PSY 1003 Study GoodNotes.pdf

Chapter 1 Terms Variables Coding - The procedure of converting a nominal or categorical variable to a numeric value. Continuous Variable - A variable measured along a continuum at any place beyond the decimal point, allowing for measurement in fractional units. Datum (Raw Score) - A sing...

Chapter 1 Terms Variables Coding - The procedure of converting a nominal or categorical variable to a numeric value. Continuous Variable - A variable measured along a continuum at any place beyond the decimal point, allowing for measurement in fractional units. Datum (Raw Score) - A single measurement or observation, usually referred to as a score or raw score. Dependent Variable (DV) - The variable that is measured in each group of a study and is believed to change in the presence of the independent variable. Independent Variable (IV) - The variable that is manipulated in an experiment, remaining unchanged between conditions being observed. Quasi-independent Variable - A pre-existing variable that differentiates groups or conditions being compared in a research study. Qualitative Variable - Varies by class, often represented as a label to describe non-numeric aspects of phenomena. Discrete Variable - Measured in whole units or categories not distributed along a continuum. Procedures Descriptive Statistics - Procedures used to summarize, organize, and make sense of a set of scores (data). Inferential Statistics - Procedures that allow researchers to infer or generalize observations made with samples to a larger population. Scales Equidistant Scale - A set of numbers distributed in equal units. Interval Scale - Measurements with no true zero, distributed in equal units (e.g., Likert scores, temperature). Nominal Scale - Measurements where a number is assigned to represent something, typically categorical variables. Ordinal Scale - Measurements where values convey order or rank. Ratio Scale - Measurements that have a true zero and are distributed in equal units. Research Experiment - The use of methods and procedures to make observations while controlling conditions to isolate cause-and-effect relationships. Levels of Independent Variable - Specific conditions of the independent variable in research. Population Parameter - A characteristic (usually numeric) that describes a population, such as the mean score. Random Assignment - A procedure to ensure participants have an equal chance of being assigned to a group or condition. Statistical Terms Sample - A set of individuals, items, or data selected from a population of interest. Sample Statistic - A characteristic (usually numeric) that describes a sample. Sample Statistic - A characteristic (usually numeric) that describes a sample. Scales of Measurement - Identify how the properties of numbers change with different uses; four scales include nominal, ordinal, interval, and ratio. True Zero - The value 0 truly indicates nothing or the absence of the phenomena being measured. General Concepts Data - A set of scores, measurements, or observations, typically numeric. Research Method - A set of systematic techniques used to acquire, modify, and integrate knowledge concerning observable phenomena. Scientific Method - See Research Method. Science - The study of phenomena through observation, evaluation, interpretation, and theoretical explanation. Statistics - A branch of mathematics used to summarize, analyze, and interpret a group of numbers or observations. Chapter 1 Term Quiz Q1 __________ describe(s) characteristics in a population, whereas _________ describe(s) characteristics in a sample A1 Parameter; Statistics Q2 _________ is a procedures used that allow researchers to infer or generalise observations made with samples to the larger population from which they were selected A2 Inferential Statistics Q3 An experiment is the use of methods and procedures make observations in which a researcher fully controls the conditions and experiences of participants by applying three required elements of controls (_______, _______ and _________) A3 Randomisation, Manipulation, Comparison/Control Q4 Descriptive statistics are procedures used to ________, _________, and make sense of a set of scores called data. A4 Summarise; Organise Q5 The dependent variable (DV) is the variable that is ________ and is believed to ________ in the presence of the _________ Q5 Measured; Change; Independent Variable Q6 List the four types of variables A6 Nominal, Ordinal, Discrete and Continuous Q7 __________ is a pre-existing variable that is often a characteristic inherent to an individual, which differentiates the groups or conditions being compared in a research study. Because the level of the variable are pre-existing, it is not possible to __________ A7 A Quasi-Independent Variable; Manipulate or Randomly; Assign Participants to Groups Q8 A _________ is the most informative scale of measurement. List the four characteristics of it. A8 Ratio Scale List: Scale for classification and order, Having equal, Meaningful intervals, A true zero Chapter 1 Exercises Q1 ______ statistics summarize data to make sense or meaning of a list of numeric values. A1 Descriptive Q2 A researcher would like to study the population of local high school students to observe a behavioral phenomenon; however, he does not have access to the entire population. Instead he only has access to a sample of students at the school. Which set of procedures should the researcher use to interpret the data they collect from the sample of students? A2 inferential statistics Q3 Having read in a science magazine that an average college student receives 35 hr of sleep in a week, a researcher wants to study the average amount of sleep college students get in a week. She visits their local college and randomly recruit 30 students and asks how much (in hours) they sleep in a week. She finds out that the average college student, among the group she studied, received 40 hours of sleep. What is the population parameter from the following example? A3 35 hr of sleep Q4 A researcher wants to study a population of 70 monkeys at their local zoo. Since he is interested in studying the entire population of monkeys at the zoo, how many monkeys should the researcher include in their study? A4 all 70 monkeys because all 70 make up the population Q5 A researcher is trying to determine the difference in types of variables. She determines two variables in her study are the location of a presenter in a room and the amount of students paying attention to the lecture. From these two variables, which is the independent variable of the study? A5 the location of a presenter in a room Q6 A researcher wants to measure differences in happiness between single people and married couples. What type of research method should the researcher use? A6 quasi-experimental Q7 A researcher measures the effectiveness of sleep on test performance. He randomly assigns participants to one of the three groups (2 hr, 4 hr, and 6 hr). After the participants awoke, they were immediately given an exam. What type of research method did the researcher use? A7 experimental Q8 A researcher wants to measure differences in recall by gender. What research method will the researcher use for his study? A8 quasi-experimental Q9 A researcher measures the amount of time students spent watching television and doing school work. If the data points for the amount of time students spend watching television are recorded 4, 6, and 8 on the x-axis while their corresponding time doing school work are 6, 4, and 2 on the y-axis, what can we infer about the relationship between these variables? A9 As the amount of time students watch television increases, the amount of time doing school work decreases. Q10 A researcher measures the effect of caffeine on test performance at a local college. She randomly assigns 30 students to one of the three groups (normal, decaf, and water) and later administers an exam, measuring test performance by how many questions the students answered correctly. What was the control group of the study? A10 ——— Q11 A movie critic wants to rank local movie theaters based on the quality of the theater. Which scale of measurement will the critic use? A11 ordinal Q12 A track coach measures the duration of time each runner on his team takes to complete a mile. What type of variable is he measuring? A12 continuous Q13 A track coach measures the duration of time each runner on his team takes to complete a mile. What type of variable is he measuring? A13 qualitative Q14 A teacher was interested in learning the opinion of his students about the way he taught the class. To do so, he hands out surveys asking questions on how the student feels about the class. The questions are structured with ratings (a scale from 1 to 5). What type of data will the teacher receive from his students? A14 quantitative Q15 A professor measures the temperature (degrees Fahrenheit). For this example, is temperature a continuous or discrete variable? Quantitative or qualitative? A15 continuous; quantitative Q16 A researcher collects hunger ratings from 15 students randomly assigned into one of the three groups (Group A, Group B, and Group C). As he enters data by column into SPSS to double check his written work, he notices that he forgot to label the columns. The same researcher who collected the hunger ratings decides that he wants to enter his data by row rather than by column. He already has his columns relabeled (Group 1, Group 2, and Group 3) however has removed his data for hunger ratings in each group. Starting from the variable view tab, what steps should the researcher take to switch from columns to rows? A16 While in the variable view tab, delete his labels for each group in the name column; then in the first column, type groups. Click on the decimal column in the same row and change the value to 0. Now click on the values column and enter 1 in the value cell and Group A in the label cell, then click the plus sign. Do the same for the other groups with 2 and 3 in the value and label cell. Click OK. Next, type hunger ratings in the column under groups in the name column. Click over into the data view tab. In the column labeled groups, enter the values 1, 2, and 3 to categorize the participants into Group A, Group B, and Group C, respectively. Now reenter his data for hunger ratings in its allocated column in accordance with its group. Q17 A researcher enters data by row into SPSS. One of the variables in her study, Group, has three levels (Group 1, Group 2, and Group 3). She already has “Group” in the name column but has forgotten what to do next. Starting from the variable view tab, what steps must she take to code for her groups? A17 Click on the values column and enter 1 in the value cell and Group 1 in the label cell then click the plus sign. Do the same for the other groups with 2 and 3 in the value and label cell. Then click OK. Q18 Parameters describe how a population is characterized. A18 True Q19 An ordinal scale is the most informative scale of measurement. A19 False Q20 A discrete variable can be measured in whole units or fractional units. A20 False Q21 The types of data researcher’s measure fall into two categories: (1) quantitative or qualitative and (2) scales and graphs. A21 False Q22 There are three ways to enter data into SPSS: (1) enter data by rows, (2) enter data by columns, and (3) enter data manually. A22 False Q23 What are two characteristics of rating scales that allow researchers to use these values on an interval scale of measurement? A23 Values on an interval scale are assumed to be equidistant but do not have a true zero. Q24 To conduct a study using the experimental method which requirement must be met? A24 all of these (randomisation, manipulation, comparison) Q25 __________ describe(s) characteristics in a population, whereas ____________ describe(s) characteristics in a sample. A25 Parameters; statistics Chapter 2 Terms Distributions Cumulative frequency distribution - a summary display that distributes the sum of frequencies across a series of intervals. Cumulative percent distribution - A summary displays that distributes the sum of relative precents across a series of intervals Cumulative relative distribution - A summary displays that distributes the sum of relative frequencies across a series of intervals. Relative frequencies can be added or cumulated from the bottom up or the top down in a frequency distribution Frequency distribution - a summary display for a distribution of data or organised or summarised in terms of how often a category, score, or range of scores occurs Relative frequency distribution - a summary display that distributes the proportion of scores occurring in each interval of a frequency distribution. It is computed as the frequency in each interval divided by the total number of frequencies recorded. Relative percent distribution - a summary display that distributes the percentage of scores occurring in each class interval relative to all scores distributed. Simple frequency distribution - 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. Graphs Bar chart (bar graph) - A graphical display used to summarise the frequency of discrete and categorical data that are distributed in whole units or classes; also called a bar graph Pie chart - a graphical display in the shape of a circle that is used to summarize the relative percent of discrete and categorical data into sectors. Frequency polygon - A dot-line graph used to summarise the frequency of continuous data at the midpoint of each interval Ogive - a dot-and-line graph used to summarize the cumulative percent of continuous data at the upper boundary of each interval. Histogram - a graphical display used to summarize the frequency of continuous data that are distributed in numeric intervals. Data Grouped data - a set of scores distributed into intervals, where frequency of each score can fall into any given interval Ungrouped data - a set of scores or categories distributed individually, where the frequency for each individual score or category is counted. Boundaries Interval boundaries - the upper and lower limits for each interval in a grouped frequency distribution. Lower boundary - the smallest value in each interval of a grouped frequency distribution. Upper boundary - the largest value in each interval of a grouped frequency distribution. Others Interval - a discrete range of values within which the frequency of a subset of scores is contained Interval width (Class width) - the range of values contained in each interval of a grouped frequency distribution; also called class width. Open class (Open interval) - an interval with no defined upper or lower boundary; also called an open class. Outliers - extreme scores that fall substantially above or below most of the scores in a particular data set. Percentile point - the value of a score on a measurement scale below which a specified percentage of scores in a distribution fall. Percentile rank - the percentage of scores with values that fall below a specified score in a distribution. Proportion - a part or portion of all measured data. The sum of all proportions for a distribution of data is 1.0. Real range - one more than the difference between the largest and smallest values in a data set. Sector - the particular portion of a pie chart that represents the relative percentage of a particular class or category. To find the central angle for each sector, multiply each relative percent by 3.6. Chapter 2 Term Quiz Q1 The _______ is the smallest value in each interval of frequency distribution; the ________ is the largest value in each interval of a frequency distribution A1 Lower Boundary; Upper Boundary Q2 The ________________ is one more than the difference between the largest and smallest value in a data set A2 Real Range Q3 A ___________ is the number of times or how often a category, score, or range of scores occurs A3 Frequency Q4 __________________ is a summary display that distributes the percentage od scores occurring in each interval relative to all scores distributed A4 Relative Percent Distribution Q5 _______ are extreme scores that fall substantially above or below most of the scores in a particular data set A5 Outlier Q6 ___________ is a summary display that distributes the proportion of scores in each interval. It is computed as the frequency in each interval divided by the total number of frequency recorded A6 Relative Frequency Distribution Q7 __________ of a score is the percentage of scores with values that fall below a specified score in a distribution A7 Percentile Rank Q8 An ogive is a dot-and-line graph used to summarise the _______ of continuous data at the upper boundary of each interval A8 Cumulative Percent Q9 _________ is a summary display that distributes the sum of relative percents across a series of intervals A9 Cumulative Percent Distribution Q10 A __________ is a dot-and-line graph used to summarise the frequency of continuous data at the midpoint of each interval A10 Frequency Polygon Q11 ________ are a set of scores or category distributed individually, where the frequency for each individual score or category is counted A11 Ungrouped Data Q12 _______ summarise graphically the frequency of continuous data that are quantitative A12 Histograms Q13__________ is a summary display that distributes the sum of frequencies across a series of intervals A13 Cumulative Frequency Distribution Q14 A bar chart, or bar graph, is a graphical display used to summarise frequency of ______ and _______ data that are distributed in whole units or classes A14 Discrete; Categorical Chapter 2 Exercises Q1 Using five intervals, what is the interval width? A1 13 Q2 Use the data in the table to answer the following questions. A2 22 Q3 Use the data in the table to answer the following questions. Which equation would equal the relative frequency of one interval used in the cumulative frequency distribution given? A3 8/45 Q4 Using the cumulative frequency distribution given, what equation would equal the relative frequency for the Interval 2130? A4 5/25 Q5 Using the relative frequency distribution above, what is the relative percent of the Interval 110? A5 16 Q6 Using the relative frequency distribution, what is the total relative percent? A6 100% Q7 Using the relative frequency distribution above, from the top down, what is the cumulative relative frequency of the Interval 2130? A7 0.63 Q8 Using the relative frequency distribution given, what is the total cumulative percent? A8 100% (give or take rounding errors) Q9 If a restaurant was to score in the 90th percentile in an upcoming top restaurant review, what does this mean in comparison to all other restaurants reviewed? A9 This result means that the restaurant scored higher than 90% of all other restaurants reviewed. Q10 A researcher is constructing a frequency polygon. Her first interval has a lower boundary of 24 and an upper boundary of 38. On the x-axis, where will the midpoint of this interval fall? A10 31 Q11 A teacher has completed the construction of a cumulative percent frequency distribution. He now wants to summarize his distribution visually. What type of graph should he use to do this? A11 Ogive Q12 A teacher states that if a student increase the amount of hours they study per day (hours per day), the higher their grade point average (on the 4.0 grading scale) will be. Based on the scatter gram below, what can we confirm about this claim? A12 Increased hours spent studying is associated with a higher grade point average. Q13 Although it is uncommon to do, a researcher wants to construct a frequency table in SPSS. They have already entered in a label in the name column and entered in their values in the data view tab. Starting in the data view tab, what steps must they now follow to complete their frequency table? A13 Go to the menu bar and click analyze, then descriptive statistics and frequencies, to bring up a dialog box. Move the labeled name into the variable box. Make sure the display frequencies box is checked, then select paste. Q14 A group of researchers want to classify the learning styles of 100 students at a local college as being verbal, visual, logical, or physical. To do this, they implement classes teaching a different topic using different learning styles which is immediately followed by a quiz. Based on the exam scores, they classified 30 students as verbal learners, 35 as visual, 15 as logical, and 20 as physical. The researchers have already entered in categories in the name column and frequencies in the second row and have reduced the value to 0 in the decimal column. Starting from the variable view tab, how would the researchers go about coding the data for the different categories? A14 Click on the values column and click on the small gray box with three dots. In the dialog box, click the plus sign to enter 1 in the value cell and students in the label cell, and then click the plus sign to repeat the steps by entering 2 for researchers, 3 for classes, and 4 for quiz scores. Now select ok. Q15 What type of data is used to construct a histogram in SPSS? A15 Quantitative Q16 The recommended number of intervals is between 5 and 20. A16 True Q25 A25 Q17 If a researcher wanted to discuss his data in terms of at or above, they would summarize their data using a bottom up cumulative frequency table. A17 False Q18 An ogive is a graphical display used to summarize the frequency of continuous data that are distributed in numeric intervals (grouped). A18 False Q19 To construct a pie chart, data are distributed as relative A19 True Q20 When making a histogram in SPSS, we typically want to make sure that the display frequency box remains unchecked. A20 True Q21 The range of scores in each interval of a grouped frequency distribution is called the ______. A21 Interval width Q22 State the problem with this simple frequency distribution A22 The class intervals overlap Q23 A researcher finds that 12 persons in a sample of 60 reported getting between 4 and 6 hr of sleep per night. What is the relative percentage for this interval? A23 20% Q24 The following is a simple frequency distribution table. Suppose we convert this table to a cumulative frequency distribution. The frequencies in each interval of the cumulative frequency distribution would be A24 It is not possible to summarize the data using a cumulative frequency distribution. Q25 The following is a simple frequency distribution table. If we convert this frequency distribution to relative percentages, which of the following gives the corresponding relative percentages in each interval listed from the top down? A25 20%, 13%, 17%, 33%, 17% Chapter 3 Terms Others Central Tendency - Statistical measures for locating a single score that is most representative or descriptive of all scores in a distribution - Examples include the mean, the median, and the mode. Median - The middle value in a distribution of data listed in numeric order Mode - The value in a data set that occurs most often or most frequently Population Size (N) - The number of individuals that constitute an entire group or population Sample mean (M or x) - The sum of a set of scores in a sample, decided by the total number of scores summed Sample size (n) - The number of individuals that constitute a subset of those selected from a larger population Population mean - The sum of a set of scores in a population, decided by the total number of scores summed Distribution Unimodal distribution - A distribution of scores, where one score occurs most often or most frequently - A unimodal distribution has one mode Skewed distribution - A distribution of scores that includes outliers or scores that fall substantially above or below most other scores in a data set Nonmodal Distribution (Rectangular) - A distribution of scores with no mode; hence, all scores occur at the same frequency; also called a rectangular distribution Normal Distribution (Gaussian/Symmetrical/Ball-Shaped) - A theoretical distribution with data that are symmetrically distributed around the mean, median, and mode; also called a symmetrical, Gaussian, or bell-shaped Bimodal Distribution - A distribution of scores in which two scores occur most often or most frequently - A bimodal distribution has two modes. Modal Distribution - A distribution of scores I which one or more scores occur most often or most frequently Multimodal Distribution - A distribution of scores in which more than two scores occur most often or most frequently - A multimodal distribution has more than two modes Means Mean (Arithmetic Mean/Average) - The sum of a set of scores in a distribution, divided by the total number of scores summed; also called an arithmetic mean or average Weighted Mean (MW) - The combined mean of two or more groups of scores, where the number of scores in each group is disproportionate or unequal Skews Positively Skewed - A distribution of scores that includes one or a few scores that are substantially larger (towards the right tail in a graph) than most other scores Negatively skewed - A distriution of scores that includes one or a few scores that are substantially smaller (toward the left tail in a grade) than most other scores - distribution Chapter 3 Exercises Q1 A psychologist records the number of bar presses by a group of rats (N = 8) to receive food. This is only a portion of rats the researcher is interested in. The psychologist records the following number of bar presses: 5, 3, 8, 2, 9, 7, 4, and 5. A psychologist records the number of bar presses by a group of rats (N = 8) to receive food. This is only a portion of rats the researcher is interested in. The psychologist records the following number of bar presses: 5, 3, 8, 2, 9, 7, 4, and 5. What type of mean should the psychologist compute? A1 Sample mean Q2 A psychologist records the number of bar presses by a group of rats (N = 8) to receive food. This is only a portion of rats the researcher is interested in. The psychologist records the following number of bar presses: 5, 3, 8, 2, 9, 7, 4, and 5. What is the mean of the number of bar presses? A2 5.37 Q3 What is the mode of the following list of scores: 5, 5, 5, 3, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 9, 9, 2, 2, 5, 5, 2, 2, 7, 8, 7, 7, 7, 7, 7, 3, 3, 5, 5, 5, 5, 7, 7, 3, 3, 3, 3, 3, 6, 6, 6, 6, 7, 8, 8, 8, 8? A3 6 Q4 What type of modal distribution can we infer from the following list of scores: 5, 5, 5, 3, 6, 6, 6, 6, 8, 8, 8, 9, 9, 2, 2, 5, 5, 2, 2, 7, 8, 7, 7, 7, 7, 7, 3, 3, 5, 5, 5, 7, 7, 3, 3, 3, 3, 3, 6, 6, 6, 6, 8, 8, 8, 8? A4 Multimodal Q5 A grade school teacher measures the height (in inches) of her students for a class project. The scores of her 12 students are 45, 41, 47, 41, 43, 41, 40, 42, 48, 39, 47, and 48. Which measure of central tendency is most appropriate for describing these data? A5 Median Q6 Use the data in the table to answer the following questions. A soccer coach records the length of time (in minutes) his players take to run a full mile. Based on the data given above, which measure of central tendency is most appropriate for describing the data? A6 Mean Q7 Looking at the table, what scale of measurement describes the data? A7 Ratio Q8 The dean of a local college wants to identify students by their class year (freshman, sophomore, junior, and senior). Based on this scale of measurement, which measure of central tendency is most appropriate for describing the data? A8 Mode Q9 The who’s who of yelp wants to rank local restaurants. Based on this scale of measurement, which measure of central tendency is most appropriate for describing the data? A9 Median Q10 Looking at the graph below, what type of modal distribution summarizes the data? What is the mean/median? A10 Bimodal; 2 Q11 A teacher is entering her student’s exam score into an online gradebook. After calculating the mean (M = 86), she remembers that each student had turned in an assignment for 5 bonus points added to their overall exam score. If the teacher adjusts each student’s score, what is will be the new mean? A11 91 Q12 A researcher’s monkeys are driving her bananas. She is trying to find the mean for how many bananas each monkey eats. At first, she calculates the mean to be 9; however, as soon as she does, a monkey eats another banana for a total of 11. While updating the mean, another monkey eats a banana for a total of 2. During this time, in what ways did the mean change? A12 Increased; increased Q13 A college professor is having a problem entering student’s grades into an online gradebook. At first, he calculates the mean to be 78; however, he notices that he is missing a score of 89. Once he inputs this value, the mean is now 82. He then notices that he put two of the same score of 82, so he deletes one and then adds the proper score of 76. Finally, he believes his gradebook is in order. Throughout this process, in what ways did the mean change? A13 Increased; no change; decreased Q14 Summing the squared difference of each score from its mean produces a minimal solution. A14 True Q15 The mean describes data that are positively skewed A15 False Q16 The mean and median tend to be at the center of bimodal distributions. A16 True Q17 The median is used to describe an ordinal scale of measurement. A17 True Q18 The mode is the only central tendency that has a zero point. A18 False Q19 Which of the following will increase the value of the mean? A19 Delete a score below the mean (None of the above, Add a score exactly equal to the mean, Add a score below the mean) Q20 The mean is a preferred descriptive statistic: A20 All of the above (For summarizing ratio scale measures, For summarizing interval scale measures, For describing normal distributions) Q21 Which type of modal distribution would not be described using the mode? A21 Nonmodal Q22 When the mean is greater than the mode, the distribution is negatively skewed. A22 False Q23 What is the median for the following distribution of numbers: 5, 2, 9, 7, 5, 6, 3, 10, 1 (n = 9)? A23 5 Q24 The median is used to describe what type of distributions? A24 Skewed Q25 The mode is typically used to describe data that are normally distributed and on a scale of data that indicates direction only such as ranked or ordinal scales of measurement. A25 False Chapter 3&4 Term Quiz Q1 The _______ is the middle value in a distribution of data listed in numeric order A1 Median Q2 The mean for a set of scores in an entire population is referred to as a _______; the mean for a sample (or subset of scores from a population) is referred to as a_______ A2 Population mean; sample mean Q3 Measures of _________ are statistical measures for locating a single score that is most representative or descriptive of all scores in a distribution A3 Central Tendancy Q4 A ____________ is a distribution of scores that includes outliers or scores that fall substantially above or below most other scores in a data set A4 Skewed Distribution Q5 ___________ have more than two modes where _____________have no mode at all. A5 Multimodal Distribution; Nonmodal Distribution Q6 The ______ is typically used to describe data distributions that are skewed and measures on an ordinal scale A6 Median Q7 The ______________ is a symmetrical distribution in which scores are similarly distributed above and below the mean, the median, and the mode at the centre of the distribution A7 Normal Distribution Q8 The ______ is the sum of a set of scores in a distribution, divided by the total number of scores summed A8 Mean Q9 The ______ is the largest value (L) minus the smallest value (S) in a data set A9 Range Q10 The _____ is the value in a data set that occurs most often or most frequently A10 Mode Q11 A ________________ is distribution of scores that includes one or a few scores that are substantially smaller (toward the left tail in a graph) than most other scores A11 Negatively Skewed Q12 The ___________ is the range of values between the upper (Q3) and lower (Q1) quartiles of a data set A12 Interquartile Range Q13 _________________ is a measure of the dispersion or spread of scores in a distribution and ranges from 0 to ∞+ A13 Measuring Variability Chapter 4 Terms Variance - A measure of variability for the average squared distance that scores deviate from their mean Population Variance (S2) - 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 known Sample Variance (s2 or SD2) - 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 Standard Deviation (Root Mean Square Deviation) - A measure of variability for the average distance that scores deviate from their mean - It is calculated by taking the square root of the variance - Also called the Root Mean Square Deviation) Population Standard Deviation (σ) - A measure of variability for the average distance that scores in a population deviate from their mean - It is calculated by taking the square root of the population variance Sample Standard Deviation (s or SD) - A measure of variability for the average distance that scores in a sample deviate from their mean - It is calculated by taking the square root of the sample variance Interquartile Range (IQR) - The range of values between the upper (Q3) and lower (Q1) quartiles of a data set Semi-Interquartile Range (SIQR) - A measure of half the distance between the upper quartile (Q3) and lower quartile (Q1) of a data set, computed by dividing the IQR in half - Also called a Quartile Deviation Range - The difference between the largest (L) and the smallest (S) value in a data set Quartiles - Divide data evenly into four equal parts Variability - A measure of the dispersion or spread of scores in a distribution - It ranges from 0 to + ∞ Examples include the range, the variance, and the standard deviation Computational Formula for variance (Raw Scores Method For Variance) - A way to calculate the population variance and the sample variance without needing to sum the squared differences of scores from their mean to compute the SS in the numerator - Also called the raw scores method Definitional Formula For Variance - A way to calculate the population variance and sample variance that requires summing the squared differences of scores from their mean to compute the SS in the numerator Sum of Squares (SS) - The sum of the squared deviations of scores from their mean - SS is the numerator in the variance formula Chebyshev’s Theorem - Defines the percent of data from any distribution that will be contained within any number of standard deviations from the mean, where SD>1 Empirical Rule - A rule that states that for data that are normally distributed - At least 99.7% of data lie within 3 SD of the mean - At least 95% of data lie within 2 SD of the mean - At least 68% of data lie within 1 SD of the mean Degrees of Freedom (df) - For a T distribution are equal to the degrees of freedom for sample variance for a given sample: n-1 - Each distribution is associated with specified degrees of freedom - As sample size increases, the degrees of freedom also increase Degrees of Freedom (df) for Sample Variance - The number of scores in a sample that are free to vary - All scores except one are free to vary in a sample: n-1 Deviation - The difference of each score from its mean - Denoted (X- µ) for a population and denoted (x-M) for a sample Biased Estimator - Any sample statistic, such as a 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 Unbiased Estimator - Any sample statistic obtained from a randomly selected sample that equals the value of its respective population parameter on average Chapter 4 Exercises Q1 Use the data in the table to answer the following questions. A research assistant measures the number of bat presses (per week) that a small population of lab rats press for food. Looking at the table below, what is the range of daya in the population? A1 48 Q2 Usr the data in the table to answer the following questions Looking at the table for Q1, what is the interquartile range? A2 23 Q3 Use the data in the table to answer the following questions Looking at the table for Q1, if the research assistant was told only to record the sample of rats in Group B, what is the interquartile range of data in this sample? Q3 23.5 Q4 A college professor records the time (in minutes) his students take, in two separate classes, to complete an exam. This information is seen in the table above. Using the definitional formula, what is the population variance and standard deviation? A4 166.68; 12.91 Q5 Use the data of Q4. Looking at the table, what is the sample variance and standard deviation of Class A? A5 224. 1; 14.96 Q6 A researcher calculates his population variance to be -37. What does this tell us about the variability in his data? A6 It tells us nothing because his σ is meaningless. Q7 A behavioral therapist measures fear response in a sample of 40 participants. To measure the variance of fear response, he computes SS = 230. In this example, what is the variance and standard deviation? A7 5.89; 2.43 Q8 In the previous question, what are the degrees of freedom for the sample? Q8 39 Q9 In the value of SS stays constant, what will happen to the sample variance if the degrees of freedom is increased? A9 Decrease Q10 A student visits a population of five local restaurants (N = 5) and rates each as follows: 4, 3, 6, 4, and 8. Using the computational formula, what is the SS and σ^2 What is the standard deviation of the population? A10 16; 3.2; 1.78 Q11 A teacher measures test anxiety in a sample of students in her class. She records the number of times a student twitches during a test. Using the computational formula, what is the SS and sample variance? A11 54; 6 Q12 In calculating the sample variance, a professor finds that the sample variance is less than the population variance. What might be the reason for this? A12 When calculating the sample variance, he divided the SS by n Q13 Which of the following is a characteristic of the standard deviation? A13 The value for the standard deviation is affected by the value of each score in a distribution. Q14 A researcher plots two standard deviations above the mean in a normal distribution. According to the empirical rule, what percentage of scores is the researcher accounting for? A14 95% Q15 The sample variance will be less than the population variance on average making it a biased estimator; however, if we divide SS by n 1, this will ensure that the sample variance equals the population variance on average thereby making it an unbiased estimator. A15 True Q16 When the sample variance is computed as SS divided by df, it will underestimate the population on average. A16 False Q17 When the scores are concentrated near the mean, the standard deviation is small. A17 True Q18 For skewed distributions, 99.7% of data will fall within the three standard deviations of the mean. A18 False Q19 A researcher has a measure of 10 scores. The range is 720 and the smallest score is 15. What is the largest score? A19 735 Q20 If the scores not listed in the previous example were as follows: 15, 22, 24, 28, 30, 34, 36, 40, and 42. What can we infer about the data set? A20 The data contain an outlier Q21 What do the following symbols (σ^2 SS, s^2) represent in inferential statistics? A21 Population Variance, Sum of Squares, Sample Variance Q22 What is the second reason for why the sample variance and population variance are computed differently? A22 All scores in a sample are free to vary except one, when the mean is known. Therefore, we divide SS by df for sample variance. Q23 A researcher measures the following bar presses: 5, 7, 9 (SD = 1.63). If the researcher, wanting to misreport his findings, multiplies each score by 3, what will the standard deviation be? A23 4.89 Q24 Each of the following is a characterestic of standard deviation exept: A24 The standard deviation is used to descrive qualitative variables (Characterestic of standard deviation: Are almost always reported with the mean. is affected by the value of every score in a distribution, is always positive) Q25 A researcher records the sound (in decibels) during a series of lessons taught by a substitute teacher at a local elementary school. In his study, he found that the sound was 80 ± 6 (M ± SD) decibels. Assuming the data are normally distributed, which of the following is an appropriate conclusion? A25 At least 95% of classes were between 68 and 92 decibels  Chap 125 Descriptive Summary - Inferential Sample - Central Tendancy Typical- Mean Average - Median - Middle Mode - Frequent Variability - How scores differ Difference between lowest Range highest to - Interquartile Range (IQR) - 50 % (Ignore excessive) Outlier - Excessive. variance & Standard deviation - Bullet Target , how spread out Probability - Assessing Lilihood Sample Space All the possibility - Normal Distribution - Most common > - Bell-Curve Standard Deviation- 2 scores - How different from Standard Deviation - Comparing different things with Standard "Normal" - Based on data (Despite idealialistics) T test -  Formulas Population Mean (M) - The sum of scores (x) divided by N > - [x/N Sample mean (M) - IS - I Weighted Mean (WMI