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# Psychological Statistics Exam 2

Chapters 4 through 6.
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Measures of central tendency are measures of...
location
With respect to other scores in a distribution, measures of central tendency...
are the points around which most of the scores are located
In order to decide which measure of central tendency is appropriate, you must first determine
the scale of measurement being used and the shape of the distribution
The mode is defined as
the most frequently occurring score
The mode is the appropriate measure of central tendency when the scale of measurement is
nominal
Which measure of central tendency should a researcher use to describe the sex of participants in a study?
mode
The median is defined as
the point at or below which 50% of the scores fall
Which measure of central tendency is appropriate if the shape of the distribution is severely skewed?
median
The median is the preferred measure of central tendency when
the scale of measurement is ordinal
Why si the median unaffected by extreme scores occurring in only one tail of the distribution?
Because the median doesn't take into account the actual values of all scores
Which measure of central tendency shiould an academic counselor use to describe a student's rank in his/her classes?
median
The mean is defined as
the mathematical center of the distribution
To obtain the mean, we would
add all the scores (sigma X) and divide by the total number of scores (N)
Which measure of central tendency is appropriate if the shape of the distribution is symmetrical and the measurement scale is interval or ratio?
mean
The mean is the preferred measure of central tendency when
the distribution is symmetical and the scale of measurement is interval or ratio
When a distribution's mode = median = mean, it is said to be
symmetrical
An experimenter investigated the ability to concentrate as a function of crowding. Concentration was measured as the amount of time it took the participant to complete a word puzzle. How should the experimenter summarize teh scores on the dependent variable?
Find the mean amount of time it took to solve the puzzle, if time scores are normally distributed.
In a skewed distribution, the mathematical center is
the mean, which is not the point around which most of the scores tend to be located
The mean is an inappropriate measure of central tendency when the distribution is severely skewed because
it does not accurately describe a skewed distribution
When a distribution's mode > median > mean, it is said to be
negatively skewed
When we refer to a score's deviation, we are referring to
how far it is from the mean
What happens to the mean of a distribution if every score is divided by 10?
It's value is divided by 10.
The mean si used most often in behavorial research because researchers tend to
measure variables that have interval or ratio scores, and the scores form approximately normal distributions.
A deviation score of -3 indicates that the raw score is
less than the mean
The sum of the deviations around the mean always equals
0
A score's deviation conveys two pieces of information about the score's location: the number indicates _____, and the sign indicates _____.
the score's distance from the mean, whether the score is greater or less than the mean
The best predictor of an individual score in a sample of scores is the
mean of the sample of the scores
When using the mean to predict scores, error is presented by
the deviation of a score from the mean
When the mean is used to predict the scores, a deviation (X - X bar) indicates
the difference between the X bar we predict and the score an individual actually gets
A deviation score is more informative than a raw score because it
gives the score's location relative to the mean
With respect to a graph of a frequency distribution, a positive deviation score
will be located to the right of the mean
Miu is the symbol for the
population mean
When it is impossible to obtain all the score in a population, the best estimate of the population mean is the
sample mean
The population mean is estimated by
calculating the mean of a random sample drawn from the population
When deciding which type of measure of central tendency is appropriate, we consider the scale of measurement used to measure the
dependent variable
A researcher has conducted an experiment in which the independent variable is room temperature. Two conditions (a hot room and a cold room) were used. The dependent variable was the length of time required to complete a jigsaw puzzle. What is the best way to state that there is a relationship?
The mean times to complete the puzzle are different for the two rooms.
In a graph of the relationship between the level of noise in an environment and the number of errors a person makes, the _____ is on the X axis and the ______ is on the Y axis.
level of noise, number of errors
When deciding which type of graph is appropriate, we consider the characteristics of the
independent variable
When we graph the results of an experiment, the Y axis indicates the
measure of central tendency we have used for the dependent variable
When we graph results from an experiment, a line graph is appropriate when
the independent variable is ratio or interval
On any graph a horizontal line of data points indicates that
the Y scores are not changing as the X scores change, and there is no relationship.
When we graph results from an experiment where the independent variable is on a nominal scale, which type of graph is appropriate?
bar graph
An experimenter investigated the abilitty to concentrate as a function of eye color. Which type of graph should the experimenter use to display the results?
bar graph
If you see the notation "Sigma X squared" you should
square all the Xs, then sum the squares
Measures of variability are used to
summarize and describe the extent to which scores in a distribution differ from one another
The term variability is most opposite to
consistency
Measures of central tendency indicate the _____ of a distribution while measures of variability indicate the _____ between the scores in a distribution
location, distance
The greater the variability in a set of scores,
the less accurately the scores are represented by one central score.
The range is the descriptive statistic that indicates the
distance between the two most extreme scores
The variance and standard deviation indicate how much the scores are spread out around
the mean
The average of the deviations can never actually be computed because
the sum of all deviations from the mean always equals zero
When computing the variance, why do we square the deviations from the mean?
to compensate for the fact that deviations about the mean always sum to zero
Variance is defined as the
average of the squared deviations around the mean
When all the scores in a set of data are the same, the variance is
0
If the variance for a sample is computed and it is found to be rather large, the numbers
are spread out around the mean
Standard deviation is defined as the square root of the
average of the squared deviations around the mean
The standard deviation is always
the square root of the variance
The standard deviation is a measure of how far scores deviate from
the mean
The variance can never be
a negative number
In roughly normal distributions, the standard deviation is approximately
one sixth of the range
Adding or subtracting a constant from each of the scores in a distribution
does not change the value of the standard deviation
Multiplying each of the scores in a distribution by a constant
multiplies the standard deviation by the same constant
Sample standard deviation and sample variance are considered biased estimates for the population standard deviation and variance because, over many calculations, they tend to be
underestimates
Sample standard deviation and sample variance are considered biased estimates for the population standard deviation and variance because
they reflect the random variability of only N - 1 scores
The quantity "N - 1" is known as the
degrees of freedom
Unbiased estimators of the population parameters will produce values that are _____ those produced the biased estimators of the sample statistics.
larger than
If we are going to predict future performance on the basis of a sample mean and the sample standard deviation, it is desirable to have a
small standard deviation
The proper way to describe errors of prediction is to compute
the variance
In the language of statistics, when we know that a relationship exists between two variables, we can use knowledge of that relationship to
account for the variance
The proportional improvement that resutls from using the relationship between two variables to predict scores compared with not using the relationship to predict scores is called
the proportion of variance accounted for.
Of the three kinds of variances, which uses N-! in the final division?
estimated population variance
The absolute value of a number is the
numeric magnitude of the number, regardless of whether is it positive or negative
An evaluation of where a score is located in relation to other scores in the distribution reflects its
relative standing
The z-score transformation is a useful statistical tool because it enables statisticians to
compare and interpret scores from virtually any distribution
z-scores can be calculated from
interval or ratio scores
z-scores communicate a score's
relative location in a distribution
When the standard deviation of a raw score distribution is large, the ocrresponding z-score distribution will be
Given any z-score, it is safe to say that the absolute value is a good indicator of ______ and the sign is a good indicator of _____.
distance, direction
A z-score of zero always means that
the raw score is equal to the mean
Given a normal distribution, as z-scores' absolute values increase, those z-scores and the raw scores that correspond to them occur
less frequently
The distribution of z-scores is always
the same as the distribution of raw scores
The mean of a z-score distribution is always _____, and the standard deviation is always _____.
0, 1
In a z-distribution, the standard deviation will always be
equal to 1
When two normal z-distributions are plotted on the same graph, what can we say about the relative frequency of each z-score?
It will always be the same.
The proportion of the total area under a normal curve between two z-scores corresponsd to the _____ of the range of scores.
relative frequency
A theoretically perfect normal curve, which serves as a model of the perfect normal z-distribution, is called the
standard normal curve
The relative frequency obtained from the standard normal curve is the _____ of the raw scores in our data, if the data formed a perfect normal distribution.
expected relative frequency
How accurately the standard normal curve model predicts the actual relative frequency of raw scores depends on three aspects of data:
1) the raw scores form an approximately normal distribution, 2) there is a large sample N, 3) the raw scores are theoretically continuous scores measured on an interval or ratio scale
We can use the standard normal curve as our model for
any approximately normal distribution, when transformed to z-scores
In sampling distributions, all the samples contain sets of raw scores
that are representative of the population mean
Which of the following statements accurately describes the sampling distribution of means?
The distribution of all possible sample means when an infinite number of samples of variously sized Ns are randonmly selected from several raw score populations.
As the N of the samples used in a sampling distribution _____, the sampling distribution becomes _____.
increases, more like a perfect normal curve
A sampling distribution is an approximately normal distribution
only when the shape of the raw score distribution is approximately normal
Sampling distributions of means are always
approximately normally distributed
The mean of the sampling distribution always equals
the mean of the underlying raw score population
According to the central limit theorem, the sampling distribution of means always approximates a _____ distribution.
normal
The mean of the sampling distribution always equals
the mean of the underlying raw score population.
The standard deviation of the sampling distribution of means is called the
standard error of the mean