Statistics in Psychology
Points about standard deviation:
1. Adding a constant to each score does not change the standard deviation 2. Multiplying each score by a constant causes the standard deviation to be multiplied by the same constant
A survey asks people to identify their age, annual income, and marital status. For each of these three variables, identify the scale of measurement that probably is used.
1. Age and annual income are measured on ratio scales. Marital status is measured on a nominal scale.
How do you calculate the median?
1. Arrange the elements in order from smallest to largest. 2. If an odd number, the middle number is the median 3. If an even number, average the two middle numbers.
How do you calculate the standard deviation?
1. Count your elements, or number of scores. This gives you the value of N or n. 2. List them in a column 3. Add them and put the score (sigma) underneath. Placing a sigma symbol helps. This is sigma X. 4. Find your mean, and list it below sigma X. 5. Create a new column to the right of your X column, and use the formula X - mean to calculate the deviation score for each element. 6. Create a new column to the right of your deviation column, and title it X squared. Square each of your elements. (aka sum of squares) 7. Find your Sigma X squared, also known as your deviation score: add all of your values. 8. Divide by N or n-1, depending on whether population or sample. This is your variance. 9. Take the square root of Variance. This is your standard deviation.
How do you calculate the weighted mean?
1. Determine the combined sum of all the scores in both samples. 2. Determine the combined number of scores in both samples (add all scores on both sides) 3. Divide the sum of all the scores by the total number of scores
What are the characteristics of the mean?
1. Every score adds to the total 2. Every score contributes one point to the number of scores
What is the process for calculating probability? Use this information for the answer to make sense: 10 dogs exist in the study- 5 black labs: 2 male and 3 female 4 german Shepards: 1 male and 3 female 1 poodle: male
1. Identify your fractions: add the number of each element together and list as your denominator. Then, take the number of each element and use them as your respective denominators. In our example, black labs represent 5/10, with males being 2/10 and females being 3/10. German shepards would be 4/10, 1/10, and 3/10 respectively; the poodle would be 1/10. 2. Segregate your groups- if each element has two groups, you would segregate them into two groups for the purpose of counting. For example, the probability of selecting a german shephard or a female- you would take the total german shephard sample of 4/10, write it down, then take the remaining females- 3/10 and write that down. 3. Count your totals, ensuring you don't double count an element. In our example, the probability of choosing a german shephard or a female is 3/10 + 4/10, or 7/10. You don't count the female german shephards a second time. 4. Divide to get your decimal. In our example, the probability is .70.
In order to accomplish the goal of an experiment, what two characteristics differentiate experiments from other types of research studies?
1. Manipulation: The researcher manipulates one variable by changing its value from one level to another. A second variable is observed (measured) to determined 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.
What two categories of variables must researchers consider?
1. Participant variables: These are characteristics such as age, gender, and intelligence that vary from one individual to another. 2. Environmental variables: These are characteristics of the environment such as lightning, time of day, and weather conditions. A researcher must ensure that the individuals in treatment A are tested in the same environment as the individuals in treatment B.
What are three basic techniques that researchers use to control other variables?
1. Random Assignment: each participant has an equal chance of being assigned to each of the treatment conditions. 2. Matching: ensures equivalent groups or equivalent environments. Example: participants' IQ's are measured and then the participants are assigned to ensure a roughly similar IQ. 3. Holding constant. Example: keeping the participants' ages the same.
What operational definitions is Dr. Peters looking for when she asks for definitions of a story problem? She said in the study session that if she asks for it, she's looking for 2 to 3 of the five factors of operational definitions.
1. Shape of the distribution. Draw it if you need to or she asks 2. Variability- is it a fat cat or skinny cat? 3. Scale of measurement used (NOIR) 4. Measure of central tendency used (Mode, median, mean) 5. Give percentages as they relate to the sample (within one standard deviation)
When you transform every standard score (X) into a Z score, what properties will be present?
1. Shape: the shape of the z score distribution will be the same as the original distribution of raw scores. If the original distribution is negatively skewed, for example, then the z score distribution will also be negatively skewed. 2. Mean: the z score distribution will always have a mean of zero. 3. Standard deviation: The distribution of z scores will always have a standard deviation of one.
What are two facets to statistics?
1. Statistics are used to organize and summarize the information so that the researcher can see what happened in the research study and can communicate the results to others. 2. Statistics help the researcher to answer the general questions that initiated the research by determining exactly what conclusions are justified based on the results that were obtained.
What must transpire in a research study for it to be considered an experiment?
1. The manipulation of an independent variable 2. The rigorous control of other extraneous variables
What is the procedure for standardizing a distribution for creating new values for mean and standard deviation?
1. The original raw scores are transformed into z scores 2. The z scores are then transformed into new X values so that specific mean and standard deviation are attained.
What are the characteristics of a sample means?
1. The sample means should pile up around the population mean. Samples are not expected to be perfect but they are representative of the population. As a result, most of the sample means should be relatively close to the population mean. 2. The pile of sample means should tend to form a normal-shaped distribution. Logically, most of the sample should have means close to mu, and it should be relatively rare to find sample means that are substantially different from mu. As a result, the sample means should pile up in the center of the distribution (around mu) and the frequencies should taper off as the distance between M (population mean) and mu (sample mean) increases. This describes a normal-shaped distribution. 3. In general, the larger the sample size, the closer the sample means should be to the population mean, mu. Logically, a large sample should be a better representative than a small sample. Thus, the sample means obtained with a large sample size should cluster relatively close to the population mean; the means obtained from small samples should be more widely scattered.
Two points about the correct usage of summation notation
1. The summation sign Sigma is always followed by a symbol or mathematical expression. The symbol or expression identifies exactly which values are to be added. 2. The summation process is often included with several other mathematical operations, such as multiplication or squaring. To obtain the correct answer, it is essential that the different operations be done in the correct sequence.
What are the distributions on each side of the mean?
34% fall to either side of the mean. Each is 1 standard deviation 14% fall to the far side of the first standard deviation. This is 2 standard deviations 2.0% fall to the far side of the second standard deviations. This is 3 standard deviations 0.1% fall to the outer limits
When measuring height to the nearest inch, what are the real limits for a score of 68 inches?
67.5 to 68.5 inches
When measuring height to the nearest half inch, what are the real limits for a score of 68 inches?
67.75 to 68.25 inches
What is a variable?
A characteristic or condition that changes or has different values for different individuals.
What is a data set?
A collection of measurements or observations.
What is a control condition?
A condition where participants do not receive treatment. No treatment or placebo.
What is an experimental condition?
A condition where participants receive treatment. Actual treatment.
Describe the data for a correlational research study. Explain how correlational research is different from other research evaluation the relationship between two variables.
A correlational study has only one group of individuals and measures two different variables for each individual. Other research evaluating relationships between variables compares two or more different groups of scores.
What is a sampling distribution?
A distribution of statistics obtained by selecting all the possible samples of a specific size from the population.
What is symmetrical distribution?
A distribution where it is possible to draw a vertical line through the middle so that one side of the distribution is a mirror image of the other side.
What is a skewed distribution?
A distribution where the scores tend to pile up toward one side of the scale and taper off gradually at the other end. The big part is the body, the small part is the tail, the real limit of which is the Z score.
What is bimodal distribution?
A distribution with two modes. More than two is called multimodal or polymodal distribution.
What is probability?
A fraction or a proportion of all the possible outcomes. Always expressed as a DECIMAL out to two places! It is calculated this way: probability of A = (number of outcomes classified as A)/(total number of possible outcomes)
When you see the term "distribution of scores," what would be an accurate way to define it?
A frequency distribution graph.
What is a scatter plot?
A graph where each individual is represented by a point so that the horizontal position corresponds to one variable and the vertical position corresponds to the other.
What is a nonequivalent group?
A group which, by its very nature, cannot be randomly assigned, such as boy groups and girl groups: boys must go to boy groups and girls must go to girl groups. Using these equals an experiment that is not a true experiment.
What is a modified histogram?
A histogram that uses stacks of blocks instead of bars above the numbers.
What is the Experimental method?
A method that involves comparing groups of scores, also known as the experimental research strategy. Produces cause and effect relationships.
If you were interested in a score for an entire group, what would that figure be called?
A parameter.
What is a random sample?
A random sample requires that each individual in the population has an equal chance of being selected. A second requirement states that the probabilities must stay constant from one selection to the next if more than one individual is selected.
What is one problem with using samples?
A sample provides only limited information about the population. Although samples are generally representative of their populations, a sample is not expected to give a perfectly accurate picture of the whole population.
What would you call a group which participates in a study?
A sample.
What is a datum?
A score or raw score based on the measurements obtained for each individual in a study, which is based on a single measurement.
What is a sample?
A set of individuals selected from a population, usually intended to represent the population in a research study.
What is "negatively skewed?"
A skewed distribution where the majority of scores are on the high end, but the extreme scores are on the low end, bringing down the average.
What is "positively skewed?"
A skewed distribution where the majority of scores are on the low end, but the extreme scores are on the high end, bringing up the average.
What is a z score?
A standard score, which is used to identify and describe the exact location of every score in a distribution. It is sample specific, although you can relate them to other z scores by using a weighted mean.
What is a standardized distribution?
A standardized distribution is composed of scores that have been transformed to create predetermined values for the mean and standard deviation. Standardized distributions are used to make dissimilar distributions comparable.
What would the average score among a participant group be called?
A statistic.
What is central tendency?
A statistical measure to determines a single score that defines the center of a distribution. The goal of central tendency is to find the single score that is most typical or most representative of the entire group.
What is a pre-post study?
A study of participants before and after therapy or treatment. There is no way to control for the passage of time, for example. Other variables may be at play that cannot be controlled for, but are usually related to time.
What is a parameter?
A value, usually a numerical value, that describes a population. A parameter is usually derived from the measurements of the individuals in the population.
What is a statistic?
A value, usually a numerical value, that describes a sample. A statistic is usually derived from measurements of the individuals in the sample.
What is a continuous variable?
A variable divisible into an infinite number of fractional parts. Two factors apply: 1. When measuring a continuous variable, it should be very rare to obtain identical measurements for two different individuals. Because the number is infinite, two individuals would almost never have the exact same score. 2. When measuring a continuous variable, each measurement category is actually an interval that must be defined by boundaries. Example: real interval is 149.5 to 150.5, and any score that falls between them is expressed as "150." Whenever you are free to choose the degree of precision or the number of categories for measuring a variable, the variable must be continuous.
What are the purposes for a z score?
A z score transforms X values, which do not provide much information (they are called raw scores), into values can tell us exactly where the original scores are located. Also, z scores standardize an entire distribution.
Name two methods for examining the relationship between two variables
A. Correlational method B. Experimental method
What are the two general categories of statistical techniques, and what is the general purpose for the techniques in each category?
A. Descriptive: organize, simplify, summarize B. Inferential: reach general conclusions
Describe the goal of an experimental research study and identify the two elements that are necessary for an experiment to achieve its goal.
A. To determine a cause-and-effect relationship. B. Random assignment and a control group.
What is the mean?
AKA arithmetic average, it is computed by adding all the scores in the distribution and dividing by the number of scores: 1+2+3 ---------- 3
What would EX (Sigma * X) mean?
Add all of the scores for X
How do you calculate mean?
Add all the numbers in a group and divide by the number of numbers in the group (known as "n")
What is a ratio scale?
An interval scale with the additional feature of an absolute zero point. With a ratio scale, ratios of numbers do reflect ratios of magnitude. In other words, you compare one to the other and can achieve a ratio, such as a 60 inch tall child being 1.5 times the height of a 40 inch tall child.
What is frequency distribution?
An organized tabulation of the number of individuals located in each category on the scale of measurement
Define or give an example of a hypothetical construct. Explain why operational definitions are needed to define and to measure constructs.
Any label given to an emotion, such as "love." In order to understand what is meant by "love," it must be defined due to the semantics of each person involved.
How do you calculate median?
Arrange your numbers in order from smallest to largest. For an odd numbered n, take the middle number. For an even numbered n, take the two middle numbers, add them, then divide by two.
What does measurement involve?
Assigning individuals or events to categories, such as names or numerical values.
What is the name for the two perpendicular lines on a distribution graph?
Axes. The vertical is x and the horizontal y, just like we learned in Algebra.
How do we represent the number of scores in a population?
By using "N"
How do we represent the number of scores in a sample?
By using "n"
What happens to the mean when you change a score?
Changing the value of any score will change the mean. Recompute. The exception is when the new score or removed score is exactly equal to the mean.
What are environmental variables?
Characteristics of the environment such as lighting, time of day, and weather conditions.
What are particpant variables?
Characteristics such as age, gender, and intelligence that vary from one individual to another.
When the measurement procedure produces numerical scores, the statistical evaluation typically involves what?
Computing the average score for each group and then comparing the averages.
What is 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.
What is 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.
What is an interval scale?
Consists of ordered categories that are all intervals of exactly the same size. Equal differences between numbers on scale reflect equal differences in magnitude. However, the zero point on an interval scale is arbitrary and does not indicate a zero amount of the variable being measured.
What is a discrete variable?
Consists of separate, indivisible categories. No values can exist between two neighboring categories. In other words, it either "is" or "isn't." You can be one or the other, but not both.
An investigator studies how concept formation ability changes with age. Age is which kind of variable: discrete or continuous?
Continuous
A research study comparing college alcohol use in the US and Canada reports that more Canadian students drink but American students drink more (Kuo, Adlaf, Lee, Gliksman, Domers, and Wechsler, 2002). Is this study an example of an experiment? Explain.
Correlational. It's based on observation. No random assignment, no manipulation of variables, no control group.
What is a bar graph used for?
Data represented by nominal or ordinal scales
Statistical methods are classified into two major categories: descriptive and inferential. Describe the general purpose for the statistical methods in each category.
Descriptive statistics: Statistical procedures used to summarize, organize, and simplify data. Inferential statistics: Consist of techniques that allow us to study samples and then make generalizations about the populations from which they were selected.
A researcher studies the factors that determine how many children couples decide to have. The variable, number of children, is which kind of variable: discrete or continuous?
Discrete
When using nominal scales, is your variable discrete or continuous?
Discrete
Explain the difference between a discrete variable and a continuous variable. Give examples of each
Discrete: either you are or you aren't. Sex is an example: you're either a boy or you aren't. You're either a girl or you aren't. Continuous: age or other time related variables. They happen on a continuum.
How do you calculate mode?
Find the numbers in a group that repeat themselves. The one that is repeated the most is your mode (19, 81, 81, 30, 81 is Mode 81). For the same mode for different numbers (you have a mode 19 and mode 81, each repeats 4 times), you have more than one mode.
What two elements are necessary for a research study to be considered an experiment?
First, the researcher must manipulate one of the two variables being studied. second, all other variables that might influence the results must be controlled.
What is the central limit theorem?
For any population with mean mu and standard deviation (small sigma), the distribution of sample means for sample size n will have a mean of mu and a standard deviation of sd/square root of n, and will approach a normal distribution as n approaches infinity.
What is an 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. It has two components: 1. It describes a set of operations for measuring a construct. 2. It defines the construct in terms of the resulting measurements.
What happens when adding or subtracting a constant from each score?
If a constant value is added to every score in a distribution, the same constant will be added to the mean. Similarly, if you subtract a constant from every score, the same constant will be subtracted from the mean.
How does a person's z score relate to research studies?
If the individuals who receive the treatment in a research study tend to have extreme z scores, we can conclude that the treatment does appear to have an effect.
What is mode?
In a frequency distribution, the mode is the score or category that has the greatest frequency.
What is a quasi-independent variable?
In a nonexperimental study, the "independent variable" that is used to create the different groups of scores- it is "quasi" because it is not manipulated.
What is the difference between calculating standard deviation in populations and samples?
In populations, divide the sum of squares (or variance) by N; in samples (n), by n-1
Strack, Martin, and Stepper (1988) found that people rated cartoons as funnier when holding a pen in their teeth (which forced them to smile) than when holding a pen in their lips (which forced them to frown). For this study, identify the independent variable and the dependent variable.
Independent variable: holding the pen in teeth or mouth Dependent variable: Measured humor in viewing cartoons (however, if it is measured by the amount of "smiling" done, then the holding of the pen in the lips is a confound, isn't it?)
Oxytocin is a naturally occurring brain chemical that is nicknamed the "love hormone" because it seems to play a role in the formation of social relationships such as mating pairs and parent-child bonding. A recent study demonstrated that oxytocin appears to increase people's tendency to trust others (Kosfeld, Heinrichs, Zak, Fischbacher, and Fehr, 2005). Using an investment game, the study demonstrated that people who inhaled oxytocin were more likely to give their money to a trustee compared to people who inhaled an inactive placebo. For this experimental study, identify the independent variable and the dependent variable.
Independent: inhaled oxytocin Dependent: likelihood of altruistic behavior.
What are constructs?
Internal attributes or characteristics that cannot be directly observed but are useful for describing and explaining behavior, such as intelligence, anxiety, and hunger because they are intangible. Also called hypothetical constructs.
What is a drawback to the correlational method?
It can demonstrate that a relationship exists between two variables, but cannot provide an explanation for that relationship. In other words, it cannot produce a cause and effect relationship.
What is the focus of most research?
It is intended to examine the relationship between variables. To establish the existence of a relationship, researchers must make observations, or taking measurements of the two variables in question.
What are the advantages of standardizing distributions?
It makes it possible to compare different scores or different individuals even thought hey come from completely different distributions.
What is variability?
It provides a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together
In a study on perception of facial expressions, participants must classify the emotions displayed in photographs of people as anger, sadness, joy, disgust, fear, or surprise. Emotional expression is measured on which kind of scale?
Nominal
What are the four scales of measurement?
Nominal Ordinal Interval Ratio
Downs and Abwender (2002) found neurological deficits in soccer players who are routinely hit on the head with soccer balls compared to swimmers, who are also athletes but who are not regularly hit in the head. Is this an example of an experimental or nonexperimental study?
Nonexperimental: it is correlational, as no variables were manipulated.
What is the experimental method?
One variable is manipulated while another variable is observed and measured. To establish a cause and effect relationship between the two variables, an experiment attempts to control all other variables to prevent them from influencing the results.
How many variables are measured in an experiment?
Only one.
An educational psychologist classifies students as high, medium and low intelligence. What kind of scale is being used?
Ordinal
Explain the Order of Operations
PEMDAS: Parenthesis, exponents, multiplication, division, addition, subtraction. It is the order in which mathematical operations are conducted- solve in the above order.
Define the terms parameter and statistic. Be sure the concepts of population and sample are included in your definition.
Parameter: A value, usually a numerical one, that describes a population, and is usually derived from measurements of the individuals in the population. Statistic: A value, usually a numerical one, that describes a sample, and is usually derived from measurements of the individuals in the sample.
A researcher is interested in the effect of an electrolytic sports drink on the endurance of adolescent boys. A group of 30 boys is selected and half are given a treadmill endurance test while consuming the sports drink and the other half take the test while drinking the water. Define the population. Define the sample.
Population: the entire population of adolescent boys Sample: the 30 boys who were tested
What is proportion?
Proportion measures the fraction of the total group that is associated with each score. Proportion: p = f/N
What is an adequate explanation for the concept of sampling error?
Sampling error is the discrepancy between the obtained value for a sample statistic and the value for the corresponding population parameter. For example, the obtained value for a sample statistic (for example, average age of 24.2 years) compared to the actual value of the group (for example, 21.9 years. The sampling error would be 2.3 years).
What are the three characteristics that completely describe any frequency distribution?
Shape, central tendency, and variability
X Find the value of each expression for the scores 4 to the left: 6 Sigma X 0 Sigma X squared 3 Sigma (X+1) 2 Sigma (X+1) squared
Sigma X = the total of X, or 11 Sigma X squared = 121 Sigma (X+1) = 121 times the sample score minus one Sigma (X+1) squared = 121 times the square of the sample score plus one
What symbol is used to refer to the sum of a set of scores?
Sigma, which looks like a capital E with diagonal supports targeted forward. It stands for summation.
How do you find the mode?
Simply identify the score located directly beneath the highest point in the distribution.
Why do we have sample error?
Size correlates to generalizability, but they aren't truly representative of the population.
In a skewed distribution, where are the mean, median, and mode located?
Starting from the apex and working toward the tail, Mode, median, and mean.
What are descriptive statistics?
Statistical procedures used to summarize, organize, and simplify data. They take raw scores and organize or summarize them in a form that is more manageable.
How are the relationship(s) between variables for non-numerical data evaluated?
The Chi-square test.
What is a weighted mean?
The average of two different samples. To get it, you need: 1. the overall sum of the scores for the combined group 2. the total number of scores in the combined group
What are real limits?
The boundaries of intervals for scores that are represented on a continuous number line. The real limit separating two adjacent scores is located exactly between the scores. Each score has two real limits: the upper real limit and the lower real limit.
What is a scale of measurement?
The complete set of categories for a study, and the relationships between the categories determine different types of scales.
What is sampling error?
The discrepancy between a sample statistic and the corresponding population parameter. It is also known as the "margin of error." It represents the unpredictable, unsystematic differences that can exist from one sample to another.
What is range?
The distance covered by the scores in a distribution, from the smallest to the largest scores. It is completely determined by the two extreme values and ignores the other scores in the distribution. It is considered a crude and unreliable measure of variability
Loftus and Palmer (1974) conducted an experiment in which participants were shown a video of an automobile accident. After the video, some participants were asked to estimate the speed of the cars when they "smashed into" each other. Others were asked to estimate the speed when the cars "hit" each other. The "smashed into" group produced significantly higher estimates than the "hit" group. Identify the independent and dependent variables for this study.
The independent variable is the phrasing of the question and the dependent variable is the speed estimated by each participant.
Define the law of large numbers
The larger the sample size (n), the more probable it is that the sample mean will be close to the population mean.
What is the difference between a line graph and a polygonal graph?
The line graph starts at the first grouping of data and ends at the last one, whereas a polygonal graph starts at 0 and drops down to the x axis after the last group of data.
What is the difference between major and minor modes?
The major mode is the larger of two mode values, minor is the smaller of the two.
What happens when you multiply or divide each score by a constant?
The mean changes the same way.
What is the expected value of M?
The mean of the distribution of sample means always is identical to the population mean.
What is the median?
The midpoint of a list in a distribution ordered from smallest to largest. The median has no symbols or notation. It defines the middle of a distribution. The mean does not (hence, the skew in some distributions)
In bimodal distribution, where are the mean, median, and mode located?
The modes are at the apex of each side, with the mean and median at the low point of the valley between the two.
What is standard deviation?
The most commonly used and the most important measure of variability: it provides a measure of the standard, or average, distance from the mean, and describes whether the scores are clustered closely around the mean or are widely scattered.
Normally, you can use all three measures of central tendency for all but one of the scales of measure. Which scale cannot use all three, and which measure of central tendency must you use?
The nominal scale can only use mode as its measure of central tendency- it uses labels, not numerical values.
What are raw scores?
The original, unchanged scores obtained in a research study. Scores for a particular variable are represented by the letter X.
What is data?
The plural of datum, where multiple measurements or observations are made.
What is meant by symmetrical distribution?
The right hand side of the graph is a mirror image of the left hand side. If a distribution is perfectly symmetrical, the median is exactly at the center because exactly half of the area in the graph will be on either side of the center. The mean is also exactly at the center.
What is a sample score?
The score an individual received upon measurement.
What is a polygon graph?
The second way to express interval or ratio data. A dot is placed above each number on the x axis, and they are connected by a line, which produces a polygon. Note: a line must connect 0 and the highest group along the x axis. Can also be used with data that have been grouped into class intervals. To do this, the midpoint must be used, which means the midpoint must be calculated: Midpoint: average the highest and lowest scores in the interval. If the interval is 20 to 29, the midpoint would be 24.9
What is a population?
The set of all the individuals of interest in a particular study.
What is the standard error of M?
The standard deviation of the distribution of sample means (small sigma M). The standard error provides a measure of how much distance is expected on average between a smaple mean (M) and the population mean (mu).
What is the sum of squares?
The sum of the squared deviation scores.
What is the definition of statistics?
The term statistics refers to a set of mathematical procedures for organizing, summarizing, and interpreting information.
What is an independent variable?
The variable manipulated by the researcher. Treatment conditions to which the participants are assigned.
What is a dependent variable?
The variable measured by the researcher. Used to obtain scores.
What are inferential statistics?
They consist of techniques that allow us to study samples and then make generalizations about the populations from which they were selected.
Why are scales of measurement important?
They influence the kind of statistics that can and cannot be used. For most statistical applications, the distinction between an interval scale and a ratio scale is not important because both scales produce numerical values that permit us to compute differences between scores, to add scores, and to calculate mean scores. On the other hand, measurements from nominal or ordinal scales are typically not numerical values and are not compatible with many basic arithmetic operations. Therefore, alternative statistical techniques are necessary for data from nominal or ordinal scales of measurement.
Researchers have observed that high school students who watched educational television programs as young children tend to have higher grades than their peers who did not watch educational television. Is this study an example of an experiment? Why or why not?
This study could be correlational or nonexperimental, but it is definitely not an example of a true experiment. The researcher is simply observing, not manipulating, the amount of educational television.
What is the goal of the experimental method?
To demonstrate a cause and effect relationship between two variables. In other words, an experiment attempts to show that changing the value of one variable causes changes to occur in the second variable.
What is the goal of a researcher when he/she finishes examining the sample?
To generalize the results back to the entire population.
What is the Correlational method?
Two different variables are observed to determine whether there is a relationship between them. Also known as the correlational research strategy.
How many minimum variables exist for an independent variable?
Two, as it must have two to be considered a variable. If one, it is a constant.
What is a histogram?
Used for interval or ratio data. A bar graph where all bars touch each other. The height corresponds to frequency and the width corresponds to the real limits, or magnitude.
What are statistical procedures?
Usually shortened to the word "statistics," statistical procedures are mathematical procedures used for research in the behavioral sciences. They help ensure that the information or observations are presented and interpreted in an accurate and informative way. They provide researchers with a set of standardized techniques that are recognized and understood throughout the scientific community.
What is open ended distribution?
When there is no upper or lower limit for one of the categories.
When is the best time to use a median score?
When you have an undetermined value.
When should you use the median measure of central tendency?
When you have skewed distribution, when using an ordinal scale, or when chunks of data are missing
What is useful about measurements from an ordinal scale?
With measurements from an ordinal scale, you can determine whether two individuals are different and you can determine the direction of difference. However, they do not allow you to determine the magnitude of the difference between two individuals.
There are two scores for each individual when observations are made in a study. How are the data usually presented or labeled?
X and Y
Ford and Torok (2008) found that motivational signs were effective in increasing physical activity on a college campus. Signs such as "step up to a healthier lifestyle" and "an average person burns 10 calories a minute walking up the stairs" were posted by the elevators and stairs in a college building. Students and faculty increased their use of the stairs during times that the signs were posted compared to times when there were no signs. a. Identify the independent and dependent variables for this study. b. What scale of measurement is used for the independent variable?
a) Independent: Signs Dependent: Stair usage b) Most likely ordinal: a ranking of which group used more.
Two researchers are both interested in the relationship between caffeine consumption and activity level for elementary school children. Each obtains a sample of n = 20 children. a) The first researcher interviews each child to determine the level of caffeine consumption. The researcher then records the level of activity for each child during a 30 minute session on the playground. Is this an experimental or a nonexperimental study? Explain b) The second researcher separates the children into two roughly equivalent groups. The children in one group are given a drink containing 300 mg of caffeine and the other group gets a drink with no caffeine. The researcher then records the level of activity for each child during a 30 minute session on the playground. Is this an experimental or nonexperimental study? Explain.
a) Nonexperimental (correlational) study. No manipulation of variables. b) Experimental study. Random assignment and manipulation of variables.
X Find the the value of each expression for the 4 scores to the left: 2 Sigma X 1 Sigma X squared 5 (Sigma X) squared Sigma (X -1)
a) Sigma X= the total of X, or 8 b) Sigma X squared = the square of the total of X, or 64. c) (Sigma X) squared = the square of the total of X, or 64. d) (Sigma X) squared - Sigma (X-1) = 64 times the sample score minus one
In an experiment examining the effects of humor on memory, Schmidt (1994) showed participants a list of sentences, half of which were humorous and half were nonhumorous. The participants consistently recalled more of the humorous sentences than the nonhumorous sentences. a. Identify the independent variable for this study b. What scale of measurement is used for the independent variable? c. Identify the dependent variable for this study. d. What scale of measurement is used for the dependent variable?
a) The sentence list b) Nominal: sentences/words c) Ordinal: ordering, or who recalled more d) Nominal
What are the 4 rules for construction of a grouped frequency distribution table?
a) Try to have 10 groups to avoid sample error b) The width of each interval should be a relatively simple number c) The bottom score in each class interval should be a multiple of the width d) All intervals should be the same width
A researcher would like to evaluate the claim that large doses of vitamin C can help prevent the common cold. One group of participants is given a large dose of the vitamin (500 mg per day), and a second group is given a placebo (sugar pill). the researcher records the number of colds each individual experiences during the 3 month winter season. a) Identify the dependent variable for this study b) Is the dependent variable discrete or continuous? c) What scale of measurement (NOIR) is used to measure the dependent variable?
a) dependent variable is the number of colds experienced by participants during the 3 month winter season. b) continuous: the number of colds is being measured, not a "you either have a cold or you don't" kind of thing. c) Ratio: a score of 0 is possible.
How do you compute percentage from proportion?
percentage: p(100) = (f/n)*100
What is the distribution of sample means?
the collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population.
What is sampling error?
the natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter.