Psychology Statistics

Nominal scales of measurement

"Name" A nominal scale consists of a set of categories that have different names. Measurements on a nominal scale label and categorize observations, but do not make any quantitative distinctions between observations. ex: names of groups ex: majors (bio, chemistry, art) quantitive example (room # 101 or 102) however we can't draw conclusions about size or label them

Ordinal scales of measurement

"Order" An ordinal scale consists of a set of categories that are organized in an ordered sequence. Measurements on an ordinal scale rank observations in terms of size or magnitude. ex: ranks (1st, 2nd, 3rd)

lowercase letter n

# of scores in a sample

Relative frequency percentage

% form of frequency "What percent are going to eat 8 cupcakes" To find percentiles, we must convert these frequencies into percentages.. 8/36 x 100 relative % = frequency/total x 100 divide the # you want by the total #

You can use statistics to

- Study the relationship between two variables - To examine the difference between 2 or more groups (who differ on a certain variable) - How confident can we be about such differences

Claim: Eating blueberries improves memory Why might you be skeptical?

-Could've been a coincidence -Could've been linked to another variable -Blueberries are expensive, people who purchased them are rich, maybe have better education

What can effect external validity

-composition ex: smoking sample is using umass Dartmouth students, umassd may not correctly represent all smokers (age, length, educational) -weather -time of day -lab sight ex: may behave differently in front of a lab scientist -controlled setting

Order of Mathematical Operations

1. Any calculation contained within parentheses is done first. 2. Squaring (or raising to other exponents) is done second. 3. Multiplying and/or dividing is done third. A series of multiplication and/or division operations should be done in order from left to right. 4. Summation using the E notation is done next. 5. Finally, any other addition and/or subtraction is done.

the experimental method has two characteristics that differentiate experiments from other types of research studies:

1. Manipulation- The researcher manipulates one variable by changing its value from one level to another. In the Polman et al. (2008) experiment examining the effect of violence in video games (Figure 1.5), the researchers manipulate the amount of violence by giving one group of boys a violent game to play and giving the other group a nonviolent game. A second variable is observed (measured) to determine whether the manipulation causes changes to occur. 2. Control- The researcher must exercise control over the research situation to ensure that other, extraneous variables do not influence the relationship being examined.

3 measures of central tendency

1. Mean 2. Median 3. Mode

A frequency distribution can be structured either as a table or as a graph, but in either case, the distribution presents the same two elements:

1. The set of categories that make up the original measurement scale. 2. A record of the frequency, or number of individuals in each category.

2 types of experiments

1. True 2. Quasi

True experiments

1. True- truly random assignment to groups

quasi-independent variables

2. Quasi- if you cannot randomly assign to groups ex: Female & Male Variables that aren't manipulated by the experimenter but that are treated as though they were manipulated on purpose.

discrete variable

A discrete variable consists of separate, indivisible categories. No values can exist between two neighboring categories. ex: on a dice theres no # in between 7 & 8 ex: cat and dog ex: male v female -nominal and ordinal data is discrete -you would use bar graph bc it has spaces in between which means its indivisible

Comparing frequency table to stem & leaf

A frequency distribution would tell you only the frequency, not the specific values. This advantage can be very valuable, especially if you need to do any calculations with the original scores. For example, if you need to add all the scores, you can recover the actual values from the stem and leaf display and compute the total. With a grouped frequency distribution, however, the individual scores are not available.

parameter

A parameter is a value, usually a numerical value, that is a characteristic of a population or describes it. A parameter is usually derived from measurements of the individuals in the population. ex: The parameter is the average height of all women aged 20 years or older.

population

A population is the set of all the individuals of interest in a particular study.

relative frequency

A ratio that compares the frequency of each category to the total. (can be a %)

sample

A sample is a set of individuals selected from a population, usually intended to represent the population in a research study.

skewed distribution

A skewed distribution with the tail on the right-hand side is positively skewed. Bc the higher scores pull it to the right. If the tail points to the left, the distribution is negatively skewed (see Figure 2.11).

a statistic

A statistic is a value, usually a numerical value, that describes a sample. A statistic is usually derived from measurements of the individuals in the sample. ex: The statistic is the average height of 63.9 inches from the sample of 45 women.

Chi-square test

A statistical method of testing for an association between two categorical variables. Specifically, it tests for the equality of two frequencies or proportions. - Tests for goodness of fit

continuous variable

A variable (such as age, test score, or height) that can take on a wide or infinite number of values. histogram bc bars touch, continuous

variable

A variable is a characteristic or condition that changes or has different values for different individuals. ex: age, sex, income

Explain why operational definitions are developed for constructs

Although constructs such as intelligence are internal characteristics that cannot be directly observed, it is possible to observe and measure behaviors that are representative of the construct. For example, we cannot "see" intelligence but we can see examples of intelligent behavior. The external behaviors can then be used to create an operational definition for the construct. An operational definition defines a construct in terms of external behaviors that can be observed and measured. For example, your intelligence is measured and defined by your performance on an IQ test, or hunger can be measured and defined by the number of hours since last eating.

nonequivalent control group design

An independent-groups quasi-experiment that has at least one treatment group and one comparison group, but *participants have not been randomly assigned to the two groups*

Bar Graph

Bar Graphs A bar graph is essentially the same as a histogram, except that spaces are left between adjacent bars. For a nominal scale, the space between bars emphasizes that the scale consists of separate, distinct categories. For ordinal scales, separate bars are used because you cannot assume that the categories are all the same size. To construct a bar graph, list the categories of measurement along the X-axis and then draw a bar above each category so that the height of the bar corresponds to the frequency for the category. An example of a bar graph is shown in Figure 2.7.

Measures of central tendency

Central = middle Tendency = generally or typically = Typical score in distribution (which falls in the middle) Helps to establish what a normal score is The purpose of central tendency is to determine the single value that identifies the center of the distribution and best represents the entire set of scores. The three standard measures of central tendency are the mode, the median, and the mean.

data or datum?

Data (plural) are measurements or observations. A data set is a collection of measurements or observations. A datum (singular) is a single measurement or observation and is commonly called a score or raw score.

When is the best central tendency of the mode

For data measured on a nominal scale, the mode is the appropriate measure of central tendency

Does puppies affect stress? How to go about this experiment

Have 2 groups Group 1= puppy therapy (IV) its whats being maniuplaed Group 2= nothing (control group) (DV) Questions- How often are they playing w them/ location/ what they do w the puppy/ kinds of puppies Results Group 1 has a stress level of 30 and group 2 has a score of 70 If the puppy therapy works group 1 has less stress

histograms (#'s)

Histograms to construct a histogram, you first list the numerical scores (the categories of measurement) along the X-axis. Then you draw a bar above each X value so that The height of the bar corresponds to the frequency for that category. For continuous variables, the width of the bar extends to the real limits of the category. For discrete variables, each bar extends exactly half the distance to the adjacent category on each side.

Sample mean

Identified by M

When can the mean be misleading?

If there is an outlier

control condition

Individuals in a control condition do not receive the experimental treatment. Instead, they either receive no treatment or they receive a neutral, placebo treatment. The purpose of a control condition is to provide a baseline for comparison with the experimental condition.

experimental condition

Individuals in the experimental condition do receive the experimental treatment.

how inferential statistics and descriptive statistics is used in a typical research study

Inferential statistics start with a sample and then generalizes to a population. This information about a population is not stated as a number. Descriptive statistics are very important because if we simply presented our raw data it would be hard to visulize what the data was showing, especially if there was a lot of it. Descriptive statistics therefore enables us to present the data in a more meaningful way, which allows simpler interpretation of the data. -graphs -charts

Chapter 1

Introduction to Statistics

explain how sampling error creates the fundamental problem that inferential statistics must address

It is very unlikely that the statistics obtained for a sample will be identical to the parameters for the entire population. This is the basic concept of sampling error: sample statistics vary from one sample to another and typically are different from the corresponding population parameters.

identify the two components of an operational definition

Note that an operational definition has two components. -First, it describes a set of operations for measuring a construct. -Second, it defines the construct in terms of the resulting measurements.

Variable X

Scores for a particular variable are typically represented by the letter X. For example, if performance in your statistics course is measured by tests and you obtain a 35 on the first test, then we could state that x=35

greek letter E

The Greek letter sigma, or E, is used to stand for summation. To find this in a frequency distribution you need to take the value of X and look at its F and multiply

weighted mean

The average of two means, calculated so that each mean is weighted by the number of scores it represents.

cumulative frequencies

The cumulative frequencies show the number of individuals located at or below each score. -That score and everything below it -Top # should equal # of participants -When you graph a cumulative frequency the bars should get higher

EX

The expression means to add all the scores for variable X.

difference between interval and ratio scales

The factor that differentiates an interval scale from a ratio scale is the nature of the zero point. An interval scale has an arbitrary zero point. That is, the value 0 is assigned to a particular location on the scale simply as a matter of convenience or reference. In particular, a value of zero does not indicate a total absence of the variable being measured. For example a temperature of Fahrenheit does not mean that there is no temperature, and it does not prohibit the temperature from going even lower. Interval scales with an arbitrary zero point are relatively rare.

Mean

The mean is the arithmetic average. It is computed by adding all the scores and then dividing by the number of scores. Conceptually, the mean is obtained by dividing the total EX equally among the number of individuals (N or n). Mean is a balance point bc if you subtract the average from every point of data and then add them up it should equal 0. -Identified by the symbol μ, -For skewed distributions, the mean is pulled toward the extreme scores in the tail.

Median

The median is the midpoint of a distribution of scores. The median is used when there are undetermined (infinite) scores that make it impossible to compute a mean. Finally, the median is the preferred measure of central tendency for data from an ordinal scale.

Mode

The mode is the most frequently occurring score in a distribution. It is easily located by finding the peak in a frequency distribution graph. It is possible for a distribution to have more than one mode. For skewed distributions, the mode is located toward the side where the scores pile up

Ratio scales of measurement

The numerals have equal intervals, and when the value of zero truly means nothing. If you have a ratio scale when you have 0 of something nothings there. ex: 0 kids. This makes it possible to compare measurements in terms of ratios. ex: a gas tank with 10 gallons (10 more than 0) has twice as much gas as a tank with only 5 gallons (5 more than 0). Also note that a completely empty tank has 0 gallons. To recap, with a ratio scale, we can measure the direction and the size of the difference between two measurements and we can describe the difference in terms of a ratio.

Interval scales of measurement

The numerals represent equal intervals between levels, and there is not a true zero. ex: temperature in degrees Fahrenheit, at 0 you still have a temperature Convience!!

The rank or percentile rank

The rank or percentile rank of a particular score is defined as the percentage of individuals in the distribution with scores at or below the particular value.

apparent limits

The score values that appear as the lowest score and the highest score in an interval. ex: a class interval of 40-49 contains scores at 39.5 and 49.5

tail of the distribution

The section where the scores taper off toward one end of a distribution is called the tail of the distribution.

statistics

The term statistics refers to a set of mathematical procedures for organizing, summarizing, and interpreting information.

Environmental Variables

These are characteristics of the environment such as lighting, time of day, and weather conditions.

Participant Variables

These are characteristics such as age, gender, and intelligence that vary from one individual to another.

stem and leaf display

This technique, called a stem and leaf display, requires that each score be separated into two parts: The first digit (or digits) is called the stem, and the last digit is called the leaf. For example, X=85 would be separated into a stem of 8 and a leaf of 5. Similarly, X=42 would have a stem of 4 and a leaf of 2. To construct a stem and leaf display for a set of data, the first step is to list all the stems in a column. For the data in Table 2.3, for example, the lowest scores are in the 30s and the highest scores are in the 90s, so the list of stems would be

polygon graph

To construct a polygon, you begin by listing the numerical scores (the categories of measurement) along the X-axis. Then, A dot is centered above each score so that the vertical position of the dot corresponds to the frequency for the category. A continuous line is drawn from dot to dot to connect the series of dots. The graph is completed by drawing a line down to the X-axis (zero frequency) at each end of the range of scores. The final lines are usually drawn so that they reach the X-axis at a point that is one category below the lowest score on the left side and one category above the highest score on the right side. An example of a polygon is shown in Figure 2.5.

Identify when it is useful to set up a grouped frequency distribution table, and explain how to construct this type of table for a set of scores.

When a set of data covers a wide range of values, it is unreasonable to list all the individual scores in a frequency distribution table. Consider, for example, a set of exam scores that range from a low of x=41 to a high of x=96 . These scores cover a range of more than 50 points.

confounded

Whenever a research study allows more than one explanation for the results, the study is said to be confounded because it is impossible to reach an unambiguous conclusion.

normal distribution

a bell-shaped curve, describing the spread of a characteristic throughout a population -very few low scores, very few high scores, most fall in the middle

how to find cumulative frequency

add each sum of preceding frequencies Cumulative frequencies indicate the number of individuals located in or below each category (class interval). To find these frequencies, begin with the bottom interval, and then accumulate the frequencies as you move up the scale. For this example, there are 4 individuals who are in or below the 5-9 interval . Moving up the scale, the 10-14 interval contains an additional 9 people, so the cumulative value for this interval is (simply add the 9 individuals in the interval to the 4 individuals below). Continue moving up the scale, cumulating frequencies for each interval.

interpolation

an estimation of a value within two known values in a sequence of values

lower real limit

at the bottom of the interval .5 below what you are looking for

pre-post study

comparing scores before and after treatment; researcher has no control over the passage of time

inferential statistics

consist of techniques that allow us to study samples and then make generalizations about the populations from which they were selected.

Variable Y

dependent or response variable ex: For example, a test score could be a dependent variable because it could change depending on several factors such as how much you studied, how much sleep you got the night before you took the test, or even how hungry you were when you took it. Usually when you are looking for a relationship between two things you are trying to find out what makes the dependent variable change the way it does.

Symmetrical Distribution

distribution in which the pattern of frequencies on the left and right side are mirror images of each other

random assignment

each participant has an equal chance of being assigned to each of the treatment conditions.

matching

ensures equivalent groups or equivalent environments. For example, the researcher could match groups by ensuring that every group has exactly 60% females and 40% males.

cumulative percentage

ex: 22 people are going to eat 5 cupcakes or fewer, what percent will eat 5 or fewer? 22/36 = 61% 36 is the total # of people and 22 people will eat 5 or fewer

internal validity

extent to which we can draw cause-and-effect inferences from a study (how we perform the study) does it make sense? ex: testing for IQ -taking there foot size to test their IQ intelligence (doesn't make sense) -taking a standardized test to test their IQ intelligence (makes sense)

external validity

extent to which we can generalize findings to real-world settings

Remember, when the scores are whole numbers, the number of rows is determined by

highest-lowest + 1

When the data consist of numerical scores that have been measured on an interval or ratio scale, there are two options for constructing a frequency distribution graph. The two types of graphs are called

histograms and polygons.

operational definition

identifies a measurement procedure (a set of operations) for measuring an external behavior and uses the resulting measurements as a definition and a measurement of a hypothetical construct. Note that an operational definition has two components. First, it describes a set of operations for measuring a construct. Second, it defines the construct in terms of the resulting measurements. (How are you measuring the experiment exactly) ex: For example, your intelligence is measured and defined by your performance on an IQ test, or hunger can be measured and defined by the number of hours since last eating.

constructs

internal attributes or characteristics that cannot be directly observed but are useful for describing and explaining behavior. ex: profienceny in a language

A frequency distribution

is an organized tabulation of the number of individuals located in each category on the scale of measurement. -# of times a score occurs -allows you to see the location of any individual score relative to all of the other scores in the set. -It is customary to list categories from highest to lowest -frequency ALWAYS go on the y axis

grouped frequency distribution table

needed when the range of scores is large, causing a regular frequency table to have too many entries in the score categories

level of measurements (4)

nominal, ordinal, interval, ratio

When is the best central tendency of the mean

normal distribution

uppercase letter N

number of scores in a population

When a score is identified by its percentile rank, the score is called a

percentile

upper real limit

sometimes, a value for X represents an entire interval at the top of the interval .5 above what you are looking for

EX^2

square each X and multiply it by the # of frequency

descriptive statistics

statistical procedures used to summarize, organize, and simplify data. -Only DESCRIBING ex: 5 ppl Chinese, 10 Caucasian, 4 African American

nonexperimental research

studies in which the researcher collects data without introducing an intervention; also called observational research

experimental research

studies that seek clues to cause-effect relationships by manipulating one or more factors (independent variables) while controlling others (holding them constant)

class intervals

the categories used in the frequency distributions for interval-ratio variables

sampling error (SE)

the naturally occurring discrepancy, or error, that exists between a sample statistic and the corresponding population parameter.

independent variable

the variable that is manipulated by the researcher. In behavioral research, the independent variable usually consists of the two (or more) treatment conditions to which subjects are exposed. The independent variable consists of the antecedent conditions that were manipulated prior to observing the dependent variable.

dependent variable

the variable that is observed to assess the effect of the treatment.

correlational research

two different variables are observed to determine whether there is a relationship between them, however they do not provide and explanation for the relationship (cause&effect) -nothing is being manipulated -used when studies are unethical such as abuse

When is the best central tendency of the median

when you have an outlier

statistical population

where you get your sample from

target population

who you want to generalize to