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Psychology Statistics
Chapter 1 - Introduction to Statistics statistics - The term statistics refers to a set of mathematical procedures for organizing, summarizing, and interpreting information. 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 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 population - A population is the set of all the individuals of interest in a particular study. target population - who you want to generalize to statistical population - where you get your sample from sample - A sample is a set of individuals selected from a population, usually intended to represent the population in a research study. The relationship between a population and a sample. - variable - A variable is a characteristic or condition that changes or has different values for different individuals. ex: age, sex, income 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. parameter -
the naturally occurring discrepancy, or error, that exists between a sample statistic and the corresponding population parameter. 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. 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 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 experimental research - studies that seek clues to cause-effect relationships by manipulating one or more factors (independent variables) while controlling others (holding them constant) the experimental method has two characteristics that differentiate experiments from other types of research studies: -
- 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.
- Control- The researcher must exercise control over the research situation to ensure that other, extraneous variables do not influence the relationship being examined.
2 types of experiments -
- True
- Quasi True experiments -
- True- truly random assignment to groups Participant Variables - These are characteristics such as age, gender, and intelligence that vary from one individual to another. external validity - extent to which we can generalize findings to real-world settings 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 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)
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. 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. 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 pre-post study - comparing scores before and after treatment; researcher has no control over the passage of time constructs - internal attributes or characteristics that cannot be directly observed but are useful for describing and explaining behavior. ex: profienceny in a language
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. 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. 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. 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 discrete variable -
ex: temperature in degrees Fahrenheit, at 0 you still have a temperature Convience!! 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 ( 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. 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. uppercase letter N - number of scores in a population lowercase letter n -
of scores in a sample
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= 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. 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 EX - The expression means to add all the scores for variable X. EX^2 - square each X and multiply it by the # of frequency Order of Mathematical Operations -
- Any calculation contained within parentheses is done first.
- Squaring (or raising to other exponents) is done second.
- Multiplying and/or dividing is done third. A series of multiplication and/or division operations should be done in order from left to right.
- Summation using the E notation is done next.
- Finally, any other addition and/or subtraction is done. 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
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. 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. 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. relative frequency - A ratio that compares the frequency of each category to the total. (can be a %)
Symmetrical Distribution - distribution in which the pattern of frequencies on the left and right side are mirror images of each other 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). tail of the distribution - The section where the scores taper off toward one end of a distribution is called the tail of the distribution. 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. When a score is identified by its percentile rank, the score is called a - percentile 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 how to find cumulative frequency - add each sum of preceding frequencies
.5 below what you are looking for 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= 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
- 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 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. 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 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. 3 measures of central tendency -
- Mean
- Median
- Mode 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. When can the mean be misleading? - If there is an outlier When is the best central tendency of the mean - normal distribution Sample mean - Identified by M weighted mean - The average of two means, calculated so that each mean is weighted by the number of scores it represents. 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. When is the best central tendency of the median - when you have an outlier
A display in which points connected by straight lines show several different means obtained from different groups or treatment conditions. Also used to show different medians, proportions, or other sample statistics. Measures of variability - How much the scores vary -How different are the scores in a complete set of data -How far they are from the mean (the mean is normal) we want to know how far away from normal most scores are variability - Variability 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. 3 ways to measure variability -
- Range
- Deviation Score (SD)
- Interquartile Range range - the difference between the highest and lowest scores in a distribution ex: 20k-35k find the range 35k minus 20k= 15k 15k is the range Disadvantage of using the range - When you have an outlier it gives you a misleading answer. -Doesn't represent the middle
ex: 35K,40K,40K,45K,200K Range 200k-35k= 165k is not accurate of the whole data Interquartile Range (Used with outliers) - Inter- In between Finds the range for the middle 50% Between 75% & 25% (percentile); Closer to Middle (Middle 50% - percentile) How to find interquartile - Make sure data is in order Cut the data in half Cut each half in half so find the median on each side (Split the data set into quarters (4)) Cut out first and last quarter Subtract the medians from both sides Odd set of data - Find the median and cut the data in half there not including the median score Standard Deviation (SD) - Standard= Normal Deviation= Differ Average distance of the points from the mean x- μ Measures variability- average distance of individual scores from the mean When is standard deviation the best measure of variability and why? -
