Stats 1midterm Flashcards
Get an A (139 cards)
1
Q
Define variables, values, and scores.
A
Variables- physical/abstract attributes/quantities to measure
value- variables’ specific values
score- value that an individual has on a particular variable.
2
Q
What is a quantitative variable?
A
values that are numbers
natural ordering
3
Q
What is a qualitative variable?
A
qualities or categories
no natural ordering
4
Q
difference between discrete and continuous variables?
A
DV-fixed values.
CV-real numbers.
5
Q
relationship between equal interval scales and units of measurement.
A
Equal interval scales have units of measurement
6
Q
Define a ratio scale.
A
equal interval scales that have an absolute zero.
relative distances from 0.
7
Q
how an ordinal variable shares characteristics with qualitative and quantitative
A
qualitative and discrete, like qualitative variables
natural ordering, like quantitative variables.
8
Q
What is a psychological construct?
A
concept cannot be measured directly with a physical measuring device.
9
Q
What is an operational measure?
A
operational measure is a tool used to measure a psychological construct
10
Q
What does measurement error refer to?
A
each time something is measured, a slightly different score (measure) will be obtained.
11
Q
What does it mean to say that a measuring device is reliable and valid?
A
reliable measuring device gives very similar (if not identical) measurements each time
valid if it measures what it is supposed to measure.
12
Q
Define population, sample, parameter, and statistic
A
population comprises the scores of individuals
sample is any subset of a population.
parameter is a numerical characteristic of a population
statistic is a numerical characteristic of a sample.
13
Q
Give an example of inferential statistics.
A
Estimating the mean weight of all bluefin tuna in the Mediterranean Ocean from a random sample of all bluefin tuna in the Mediterranean Ocean
14
Q
What is sampling bias and sampling error?
A
bias means that not all members of the population had an equal chance
error is the difference between a statistic and the parameter it estimates. Sampling error cannot be avoided; it is an inevitable feature of random samplin
15
Q
What is a convenience sample?
A
sample that is conveniently available. It is the most common type of sampling bias.
16
Q
T/F: All variables whose values are numbers are quantitative variables.
A
False. Ordinal variables are qualitative but can have numbers as values.
17
Q
T/F: Eye color is an ordinal variable.
A
False. There is no natural ordering to eye color.
18
Q
T/F: A questionnaire allows the responses strongly disagree, disagree, neither agree nor disagree, agree, and strongly agree. Therefore, this variable is associated with an equal interval scale.
A
False. This is an ordinal variable with no units of measurement.
19
Q
T/F: If a scale has units of measurement, then it is an equal interval scale.
A
True
20
Q
T/F: Determination is a psychological construct.
A
True
21
Q
T/F: Measurement error is inevitable.
A
True
22
Q
T/F: The Celsius scale is a ratio scale
A
False. 0° Celsius does not mean the absence of heat.
23
Q
T/F: Time to solve a sudoku puzzle is a valid measure of intelligence.
A
False. One could be highly intelligent but not know the rules of sudoku.
24
Q
T/F: Estimating the average monthly income of Australians from a random sample of monthly incomes of Australians is an instance of inferential statistics.
A
True
25
T/F: Simple random sampling is essential for valid inferences from samples to populations.
True
26
T/F: Simple random sampling is essential for valid inferences from samples to populations.
True
27
T/F:A statistic is computed from all scores in a population
False. A parameter is computed from all scores in a population.
28
T/F:A convenience sample is an instance of sampling error.
False. This is an example of sampling bias.
29
T/F:The worms living in a backyard in Cleveland, Ohio, represent a sample of all worms living in North America.
True
30
T/F:A parameter is a numerical characteristic of a sample.
False. A parameter is a numerical characteristic of a population.
31
T/F:The average annual income of working Britons is £26,000, but the average annual income in a random sample of working Britons is only £23,000. This is an example of sampling bias.
False. This is an example of sampling error.
32
T/F:Measurement error is more like sampling error than sampling bias.
True
33
T/F:A jar contains 100 black beans and 100 white beans. A handful of beans drawn from this jar has 15 black beans and 19 white beans. This illustrates sampling error.
True
34
T/F:The worms living in a backyard in Charleston, South Carolina, represent a random sample of all worms living in North America.
False. This is a biased sample because not all members of the population had an equal chance of being part of the sample.
35
What is a frequency table?
a depiction of the number, or proportion of scores in a sample or population having each value--or range of values--of a variable.
36
What are raw frequency counts (or tallies)?
A raw frequency count (or tally) is the number of scores having a particular value, or falling within a range of values, for a given variable.
37
How are relative frequencies different from raw frequencies?
A relative frequency is the proportion of scores (as opposed to the number of scores) having a particular value, or falling within a range of values, for a given variable.
38
What is a bar graph and how does it differ from a histogram?
A bar graph is a graphical depiction of the information in a frequency table for a QUALITATIVE variable. Each value of the variable is represented by a bar, and the height of each bar represents the number or proportion of scores having that value of the variable. A histogram is a graphical depiction of the information in a frequency table for a QUANTITATIVE variable. Each value of the variable (or interval) is represented by a bar, and the height of each bar represents the number or proportion of scores having that value of the variable, or falling in the given interval. The bars in a bar graph DO NOT touch, whereas they do in a histogram.
39
What is the difference between relative frequency and cumulative relative frequency?
Relative frequency is the proportion of scores having some value or falling within a given interval. Cumulative relative frequency is the proportion of scores at or below a given value or interval of a quantitative variable.
40
Explain why the concept of an interval does not pertain to qualitative variables.
Because there is no natural ordering to qualitative variables, it is not possible to combine them into meaningful intervals.
41
whatare real limits
The real limits of an interval are the minimum and maximum real values that define the interval. The real limits are defined as midpoint ± width/2.
42
What are the score limits of an interval?
The score limits of an interval are the minimum and maximum whole values of the units of measurement that define the interval.
43
What is a sampling experiment?
A sampling experiment is the random selection of one of the possible values of a variable.
44
What is the outcome of a sampling experiment?
The outcome of a sampling experiment is the value of the variable that was selected.
45
Is an event different from an outcome? Explain.
An outcome is a single value of a variable, whereas an event may involve many values of a variable. For example, an event might be “drawing an Ace or a Queen,” whereas the Ace of Hearts is an outcome.
46
How does a proportion relate to probability?
The probability of an event is the proportion of times the event would occur if the same sampling experiment were repeated infinitely many times.
47
What does it mean to say that two events are mutually exclusive?
Mutually exclusive events are events that cannot co-occur.
48
What does it mean to say that two events are independent?
Events are independent if the occurrence of one does not affect the probability of the other occurring.
49
*Give an example of a conditional probability.
An example of a conditional probability would be drawing an Ace on the second draw from a deck, given that a King had been drawn on the first draw.
50
Is there a difference between a relative frequency distribution and a probability distribution? Please explain
Any relative frequency distribution can be a probability distribution. Probability involves the notion of an infinite number of identical sampling experiments. Therefore, any relative frequency distribution shows the proportion of times a value or interval of the variable (shown in the distribution) would occur in an infinite number of identical sampling experiments.
51
T/F A frequency table can be thought of as a probability distribution.
True.
52
T/F A frequency table can be thought of as a probability density function.
False. Frequency tables do not show the density of scores.
53
T/F A value of 19.4999 falls in an interval with score limits of 20–29.
False. 19.4999 would fall in the interval 10–19; it is below the lower real limit of the interval 20–29.
54
T/F The probability of drawing a face card from a deck of 52 cards is .2308.
True.
55
T/F . The probability of drawing a red ace from a deck of 52 cards is .0385.
True.
56
T/F . The probability of drawing a red ace from a deck of 52 cards is .0385.
True.
57
T/F For large samples with many different values of the variable, we should have a small number of intervals when constructing a frequency table.
False. If our sample is large and there are many values of the variable, we can have a large number of intervals.
58
T/F In 50 flips of a fair coin it came up heads 28 times. Therefore, the probability of coming up heads is .56.
False. The proportion of successes is .56.
59
T/F If the interval width is 10, then 35–44 is a possible interval for the lowest score limits.
False. The lower score limit must be a multiple of 10.
60
T/F . In a frequency table for a qualitative variable, values of the variable should be listed from largest to smallest.
False. There is no natural ordering to a qualitative variable.
61
T/F The only difference between a bar graph and a histogram is the labeling of the y-axis.
False. For a histogram, there is a natural ordering to values on the x-axis and the bars for the histogram touch. For a bar graph, there is no natural ordering to values on the x-axis and the bars for the histogram do not touch.
62
T/F The range of 100 scores is 50; therefore, 20 would be a reasonable interval width.
False. This would produce only three or four intervals.
63
T/F A collection of reaction times ranges from .936 seconds to 2.301 seconds. Therefore, a reasonable interval width would be 20 milliseconds.
False. The range in milliseconds is 1,365, so an interval width of 20 would produce about 70 intervals.
64
T/F A collection of IQs range from 75 to 141. If interval width is 15, then our grouped frequency distribution would have 5 intervals.
True.
65
What is the central tendency of a distribution?
Central tendency is a number that represents a typical score in a distribution.
66
What is the mean of a distribution?
The mean of a distribution is the sum of all scores in the distribution divided by the number of scores in the distribution.
67
What is the median of a distribution?
The median is the number that divides a set of numbers into two groups of equal size.
68
What is the mode of a distribution?
The mode is the most frequently occurring score in a distribution.
69
What do we mean by dispersion?
Dispersion refers to how spread out scores are in a distribution of a quantitative variable.
70
What is the range of a distribution?
The range is the difference between the largest and smallest scores in a set.
71
What is a deviation score?
A deviation score is the difference between a score and the mean of the sample or population from which the score came.
72
What do we mean by the sum of squares?
The sum of squares is the sum of all squared deviation scores in a sample or population.
73
Show the formula for the population variance and put into words what it represents.
In a population, the variance is the average squared deviation from the mean
FORMULA[].
74
How does the sample variance differ from the population variance? Why is the sample variance computed differently from the population variance?
The population variance is the sum of squares divided by the number of scores in the population (N). The sample variance is the sum of squares divided by the number of scores in the sample minus 1 (n – 1). The sample variance computed with n – 1 in the denominator is a better estimator of σ2 than the sample variance computed with n in the denominator.
75
How does the standard deviation of a population or sample relate to the variance?
The standard deviation is the square root of the variance.
76
What are the features of a normal distribution?
A normal distribution is symmetrical and looks like the cross-section of a bell.
77
What does it mean for a distribution to be skewed?
A skewed distribution is an asymmetrical distribution, with one tail longer than the other.
78
Explain the term kurtosis.
The kurtosis of a distribution refers to how sharp or flat its peak is.
79
What does it mean for a distribution to be multimodal?
A multimodal distribution has more than one peak.
80
The expression ∑(y – m) will always evaluate to the same number, no matter what the scores in y are. What is the number? Please explain why this number is always obtained.
This expression will always evaluate to 0. It is the sum of deviation scores. The sum of the absolute values of negative deviation scores always equals the sum of the absolute values of the positive deviation scores. Therefore, the sum of the positive and negative deviation scores will always be zero.
81
T/F In a normal distribution, the mean equals the mode.
True.
82
T/F In a population, the variance is the average squared deviation from the mean.
True.
83
T/F In a sample, the variance is the average squared deviation from the mean.
False. The variance is the sum of squares divided by n – 1.
84
T/F The sample variance computed with n−1 in the denominator is a poor estimator of the population variance.
False. Dividing the sum of squares by n – 1 makes the sample variance a good estimator of the population variance.
85
T/F Kurtosis is a property of distributions that cannot be computed from the scores.
False. Kurtosis can be easily computed from scores.
86
T/F Multiplying all scores in a sample by 10 will increase the variance by a factor of 20.
False. It will increase the variance by a factor of 100.
87
T/F Adding 10 to all scores in a sample will increase the variance by a factor of 100.
False. Adding a constant will have no effect on the variance.
88
T/F If y = {1, 2, 3, 3, 3, 4, 5}, then the mean equals the mode.
True.
89
T/F If y = {1, 2, 3, 4, 5, 6, 7, 8, 9}, then the mean equals the median.
True.
90
T/F . A very easy test will produce a positively skewed distribution of scores.
False. It will produce a negatively skewed distribution.
91
T/F The mean, like the range, does not make use of all scores in a set.
False. The mean is based on all scores in a set.
92
T/F $500,000 and $5,000,000 represent two measures of central tendency for the salaries of professional baseball players. $5,000,000 is the median and $500,000 is the mean.
False. For right skewed distributions (like income), the mean is greater than the median.
93
T/F Outliers will have more of an effect on the median than the mean
False. Because the mean uses all scores in a set, outliers will have more of an effect on the mean than the median.
94
T/F Outliers will have more of an effect on the range than the variance.
True.
95
What is a z-score?
A z-score, or standard score, expresses the distance of a score from the mean (μ) of its distribution in units of standard deviation (σ).
96
What two parameters completely describe a normal distribution?
The mean (μ) and standard deviation (σ) completely describe a normal distribution.
97
What is the standard normal distribution?
The standard normal distribution is a distribution of z-scores. The standard normal distribution has a mean of μ = 0, a standard deviation of σ = 1, and variance of σ2 = 1.
98
Put into words the meaning of P(z).
P(z) denotes the proportion of the standard normal distribution falling below a given z-score.
99
T/F All normal distributions can be transformed to the standard normal distribution.
True.
100
T/F Skewed distributions can be transformed to the standard normal distribution.
False. Only normal distributions can be transformed to the z-distribution.
101
T/F All normal distributions have a mean of zero and a standard deviation of 1.
False. Only the standard normal distribution has a mean of zero and standard deviation of 1.
102
T/F P(z) conveys the proportion of the z-distribution above z.
False. P(z) is the proportion of the z-distribution below z.
103
T/F P(z2) − P(z1) conveys the proportion of the z-distribution between z1 and z2.
True.
104
T/F . Approximately 14% of the standard normal distribution lies between −1 and 0.
False. Approximately 34% of the standard normal distribution lies between –1 and 0.
105
T/F If z = 1, then P(z) = .8413.
True.
106
T/F If z = −1, then P(z) is approximately .34.
False. P(z) is approximately .16
107
T/F If z1 = 1 and z2 = 2, then P(z2) − P(z1) is the proportion of a normal distribution outside the interval x1 to x2.
False. P(z2) – P(z1) is the proportion of a normal distribution within the interval x1 to x2.
108
Put into words the meaning of the distribution of means.
The distribution of means is a probability distribution of all possible values of a sample mean based on n scores. The distribution of means is also referred to as the sampling distribution of the mean.
109
Explain the difference between sampling with replacement and sampling without replacement.
Sampling with replacement means that each time a score is drawn from a population, it is returned to the population before the next score is drawn. Sampling without replacement means that when a score is drawn from a population, it is not returned to the population before the next score is drawn.
110
How does µm relate to µ?
µm is the mean of the distribution of means. µm always equals µ, the mean of the distribution of scores from which samples were drawn.
111
Define expected value of a statistic
The expected value of a statistic is the mean of its sampling distribution. We denote the expected value of m as E(m).
112
What does it mean for a statistic to be unbiased? Give an example.
A statistic is unbiased when its expected value equals the parameter it estimates. The sample mean is an unbiased statistic.
113
What does it mean for a statistic to be biased? Give an example.
A statistic is biased when its expected value does not equal the parameter it estimates. The sample variance, computed with n in the denominator, is a biased statistic.
114
How does σ2m
relate to σ2?
is that variance of the distribution of means. always equals σ2/n, the variance of the population of scores divided by sample size.
115
What is the standard error of the mean?
The standard error of the mean (σm ) characterizes the average distance of sample means from the population mean.
116
When do we use the term “standard error” and when do we use “standard deviation”?
We use the term “standard error” when referring to the variability in the distribution of a statistic and we use “standard deviation” when referring to the variability in a distribution of scores.
117
State the central limit theorem.
The central limit theorem states (roughly) that the distribution of sample means will be a normal distribution if the distribution being sampled is normal, and that the distribution of sample means will converge on a normal distribution as sample size increases, irrespective of the shape of the distribution being sampled.
118
What is a sampling distribution?
A sampling distribution is a probability distribution of all possible values of a sample statistic based on samples of the same size.
119
T/F Some sampling distributions are not normal distributions.
True.
120
T/F The distribution of means is always normal if the population being sampled is normal.
True.
121
T/F
Sigma^2/n
is the standard error of the mean.
False is the variance of the distribution on means.
122
T/F If a normal distribution has a mean of 100 and standard deviation of 10, then the expected value of s2 is 100 no matter what sample size is.
True, because s2 is an unbiased statistic.
123
T/F The expected value of the biased sample variance is σ2(n−1)/n.
True.
124
T/F If a distribution has a mean of 100 and standard deviation of 10, then the standard error of the mean is 10.
False. This can’t be answered without knowing sample size.
125
T/F *The sampling distribution of the range is a biased statistic.
*True.
126
T/F *The distribution of sample variances is generally left skewed.
*False. The distribution of sample variances is generally right skewed.
127
T/F Strictly speaking, the central limit theorem requires sampling with replacement.
True.
128
T/F *The distribution of variances approaches a normal distribution as sample size increases.
*True.
129
T/F The standard error of the mean is
False. The estimated standard error of the mean is .
130
what is the observed score
true score +error
131
difference between descriptive and inferential statistics
D:organize,summarize, and communicate info
I:use samples to draw conc abt pop
132
Whats a point estimate and interval estimate?
single number that estimates a population parameter
interval estimate is a range of values believed to contain the population parameter.
133
What is a confidence interval?
interval that expresses the confidence we have that it contains the parameter.
134
What does it mean to say that we have 95% confidence in an interval?
we know that 95% of all intervals calculated this way will contain pop mean
135
What are the four quantities required to calculate a confidence interval when σ is known, and how does each of these affect the width of the confidence interval?
m is the center of the interval and has no effect on the width of the interval. Interval width increases as σ increases. Interval width decreases as n increases. Interval width decreases as α increases.
136
95% of all sample means will fall in the interval m ± 1.96(σm).
False. The population mean, μ, will fall in 95% of all intervals computed as m ± 1.96(σm).
137
90% of all intervals computed as m ± 1.96(σm) will contain µ.
False. 95% of all intervals computed as m ± 1.96(σm) will contain μ.
138
m ± 1.96(σm) = [5.6, 9.3]; therefore, the probability is .95 that this interval contains µ.
False. The interval either contains μ or it does not so the probability is either 0 or 1.
139
As sample size increases, confidence intervals become narrower
True
