Quantitative Methods Exam 1

How to graph ungrouped data:

Bar charts- - Summarizes the frequency of discrete and categorical data in whole units or categories

1. Descriptive statistics

CH 1 Learning Check 1 1. ____________ are procedures used to summarize, organize, and make sense of a set of scores or observations.

1. To summarize large data sets.

CH 2 Learning Check 3 1. When would a researcher construct a relative frequency table?

2. 1.00

CH 2 Learning Check 3 2. The sum of relative frequencies across all intervals is equal to _____________.

1. True

CH 2 Learning Check 4 1. True or False: Cumulative relative frequencies are added from the top down or bottom up.

2. 1.00

CH 2 Learning Check 4 2. Cumulative relative frequencies sum to __________(give or take rounding number).

3. The student scored higher than 80% of all other students who took the same exam.

CH 2 Learning Check 4 3. A student scores in the 80th percentile on an exam. What does this mean in comparison to all other students?

3. Readers often find percents easier to read than decimals.

CH. 2 Learning Check 3 3. Relative Frequencies are commonly reported in academic journals as percents. Why?

4. False. A relative percent sums to 100%.

CH. 2 Learning Check 3 4. True or False: A relative percent sums to the total frequency count.

3. SD most informative when reported with the mean (Characteristics of Standard Deviations)

- Reporting mean and SD can inform reader of distribution for close to all recorded data - Reported as the mean plus or minus SD (M±SD)

Nominal Scale

- Researchers, for example, may code men as 1 and women as 2. They may code the seasons of birth as 1,2,3, and 4 for spring, summer, fall, and winter.

2. The SD is used to describe quantitative variables (Characteristics of Standard Deviations)

- SD is a numeric value and used to describe variables measured in numeric units

Descriptive Statistics

- Scientists organize and summarize information such that the information is meaningful to those who read about the observations scientists made in a study. This describes ________________ ______________.

Random Assignment

- _____________ _____________ is a random procedure used to ensure that participants in a study have an equal chance of being assigned to a particular group or condition.

Ungrouped Data

- ______________ _______ is a set of scores or categories distributed individually, where the frequency for each individual score or category is counted.

- Types of Central Tendency:

Mean Median Mode

Fractiles include

Median - splits data in half Quartiles - splits data into four parts Deciles - splits data into ten parts Percentiles - splits data into one hundred parts

Deviation

- A ________ is the difference of each score from its mean

Variables for which researchers measure data fall into two broad categories:

(1) continuous or discrete and (2) quantitative or qualitative.

Median position

- (𝒏+𝟏)/𝟐

The median is reported for:

- *Skewed distributions of data - Data set includes a score or group of scores that fall substantially above (positively skewed) or below (negatively skewed) other scores - The median is not influenced by the value of outliers

lower quartile

- 25th percentile ( Q1 )

Quartiles of a distribution are the range of scores split into four equal parts

- 25th percentile ( Q1 ) - lower quartile - 50th percentile ( Q2 ) - median quartile - 75th percentile ( Q3 ) - upper quartile

median quartile

- 50th percentile ( Q2 )

upper quartile

- 75th percentile ( Q3 )

Quantitative and Qualitative Variables

- Variables can also be categorized as ___________ or ___________.

Percentile rank

- A Percentile point is the value of an individual or score within a larger distribution. The corresponding percentile of a percentile point is the _______________ _______.

Biased estimator

- A ________ ___________ is any sample statistic, such as the sample variance when we divide SS by n, obtained from a randomly selected sample that does not equal the value of its respective population parameter, such as a population mean, on average.

Quasi-independent variable

- A _________-_______________ ___________ is a preexisting variable that is often a characteristic inherent to an individual, which differentiates the groups or conditions being compared in a research study. Because the levels of the variable are preexisting, it is not possible to randomly assign participants to groups.

Discrete Variable

- A __________ __________ is measured in whole units or categories that are not distributed along a continuum. - Ex. number of brothers or sisters you have and your family's socioeconomic status (lower class, middle class, upper class) are examples of ___________ ___________s.

Sample Statistic

- A __________ _____________ is measured to estimate the population parameter. In this way, a sample is selected from a population to learn more about the characteristics in the population of interest.

Cumulative Frequency Distribution ("Bottom Up")

- A __________ ______________ ____________ is a summary display that distributes the sum of frequencies across a series of intervals.

Sample

- A __________ is a set of individuals, items, or data selected from a population of interest.

Quantitative Variable

- A ____________ ___________ varies by amount, so it is measured in numeric units. Thus, continuous and discrete variables can be ________________. - For ex., we can measure food intake in calories (a continuous variable), or we can count the number of pieces of food consumed (a discrete variable). In both cases, the variable, food intake, is measured by amount (in numeric units).

Discrete Variable

- A ____________ ___________, on the other hand, is measured in whole units or categories. So _________ ___________ are not measured along a continuum.

Qualitative Variable

- A ____________ ___________, on the other hand, varies by class. These variables are often labels for the behaviors we observe- so only discrete variables can fall into this category. - For ex., socioeconomic class (working class, middle class, upper class) is discrete and ____________; so are many behavioral disorders such as categories of depression (unipolar, bipolar) and drug use (none, experimental, abusive).

Percentile point

- A _____________ ________ is the value of an individual or score within a larger distribution. The corresponding percentile of a percentile point is the percentile rank. - Thus the 75th percentile point, for example, is the value (the percentile point).

Simple frequency distribution

- A _____________ ___________ _____________ is a summary display for (1) the frequency of each individual score or category (ungrouped data) in a distribution or (2) the frequency of scores falling within defined groups or intervals (grouped data) in a distribution.

Qualitative Variable

- A _____________ ___________ varies by class. This variable is often represented as a label and describes nonnumeric aspects of phenomena.

Frequency

- A _____________ is the number of times or how often a category, score, or range of scores occurs.

Continuous Variables

- A ______________ ____________ is measured along a continuum at any place beyond the decimal point. A ____________ _____________ can thus be measured in fractional units.

Quantitative Variable

- A ______________ _____________ varies by amount. This variable is measured numerically and is often collected by measuring or counting.

Percentile rank

- A _______________ _________ of a score is a percentage of scores with values that fall below a specified score in a distribution

Continuous Variables

- A _______________ __________ is measured along a continuum. So ___________ ____________ are measured at any place beyond the decimal point. - Ex. olympic sprinters are clocked to the nearest hundredths place (in seconds), but if the Olympic judges wanted to clock them to the nearest millionths place, they could.

Percentile point

- A _______________ ___________ is a value of a score on a measurement scale below which a specified percentage of scores in a distribution fall.

Cumulative Percent Distribution

- A _______________ ______________ _____________ is a summary display that distributes the sum of relative percents across a series of intervals.

Frequency Distributions

- A _______________ _______________ is a summary display for a distribution of data organized or summarized in terms of how often a category, score, or range of scores occurs.

Population

- A ________________ is the set of all individuals, items, or data of interest. This is the group about which scientists will generalize.

Population Parameter

- A characteristic (usually numeric) that describes a population is called a ________________ ______________.

Sample Statistic

- A characteristic (usually numeric) that describes a sample is referred to as a ______________ ____________.

Sample Statistic

- A characteristic that describes a sample, such as learning, is called a __________ ______________ and is the value that is measured in the study.

Frequency

- A more meaningful arrangement is to place the data in a summary table that shows the ___________ of exam scores, which in this case is the number of scores for each grade range.

Quasi-independent variable

- A preexisting variable, or one which participants cannot be randomly assigned, is called a __________-_______________ __________.

Quasi-Experimental Method

- A research study is structured similar to an experiment but lacks one or both of the following is called a ________-_______________: 1. The study includes a quasi-independent variable. 2. The study lacks a comparison/control group.

2. Adding a new score or completely removing an existing score will change the mean, unless the value equals the mean (Characteristics of the Mean)

- Add a score above the mean and the mean will increase - Add a score below the mean and the mean will decrease

4. The value for the SD is affected by the value of every score in the distribution (Characteristics of Standard Deviations)

- Adding or subtracting the same constant to each score will not change the value of the SD - Multiplying or dividing each score using the same constant will cause the SD to change by that constant

Open Interval or Open class

- An ________ ___________, or _______ _________, is an interval with no defined upper or lower boundary. - ex. "126 and above" b/c only two values were counted

Interval

- An ___________ is a discrete range of values within which the frequency of a subset of scores is contained.

Ordinal Scale

- An ____________ __________ of measurement is one that conveys only that some value is greater or less than another value. - Ex. of ___________ ___________ include finishing order in a competition, education level, and rankings.

Unbiased Estimator

- An ____________ ______________ is any sample statistic, such as the sample variance when we divide SS by n-1, obtained from a randomly selected sample that equals the value of its respective population parameter, such as a population variance, on average.

Equidistant Scale

- An _____________ __________ is a scale with intervals or values distributed in equal units.

Interval Scale

- An ______________ ____________ of measurement can be understood readily by two defining principles: equidistant scales and no true zero. - Common example for this in behavioral science is the rating scale. - This type of scale is a numeric response scale used to indicate a participant's level of agreement or opinion with some statement

Operational Definition

- An _______________ ______________ is a description of some observable event in terms of the specific process or manner by which it was observed or measured.

Independent Variable (IV)

- An ________________ _________________ (__ __) is the variable that is manipulated in an experiment. This variable remains unchanged (or "independent") between conditions being observed in an experiment. It is the "presumed cause." The specific conditions of an IV are referred to as the levels of the independent variable.

Sample

- An alternative to selecting all members of a population is to select a portion or ____________ of individuals in the population.

Correlational Method

- Another method for examining the relationship between variables is to measure pairs of scores for each individual. The _________________ method can determine whether a relationship exists between variables, but it lacks the appropriate controls needed to demonstrate cause and effect.

experiment

- Any study that demonstrates cause is called an ___________________.

How to graph ungrouped data

- Bar chart

Quasi-independent variable

- Because participants cannot be randomly assigned to the levels of sex (male, female), sex is a _________-________________ _____________, and this study is therefore regarded as a _________-experiment.

The Weighted Mean

- Combined mean of two or more groups of scores, where the number of scores in each group are unequal

Datum

- Data (plural) are measurements or observations that are typically numeric. A ___________ (singular) is a single measurement or observation, usually referred to as a score or raw score.

Score

- Data (plural) are measurements or observations that are typically numeric. A datum (singular) is a single measurement or observation, usually referred to as a _________ or raw score.

Raw Score

- Data (plural) are measurements or observations that are typically numeric. A datum (singular) is a single measurement or observation, usually referred to as a score or _____ __________.

Order: (Scales of Measurement)

- Does a larger number indicate a greater value than a smaller number?

Ratio: (Scales of Measurement)

- Does dividing (or taking the ratio of) two numbers represent some meaningful value?

Difference: (Scales of Measurement)

- Does subtracting two numbers represent some meaningful value?

Interval Scale

- Ex. If you are asked to rate your satisfaction with a spouse or job on a 7-point scale from 1 (completely unsatisfied) to 7 (completely satisfied), then you are using an _____________ ___________.

Three Research Methods Commonly used in Behavioral Research:

- Experimental, Quasi-experimental, and Correlational

Interval Width

- Find the _________ _________. The ___________ ___________ is the range of values contained in each interval of a grouped frequency distribution. - TO FIND: we divide the real range by the number of intervals chosen. The recommended number of intervals is between 5 and 20. ex. 176/10, the _________ ________ is 17.6 and round to the nearest whole number, so round up to an _________ ________ of 18.

experiment

- For this study to be called an ______________, (teacher rattling papers and sitting still while kids take test) researchers must satisfy three requirements.

1. Manipulation ( of variables that operate in an experiment) 2. Randomization ( of assigning participants to conditions) 3. Comparison/control (a control group)

- For this study to be called an experiment, (teacher rattling papers and sitting still while kids take test) researchers must satisfy three requirements. These requirements are regarded as the necessary steps to ensure control to allow researchers to draw cause-and effect conclusions. These requirements are the following: 1. ___________________ ( ) 2. ____________________ ( ) 3. _____________/_____________ ( )

Population

- If we are interested in students in the United States, then all U.S. students would constitute the _________________.

Quasi-experiment

- In a typical _______-______________, the variable being studied cannot be manipulated, which makes random assignment impossible.

Scales of Measurement

- In all, ________ ___ _______________ are characterized by three properties: order, difference, and ratio.

Nominal Scale

- In science, values on a ___________ __________ are typically categorical variables that have been coded - converted to numeric values. - Ex. of ___________ variables include a person's race, sex, nationality, sexual orientation, hair and eye color, season of birth, marital status, or other demographic or personal information.

Scales of Measurement

- In the early 1940's Harvard psychologist S.S. Stevens coined the terms nominal, ordinal, interval, and ratio to classify _________ ___ __________________.

Construct frequency distribution

- In this case we chose 10 intervals. The table shows that each interval has a width of 18. 0-17, it does have a width of 18. In a frequency distribution, the INTERVAL BOUNDARIES mark the cutoffs for a given interval. The LOWER BOUNDARY is the smallest value in each interval, and the UPPER BOUNDARY is the largest value in each interval.

Upper Boundary

- In this case we chose 10 intervals. The table shows that each interval has a width of 18. 0-17, it does have a width of 18. In a frequency distribution, the INTERVAL BOUNDARIES mark the cutoffs for a given interval. The LOWER BOUNDARY is the smallest value in each interval, and the _____________ ________________ is the largest value in each interval.

Lower Boundary

- In this case we chose 10 intervals. The table shows that each interval has a width of 18. 0-17, it does have a width of 18. In a frequency distribution, the INTERVAL BOUNDARIES mark the cutoffs for a given interval. The __________ ______________ is the smallest value in each interval, and the UPPER BOUNDARY is the largest value in each interval.

Interval Boundaries

- In this case we chose 10 intervals. The table shows that each interval has a width of 18. 0-17, it does have a width of 18. In a frequency distribution, the _______________ _________________ mark the cutoffs for a given interval. The LOWER BOUNDARY is the smallest value in each interval, and the UPPER BOUNDARY is the largest value in each interval.

Mean is reported for:

- Interval and ratio scale data - Data on these scales can meaningfully convey information regarding differences between scores and their mean - Normal distributions of data - The mean includes all scores in its calculation

Central Tendency

- Measures that tend to be toward the center of a distribution - Used to locate a single score that is most representative or descriptive of all scores in a distribution - Types of Central Tendency: Mean Median Mode - Notation: Population size is N Sample size is n (Calculations are largely the same)

The mode is reported for:

- Nominal scale data - Nominal scale data represent something or someone; it is not a quantity - Key phrases: most often, typical, or common - Modal distributions of data - Unimodal distribution - one mode - Bimodal distribution - two modes - Multimodal distribution - more than two modes - Nonmodal distribution - no modes

Nominal Scale

- Numbers on a ___________ _________ identify something or someone; they provide no additional information. - Ex. of ____________ numbers include ZIP codes, license plate numbers, credit card numbers, country codes, telephone numbers, and Social Security numbers. - These numbers simply identify locations, vehicles, or individuals and nothing more. - One credit card number, for example, is not greater than another; it is simply different.

Simple frequency distribution

- One way to make these data more meaningful is to summarize how often scores occur in this list using a ___________ _____________ ______________. In a __________ ____________ _____________, we can summarize how often each individual score occurs (i.e., ungrouped data, defined in Section 2.5) or how often scores occur in defined groups or intervals (i.e., Grouped Data).

Ratio Scales

- Order is informative - Differences are also informative - Ratios are also informative on ________ ________ because a true zero is defined - it truly means nothing. Hence, it is meaningful to state that 60 pounds is twice as heavy as 30 pounds.

Research Method or Scientific Method

- To use the ______________ _____________, we make observations using systematic techniques of scientific inquiry.

Inferential Statistics

- Scientists use information to answer a question (e.g., Is diet related to obesity?) or make an actionable decision (e.g., Should we implement a public policy change that can reduce obesity rates?). This describes ________________ ______________.

1. The SD is always positive (Characteristics of Standard Deviations)

- Scores can either vary (greater than 0) or not vary (equal to 0) - A negative variability is meaningless

Population Parameter

- Specifically, we want to test if a new learning tool can improve learning in this population; the characteristic (learning) in the population is called a _______________ ________________.

Four Basic Steps to find the percentile point in a cumulative percent distribution

- Step 1. Identify the interval within which a specified percentile point falls. - for example, we want to identify the 75th percentile point, which falls in the interval 90-98 on the example frequency table. - Step 2. Identify the real range for the interval identified Real limits: - 0.5 less than lower limit = 89.5 - 0.5 greater than upper limit = 98.5 Real Range: - one point greater than observed range = (98-90) + 1 = 9 - Step 3. Find the position of the percentile point within the interval. - Distance of percentile from top of the interval (85-75) = 10 - Divide distance from top by total range width of percentages - 10/ (85-61) = 10/24 - Multiply fraction by width of real range (10/24) * 9 = 3.75 points - Step 4. Identify the percentile point. - Subtract position of percentile point from top of the real interval - 98.5 - 3.75 = 94.75 - The percentile point at the 75% percentile is 94.75 Final * 75% of scores are less than 94.75

Sum of squares (SS)

- The _____ ___ _________ is the sum of the squared deviations of scores from their mean. The SS is the numerator in the variance formula.

Interval Width

- The ________ __________ or class width is the range of values contained in each interval of a grouped frequency distribution.

The real range

- The _________ _________ is one more than the difference between the largest and smallest number in a list of data. - Ex. smallest value is 0, and the largest value is 175; therefore, 175-0 = 175. The ______ _________ is 175 + 1 = 176.

Cumulative Relative Frequency Distribution

- The ___________ ____________ ______________ ______________ is a summary display that distributes the sum of relative frequencies across a series of intervals.

Ordinal Scales

- The ____________ ___________ only indicate that one value is greater than or less than another, so differences between ranks do not have meaning.

Cumulative Frequency Distribution ("Bottom Up")

- The _____________ ______________ ________________ describes the sum of scores across each range and always sums to the total number of scores in a distribution.

Range

- The ______________ is difference between the largest value (L) and smallest value (S) in a set of data

Research Method or Scientific Method

- The _______________ ______________ or _______________ _____________, is a set of systematic techniques used to acquire, modify, and integrate knowledge concerning observable and measurable phenomena.

Correlational Method

- The _________________ ___________ involves measuring pairs of scores for each individual and examine the relationship between pairs of scores.

Dependent Variable (DV)

- The __________________ _________________ (__ __) is the variable that is measured in each group of a study, and is believed to change in the presence of the independent variable. It is the "presumed effect."

The Mean

- The computation of the mean for samples and populations are the same, just the notation is different - The population mean: 𝜇=(∑▒𝑥)/𝑁 - The sample mean: 𝑀=(∑▒𝑥)/𝑛

4. The sum of the differences of scores from their mean is zero (Characteristics of the Mean)

- The mean is the only constant that you can subtract from every score in a distribution, where the sum of the differences is equal to zero - This makes the mean a zero point or balance point in a distribution.

The Median

- The middle value in a distribution of data listed in numeric order - Represents the midpoint(half the scores fall above and half fall below) - Not influenced by outliers in data

Find the ranges for the follow sets of scores: 1,2,3,4, and 5 2,4,6,8, and 100

- The range is 5 - 1 = 4 - The range is 100 - 2 = 98

3. Adding, subtracting, multiplying, or dividing each score in a distribution by a constant will cause the mean to change by that constant (Characteristics of the Mean)

- This rule applies only when every score in the distribution is changed by the same positive or negative constant

Comparison/control

- This satisfies the requirement of comparison (Requirement 3), which requires that at least two groups be observed in an experiment so that scores in one group can be compared to those in at least one other group.

experiment

- To demonstrate cause, though, an __________________ must follow strict procedures to ensure that all other possible causes are eliminated or highly unlikely.

Cumulative Percent Distribution

- To distribute ___________ ____________, we can sum the relative percent in each interval, following the same procedures for adding as we did for the cumulative relative frequencies. - The total ________________ ___________ is equal to 100% (give or take rounding errors).

Independent Variable (IV)

- To do this, a researcher must be able to manipulate the levels of an _______________ _________________ (__ __) (Requirement 1) to create the groups.

Random Assignment

- To meet the requirement of randomization, researchers must use _____________ _______________ (Requirement 2) to assign participants to groups.

Continuous and Discrete Variables

- Variables can be categorized as _______________ or ____________. - _____________ variables are measures along a continuum, and thus can be measured in fractional units; ___________ variables, however, are measured only in whole units or categories.

Relative Frequency

- When researchers summarize larger data sets (with thousands or even millions of counts), they often distribute the _____________ ______________ of scores rather than counts. The ______________ ______________ is a proportion from 0 to 1.0 that describes the portion of data in each interval. - It is often easier to list the ______________ _______________ of scores because a list with very large frequencies in each interval can be more confusing to read.

1. Changing an existing score will change the mean (Characteristics of the Mean)

- When you increase the value of an existing score, the mean will increase - When you decrease the value of an existing score, the mean will decrease

Interval

- With such large data sets with many different values recorded, it is generally clearer to summarize the frequency of scores in groups or ______________. - When summarizing data this way, the data are called grouped data.

Pie Chart

- ______ _________ summarizes the relative percent of discrete and categorical data into sectors - Each sector represents the relative percent of a particular category

Semi-interquartile Range (SIQR)

- ______-______________ _________measure of half the distance between the cutoffs for the upper and lower quartiles of a data set - Computed by dividing the IQR in half - SIQR for Example 4.1: 16/2 = 8 - Q3-Q1/2.

Scales of Measurement

- ________ __ ______________ are rules that describe the properties of numbers. These rules imply that the extent to which a number is informative depends on how it was used or measured.

Ratio Scale

- ________ _______ is an ideal scale in behavioral research because any mathematical operation can be performed on the values that are measured. - Common examples of ________ _________ include counts and measures of length, height, weight, and time.

Outliers

- ________ are extreme scores that fall substantially above or below most of the scores in a particular data set. - In the example in the book, 175 is an ___________ in the data b/c this value falls substantially above most of the other values recorded.

Nominal Scale

- _________ _______ are measurements in which a number is assigned to represent something or someone. - Ex. seasons, months, sex.

True Zero

- _________ ________ is when the value 0 truly indicates nothing on a scale of measurement. Interval scales do not have a true zero.

Population Variance

- _________ ___________ is a measure of variability for the average squared distance that scores in a population deviate from the mean. It is computed only when all scores in a given population are recorded.

Sample Variance

- _________ ___________ is a measure of variability for the average squared distance that scores in a sample deviate from the mean. It is computed when only a portion or sample of data is measured in a population.

Coding

- _________ is the procedure of converting a nominal or categorical variable to a numeric value.

Coding

- _________ words with numeric values is useful when entering names of groups for a research study into statistical programs such as SPSS because it can be easier to enter and analyze data when group names are entered as numbers, not words.

Ratio Scales

- __________ ________ are measurements that have a true zero and are distributed in equal units. - Ex. weight, height, calories.

Ratio Scales

- __________ ___________ are similar to interval scales in that scores are distributed in equal units. Yet, unlike interval scales, a distribution of scores on a ___________ __________ has a true zero.

Statistics

- __________ is a branch of mathematics used to summarize, analyze, and interpret a group of numbers or observations.

Grouped Data

- ___________ _______ are a set of scores distributed into intervals, where the frequency of each score can fall into any given interval.

Fractiles

- ___________ are measures that divide data sets into two or more equal parts

Science

- ___________ is the study of phenomena, such as behavior, through strict observation, evaluation, interpretation, and theoretical explanation.

Data

- ___________(plural) are measurements or observations that are typically numeric. A datum (singular) is a single measurement or observation, usually referred to as a score or raw score.

Range

- ____________ = L - S - Simplest way to describe the dispersion of scores - Most informative for data without outliers

Interval Scale

- ____________ _________ are measurements that have no true zero and are distributed in equal units. - Ex. rating score values, temperature

Inferential Statistics

- ____________ ___________ are procedures used that allow researchers to infer or generalize observations made with samples to the larger population from which they were selected.

Relative Frequency

- ____________ _____________ is the number of times a specific event occurs compared to the total number of events - ______________ ______________ equals the frequency in an interval divided by the total frequency count - Distributes the proportion of scores in each interval - Often used to summarize large data sets

Inferential Statistics

- ____________ _____________: applying statistics to interpret the meaning of information

Standard Deviation

- _____________ ____________ is the measure of variability for the average distance that scores deviate from their mean - Calculated by taking the square root of the variance

Descriptive Statistics

- ______________ ___________ are procedures used to summarize, organize, and make sense of a set of scores or observations. ____________ ____________ are typically presented graphically, in tabular form (in tables), or as summary statistics (single values).

Frequency Polygon

- ______________ _______________ Summarizes the frequency of continuous data at the midpoint of each interval (dot-and-line) - Calculate midpoint of each interval by adding upper and lower boundary of interval, then dividing by 2

Variance

- ______________ is the measure of variability for the average squared distance that scores deviate from their mean - Value can be 0 (no variability) or greater than 0 (there is variability) - A negative variance is meaningless

Relative Percent

- _______________ _____________ Distributes the percent of scores across the categories - Multiply each relative frequency times 100

Frequency Distributions

- _______________ ______________ summarize how often (or frequently) scores occur in a data set. ____________ _____________ are most often published when researchers measure counts of behavior.

Variability

- ________________ of scores can never be negative - Scores can either not vary (variability is 0) or they can vary (variability is greater than 0)

Cumulative Relative Frequencies and Cumulative Percents

- __________________ ______________ _______________ and _______________ _______________are a sum of the proportion and percent of scores, respectively, across intervals. - These sum to 1.00 or 100%.

Interquartile Range (IQR)

- the 75th percentile minus the 25th percentile - Eliminating the top and bottom 25% of data rids data set of outliers - IQR for Example 4.1: 92-76 = 16 - Q3-Q1.

Ordinal Scales

-___________ __________ are measurements that convey order or rank alone.

Descriptive Statistics

-_____________ ___________: applying statistics to organize and summarize information

Variability

-________________is a measure for the dispersion or spread of data in a distribution and ranges from 0 to +oo

Empirical Rule

1. At least 68% of all scores lie within one SD of the mean 2. At least 95% of all scores lie within two SD of the mean 3. At least 99.7% of all scores lie within three SD of the mean

Three Steps to Summarize Grouped Data:

1. Find the real Range - The real range is one more than the difference between the largest and smallest value in a list of data - Subtract the smallest value from the largest value, then add 1 2. Find the interval width. - The interval width is the range of scores in each interval - Decide on the number of intervals (e.g.,10) - Divide real range by number of intervals chosen - Round to nearest whole number...18 3. Construct the frequency distribution. - Rules for a simple frequency distribution: - Each interval is defined - Each interval is equidistant - No interval overlaps - All values are rounded to same degree of accuracy measured in original data - Check: - Total counts in distribution = total counts made

Experimental Method : Three Requirements that must be satisfied to be called an Experiment:

1. Manipulation (of variables that operate in an experiment) 2. Randomization (of assigning participants to conditions) 3. Comparison/control (a control group)

c. All 40 students, because all students constitute the population.

CH 1 Learning Check 1 3. A psychologist wants to study a small population of 40 students in a local private school. If the researcher was interested in selecting the entire population of students for this study, then how many students must the psychologist include? a. None, b/c it is not possible to study an entire population in this case. b. At least half, b/c this would constitute the majority of the population. c. All 40 students, because all students constitute the population.

4. True

CH 1 Learning Check 1 4. True or False: Inferential statistics are used to help the researcher infer the unknown parameters in a given population.

b. Parameter; statistics

CH 1 Learning Check 1 2. _______________ describe(s) characteristics in a population, whereas ________________ describe(s) characteristics in a sample. a. Statistics; parameters b. Parameter; statistics c. Descriptive; inferential d. Inferential; descriptive

1. Science

CH 1 Learning Check 2 1. ________________ is the study of phenomena through strict observation, evaluation, interpretation, and theoretical explanation.

a. Experiment b. quasi-experiment c. correlational method

CH 1 Learning Check 2 2. State whether each of the following describes an experiment, a quasi-experiment, or a correlational method. a. A researcher tests whether dosage level of some drug (low, high) causes significant differences in health. b. A researcher tests whether citizens of differing political affiliations (Republican, Democrat) will show differences in attitudes toward morality. c. A researcher measures the relationship between annual income and life satisfaction.

3. True

CH 1 Learning Check 2 3. True or False: An experiment is the only method that can demonstrate cause-and-effect relationships between variables.

1. Scales of Measurements

CH 1 Learning Check 3 1. ______________ are rules for how the properties of numbers can change with different uses.

2. Ordinal

CH 1 Learning Check 3 2. In 2010, Fortune magazine ranked Apple as the most admired company in the world. This ranking is on a(n)________________ scale of measurement.

4. Movie ratings (from 1 to 4 stars).

CH 1 Learning Check 3 4. A researcher measures four variables: age (in days), speed (in seconds), height (in inches), and movie ratings (from 1 to 4 stars). Which of these variables is not an example of a variable measured on a ratio scale?

d. Values on an interval scale are assumed to be equidistant but do not have a true zero.

CH 1 Learning Check 3 3. What are two characteristics of rating scales that allow researchers to use these values on an interval scale of measurement? a. Values on an interval scale have a true zero but are not equidistant. b. Values on an interval scale have differences and a true zero. c. Values on an interval scale are equidistant and have a true zero. d. Values on an interval scale are assumed to be equidistant but do not have a true zero.

1. True

CH 1 Learning Check 4 1. True or False: A ratio scale variable can be continuous or discrete.

a. Continuous b. Discrete c. Discrete d. Discrete

CH 1 Learning Check 4 2. State whether each of the following is continuous or discrete. a. Delay (in seconds) it takes drivers to make a lefthand turn when a light turns green b. Number of questions that participants ask during a research study c. Type of drug use (none, infrequent, moderate, or frequent) d. Season of birth (spring, summer, fall, or winter)

a. Quantitative b. Quantitative c. Qualitative d. Qualitative

CH 1 Learning Check 4 3. State whether the variables listed in Question 2 are quantitative or qualitative.

4. False

CH 1 Learning Check 4 4. True or False: Qualitative Variables can be continuous or discrete.

5. Quantitative

CH 1 Learning Check 4 5. A researcher is interested in the effects of stuttering on social behavior with children. He records the number of peers a child speaks to during a typical school day. In this example, would the data be qualitative or quantitative?

5. b. "At or above"

CH 2 Learning 2 5. When cumulating frequencies from the top down, you typically want to discuss the data in terms of: a. "Less than" b. "At or above" c. " At most" d. All of the above

1. Frequency Distribution

CH 2 Learning Check 1 1. A ___________________ is a summary display for a distribution of data organized or summarized in terms of how often (or frequently) scores occur.

2. True

CH 2 Learning Check 1 2. True or False: A researcher observes that a single parent works 42.25 hours per week. The degree of accuracy of 42.25 is to the hundredths place (.01).

3. d

CH 2 Learning Check 1 3. Each of the following is a rule for the simple frequency distribution except: a. Each interval is equidistant. b. The same score cannot occur in more than one interval. c. Each interval is defined (it has a lower and an upper boundary). d. The interval width is equal to the number of intervals in a frequency distribution.

4. 5 to 20 intervals

CH 2 Learning Check 1 4. What is the recommend number of intervals that should be included in a simple frequency distribution?

5. Including an open interval can make it difficult to identify if outliers exist in a data set.

CH 2 Learning Check 1 5. Why is it generally inappropriate to include an open interval in a simple frequency distribution?

1. Cumulative Frequency Distribution

CH 2 Learning Check 2 1. A ______________ is a summary display that distributes the sum of frequencies across a series of intervals.

2. Down, up.

CH 2 Learning Check 2 2. Cumulative frequencies can be added from the top _________ and the bottom ________.

d. All of the above.

CH 2 Learning Check 2 3. When cumulating frequencies from the bottom up, you typically want to discuss the data in terms of: a. "At most" b. "Less than" c. "At or below" d. All of the above

4. True

CH 2 Learning Check 2 4. True or False: WHether you cumulate a frequency distribution from the bottom up or the top down depends on how you want to discuss the data.

Operational Definition

Dependent variables can often be measured in many ways, and therefore require an _____________ ______________.

Standard Deviations and Normal Distributions

For normal distributions with any mean and any variance, we can make the following three statements (Empirical Rule): 1. At least 68% of all scores lie within one SD of the mean 2. At least 95% of all scores lie within two SD of the mean 3. At least 99.7% of all scores lie within three SD of the mean

Chapter 1

Introduction to Statistics

Population size

N

Scales of Measurement Nominal || Ordinal || Interval || Ratio Order NO Yes Yes Yes Differ- ence NO NO Yes Yes Ratio NO NO NO Yes

Scales of Measurement Nominal || Ordinal || Interval || Ratio Order _______ ______ _______ ______ Differ- ence _______ _______ _______ ______ Ratio _______ _______ _______ ______

Chapter 2

Summarizing Data

Chapter 3

Summarizing Data Central Tendency

Chapter 4

Summarizing Data Variability

Dependent Variable (DV)

The measured variable in an experiment is referred to as the _______________ _____________ (__ __).

The Mean

The most commonly reported measure of central tendency The "balance point" in a distribution

5. The sum of the squared differences of scores from their mean is minimal (Characteristics of the Mean)

To obtain a value greater than 0, square each deviation before summing This produces the smallest possible positive number greater than 0 Larger outcomes indicate that scores deviate further from their mean

Sample size is

n