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Statistics: Population, Sample, Parameters, and Statistical Methods, Study Guides, Projects, Research of Statistics for Psychologists

Virginia State University (VSU)Statistics for Psychologists

An introduction to statistics, focusing on the concepts of population and sample, parameters and statistics, descriptive and inferential statistics, independent and dependent variables, research methods, discrete and continuous variables, scales of measurement, and various statistical calculations and distributions. It also includes sample questions for multiple choice and problem-solving exercises.

Typology: Study Guides, Projects, Research

2023/2024

Available from 05/06/2024

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PSYC 2613 Mid-term Exam Study Guide
The midterm exam covers seven (7) topics up-to-date and all multiple-choice. It will have 50
questions.
Instructions on How to Use this Study Guide : Review this study guide and do the sample
questions for each topic. After completion of the sample questions, check your answers on
pages 10 -11 of this handout.
Introduction to Statistics
Population and Sample
oA population consists of all individuals of interest to the research (e.g.,
all individuals in the state of Florida)
oA sample is a subset of the population (e.g., a sample of 25 teenagers in the state
of Florida who are under the age of 19)
oParameter and Statistic
A parameter is a characteristic of a population (e.g., the average GPA of
students attending PVAMU). The population consists of all students
attending PVAMU). If the average GPA of the students attending
PVAMU is 2.00, then the parameter is 2.00
A statistic is a characteristic of a sample. We can compute the average
GPA for a sample 35 students attending PVAMU. If the average GPA for
the sample of the 25 students is 2.25, then this value becomes the statistic.
Note: Sampling error is amount of difference between a statistic and
a parameter. In the previous example, a difference of .25 (2.25 –
2.00) constitutes sampling error
Descriptive and Inferential Statistics
oDescriptive: mathematical procedures for organizing, summarizing,
describing, and simplifying data (i.e., numerical information, measurements,
observations, and scores of any kind)
Examples: Frequency distributions (Tables and Graphs), measures of
averages (central tendency), variability (range, variance, and
standard deviation)
oInferential statistics: A procedure that uses sample data to make a conclusion
(inference) about a population. This area of statistics deals mainly with hypothesis
testing (hypothesis tests).
Examples: Using z or t statistic to test hypothesis about a
population parameter
Independent and Dependent Variables
Research Methods
oExperimental method
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Download Statistics: Population, Sample, Parameters, and Statistical Methods and more Study Guides, Projects, Research Statistics for Psychologists in PDF only on Docsity!

PSYC 2613 Mid-term Exam Study Guide

The midterm exam covers seven (7) topics up-to-date and all multiple-choice. It will have 50

questions.

Instructions on How to Use this Study Guide : Review this study guide and do the sample

questions for each topic. After completion of the sample questions, check your answers on

pages 10 -11 of this handout.

Introduction to Statistics

 Population and Sample

o A population consists of all individuals of interest to the research (e.g.,

all individuals in the state of Florida)

o A sample is a subset of the population (e.g., a sample of 25 teenagers in the state

of Florida who are under the age of 19)

o Parameter and Statistic

 A parameter is a characteristic of a population (e.g., the average GPA of

students attending PVAMU). The population consists of all students

attending PVAMU). If the average GPA of the students attending

PVAMU is 2.00, then the parameter is 2.

 A statistic is a characteristic of a sample. We can compute the average

GPA for a sample 35 students attending PVAMU. If the average GPA for

the sample of the 25 students is 2.25, then this value becomes the statistic.

 Note: Sampling error is amount of difference between a statistic and

a parameter. In the previous example, a difference of .25 (2.25 –

2.00) constitutes sampling error

 Descriptive and Inferential Statistics

o Descriptive: mathematical procedures for organizing, summarizing,

describing, and simplifying data (i.e., numerical information, measurements,

observations, and scores of any kind)

 Examples: Frequency distributions (Tables and Graphs), measures of

averages (central tendency), variability (range, variance, and

standard deviation)

o Inferential statistics: A procedure that uses sample data to make a conclusion

(inference) about a population. This area of statistics deals mainly with hypothesis

testing (hypothesis tests).

 Examples: Using z or t statistic to test hypothesis about a

population parameter

 Independent and Dependent Variables

 Research Methods

o Experimental method

 Used to demonstrate cause-effect

 1 variable is measured and 2 groups are compared

 Independent Variable (IV)

 Manipulated variable. In the effects of illumination on task

performance, illumination (dim or bright) is the IV.

 Dependent Variable (DV)

 Measured variable or response. In the preceding example, task

performance is the DV.

o Quasi-experimental method

 Lack random assignment of subjects

 Lack manipulation

 Based on existing participant variables or subject characteristics (e.g.,

gender differences in reaction time)

o Correlational method

 Used to describe relationship between variables

 Causation cannot be implied

 Discrete and Continuous Variables

o Discrete variables (finite). Example: the number of siblings one has, can be 4 or 5,

not 4.5.

o Continuous variables (infinite). Example, time used to solve a puzzle could be

11.3 secs.

 Scales of Measurement

o Nominal: Name observations into categories, like gender (male or

female), political affiliation (democrat, republican, or independent)

o Ordinal: Ranked observations (first, second, third, and so on)

o Interval: equal points between adjacent values. Example, temp.

o Ratio: Same properties with interval, but with absolute zero. Example: reaction

time

 Statistical Notation: computations and expression in words

Sample Questions:

Multiple Choice Identify the choice that best completes the statement or answers the question.

  1. The relationship between a statistic and a parameter is the same as the relationship between. a. a sample and a population b. a statistic and a parameter c. a parameter and a population d. descriptive statistics and inferential statistics

a. 5 c. 11 b. 10 d. cannot be determined

  1. If the following distribution was shown in a histogram, the bar above the 15-19 interval would reach from to. X f 20-25 2 15-19 5 10-14 4 5-9 1 a. X = 14.5 to X = 19.5 c. X = 15.5 to X = 19. b. X = 15.5 to X = 18.5 d. X = 15.0 to X = 19.
  2. In a distribution with positive skew, scores with the highest frequencies are. a. on the right side of the distribution c. in the middle of the distribution b. on the left side of the distribution d. represented at two distinct peaks
  3. What is the shape of the distribution for the following set of data? Scores: 1, 2, 3, 3, 4, 4, 4 5, 5, 5, 5, 6 a. symmetrical c. negatively skewed b. positively skewed d. cumulative Figure 2-
  4. For the scores shown in the accompanying stem and leaf display, what is the highest score in the distribution? a. 8 c. 84 b. 83 d. 7042

Central Tendency

 Measures of Central Tendency, their characteristics, computations, and the most

commonly used measure of central tendency

 Computations of central tendency from a frequency distribution table

 When to use a particular measure of central tendency

 Central Tendency and the shape of a distribution

Sample Questions:

Multiple Choice Identify the choice that best completes the statement or answers the question.

  1. What is the mean for the population of scores shown in the frequency distribution table? X f
  1. One sample has n = 4 scores and M = 10.^ A second sample has n = 6 scores and M = 5.^ If the two samples are combined, then what is the mean for the combined sample? a. 70/4 = 17. b. 70/6 = 11. c. 70/10 = 7 d. It cannot be determined with the information given.
  2. What is the mode for the population of scores shown in the frequency distribution table? X f 5 1 4 2 3 3 2 4 1 2 a. 2 c. 3. b. 3 d. 4
  3. For a perfectly symmetrical distribution with μ = 30, what is the most probable value for the mode?
  4. For a negatively skewed distribution with a mode of X = 25 and a median of 20, what is the most likely value for the mean? a. greater than 25 b. less than 20 c. between 20 and 25 d. It cannot be determined from the information given.

Variability

 Measures of variability, characteristics, computations (for both samples and populations),

and the most commonly used measure of variability

 Symbols for measures of variability

 Relationship between variance and standard deviation

a. 15/5 = 3 c. 32/5 = 6. b. 15/12 = 1.25 d. 32/12 = 2. a. 30 b. greater than 30 c. less than 30 d. It cannot be determined from the information given.

Sample Questions:

Multiple Choice Identify the choice that best completes the statement or answers the question.

  1. For a population with μ = 80 and = 6, what is the z-score corresponding to X = 68? a. –0.50 c. +2. b. –2.00 d. –12.
  2. For a sample of n = 30 scores, X = 65 corresponds to z = 1.50 and X = 40 corresponds to z = +1.00. What are the values for the sample mean and standard deviation? a. M = 55 and s = 10 c. M = 55 and s = 15 b. M = 50 and s = 15 d. M = 50 and s = 10
  3. Under what circumstances is a score that is 15 points above the mean an extreme score relatively far from the mean? a. When the population mean is much larger than 15 b. When the population standard deviation is much larger than 15 c. When the population mean is much smaller than 15 d. When the population standard deviation is much smaller than 15
  4. For any distribution, what is the z-score corresponding to the mean? a. 0 b. 1 c. N d. It cannot be determined from the information given.
  5. Using z-scores, a population with μ = 37 and = 6 is standardized so that the new mean is μ = 50 and =
    1. After the standardization, one individual has a score of X = 55. What was this individual’s score in the original distribution? a. X = 40 b. X = 42 c. X = 43 d. It cannot be determined with the information given.

Probability

 Values for probability (0 – 1)

 Requirements for random sampling

 Laws of Probability (Addition and Multiplication Laws)

 Finding simple probability

 Finding probability (proportion) using the Unit Normal Table

 Using the Unit Normal Table to find percentile and percentile ranks

 Finding scores for a specific proportion using the Unit Normal Table

 Binomial distribution and approximation to a normal distribution

Sample Questions:

Multiple Choice Identify the choice that best completes the statement or answers the question.

  1. What proportion of a normal distribution is located between z = –0.25 and z = +0.25? a. 0.5987 c. 0. b. 0.4013 d. 0.
  2. What proportion of a normal distribution is located between z = –1.50 and z = +1.50? a. 0.9332 c. 0. b. 0.0668 d. 0.
  3. A normal distribution has a mean of μ = 80 with = 20. What score separates the lowest 30% of the distribution from the rest of the scores? a. X = 90.4 c. X = 110 b. X = 69.6 d. X = 50
  4. Scores on the SAT form a normal distribution with a mean of μ = 500 with = 100. If the state college only accepts students who score in the top 60% on the SAT, what is the minimum score needed to be accepted? a. X = 475 c. X = 440 b. X = 525 d. X = 560
  5. Under what circumstances does the binomial distribution approximate a normal distribution? a. When pn > 10 c. When pn and qn are both > 10 b. When qn > 10 d. When npq > 10

Distribution of Sample Means

 Definition of the distribution of sample means

 Expected value of M

 Standard error of the mean

 Relationship between standard error and sample size

 Relationship between expected value of the mean and sample size

 Computing z-score for the distribution of sample means

 Probability questions on the distribution of sample means

Sample Questions:

Multiple Choice Identify the choice that best completes the statement or answers the question.

  1. A sample of n = 16 scores is selected from a population with = 80 with = 20. On average, how much error would be expected between the sample mean and the population mean? a. 20 points c. 4 points b. 5 points d. 1.25 points
  2. For a particular population a sample of n = 4 scores has an expected value of 10. For the same population, a sample of n = 25 scores would have an expected value of.

Answers to Sample Questions by Topic

Introduction to Statistics

1. A

2. C

3. A

4. B

5. C

Frequency Distributions

1. D

2. A

3. B

4. C

5. C

Central Tendency

1. D

2. C

3. A

4. A

5. B

Variability

1. A

2. C

3. A

4. C

5. B

Z-scores

1. B

2. D

3. B

4. A

5. A

Probability

1. D

2. D

3. A

4. B

5. C

Distribution of Sample Means

1. B

2. C

3. B

4. C

5. C