores on the other variable plotted on the y-axis
negative correlation
a high score on one variable is associated with a low score on the other
zero correlation
no relationship between two variables
Pearson r
mean of the z-score products for X and Y pairs
covariance
the extent to which two variables vary together
regression coefficient
the slope of the regression line
regression equation
the equation for the straight line that best describes the relationship between the variables
least square line
line generated by the regression equation
coefficient of determination
(r^2) amount of variability in one variable explained by variability in another
Spearman rank order correlation coefficient
(r sub s) non-parametric alternative to the Pearson r
point-biserial correlation
(r sub pbis) correlation useful when one variable is dichotomous (has only two values) and the other is continuous
phi coefficient
correlation used when both variables are dichotomous (have only two values)
parametric tests
tests (t, F) designed to test hypotheses about population parameters
Non-parametric tests
tests that do not test hypotheses about population parameters and do not assume any particular distribution
chi-square test
non-parametric test for nominal scale data
chi-square goodness-of-fit test
chi-square test on different levels of a single categorical variable
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Verified questions
STATISTICS
Sickle cell anemia is an inherited blood disease that occurs primarily in blacks. In the United States, about 15 of every 10,000 black children have sickle cell anemia. The red blood cells of an affected person are abnormal; the result is severe chronic anemia (inability to carry the required amount of oxygen), which causes headaches, shortness of breath, jaundice, increased risk of pneumococcal pneumonia and gallstones, and other severe problems. Sickle cell anemia occurs in children who inherit an abnormal type of hemoglobin, called hemoglobin S, from both parents. If hemoglobin S is inherited from only one parent, the person is said to have sickle cell trait and is generally free from symptoms. There is a 50% chance that a person who has sickle cell trait will pass hemoglobin S to an offspring. a. Obtain the probability that a child of two people who have sickle cell trait will have sickle cell anemia. b. If two people who have sickle cell trait have five children, determine the probability that at least one of the children will have sickle cell anemia. c. If two people who have sickle cell trait have five children, find the probability distribution of the number of those children who will have sickle cell anemia. d. Construct a probability histogram for the probability distribution in part (c). e. If two people who have sickle cell trait have five children, how many can they expect will have sickle cell anemia?
STATISTICS
A researcher studying violent behavior in elementary school children asks the children's parents how much time each child spend s playing computer games and has their teachers rate each child on the level of aggressiveness they display while playing with other children. Suppose that the researcher finds a moderately strong positive correlation. Describe three different possible cause-and-effect explanations for this relation ship.
PROBABILITY
A knock-out tournament is being held with 2n tennis players. This means that for each round, the winners move on to the next round and the losers are eliminated, until only one person remains. For example, if initially there are 24 = 16 players, then there are 8 games in the first round, then the 8 winners move on to round 2, then the 4 winners move on to round 3, then the 2 winners move on to round 4, the winner of which is declared the winner of the tournament. (There are various systems for determining who plays whom within a round, but these do not matter for this problem.) (a) How many rounds are there? (b) Count how many games in total are played, by adding up the numbers of games played in each round. (c) Count how many games in total are played, this time by directly thinking about it without doing almost any calculation. Hint: How many players need to be eliminated?
STATISTICS
The U.S. adult population by age is as follows (The World Almanac, 2009). The data are in millions of people. $$ \begin{matrix} \text{Age} & \text{Number}\\ \text{18 to 24} & \text{29.8}\\ \text{25 to 34} & \text{40}\\ \text{35 to 44} & \text{43.4}\\ \text{45 to 54} & \text{43.9}\\ \text{55 to 64} & \text{32.7}\\ \text{65 and over} & \text{37.8}\\ \end{matrix} $$ Assume that a person will be randomly chosen from this population. a. What is the probability the person is 18 to 24 years old? b. What is the probability the person is 18 to 34 years old? c. What is the probability the person is 45 or older?
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