Chapter 1: Displaying the Order in a Group of numbers Using Tables and Graphs

Chapter 1: Displaying the Order in a Group of numbers Using Tables and Graphs Psyc115: Psychological Statistics Ms. Rosian Mae S.P. Bermudo, RPm Objectives: At the end of this lesson, you will be going to learn the following: ✤ The Two Branches of Sta...

Chapter 1: Displaying the Order in a Group of numbers Using Tables and Graphs Psyc115: Psychological Statistics Ms. Rosian Mae S.P. Bermudo, RPm Objectives: At the end of this lesson, you will be going to learn the following: ✤ The Two Branches of Statistical Methods ✤ Some Basic Concepts ✤ Frequency Tables ✤ Histograms ✤ Shapes of Frequency Distributions ✤ Frequency Tables and Histograms Welcome to the Statistics of Psychology  Statistics - is a branch of mathematics that focuses on the organization, analysis, and interpretation of a group of numbers.  It is also the method of pursuing truth.  Psychologists use statistical methods to help them make sense of the numbers they collect when conducting research.  Psychologists usually use statistical software to carry out statistical procedures such as the ones you will learn in this book. (SPSS) The Two Branches of Statistical Methods Descriptive statistics: Inferential statistics: Psychologists use Psychologists use inferential descriptive statistics to statistics to draw summarize and describe conclusions and to make a group of numbers inferences that are based on from a research study. the numbers from a It is the procedures research study but that go for summarizing a beyond the numbers. group of scores or For example, inferential other wise making statistics allow them more researchers to make understandable. inferences about a large group of individuals based on a research study in Basic Concepts that we need to know: As part of a larger study (Aron, Paris, & Aron, 1995), researchers gave a questionnaire to students in an introductory statistics class during the first week of the course. One question asked was, “How stressed have you been in the last 21⁄2 weeks, on a scale of 0 to 10, with 0 being not at all stressed and 10 being as stressed as possible” How would you answer? What tool will you use? Basic Concepts that we need to know: In this study, the researchers used a survey to examine students’ level of stress. Other methods that researchers use to study stress include creating stress with laboratory tasks (such as having to be videotaped giving a talk for humans or swimming in water for rats) and measuring stress-related hormones or brain changes. In this example, level of stress is a variable, which can have values from 0 to 10, and the value of any person’s answer is the person’s score. If you answered 6, your score is 6; your score has a value of 6 on the variable called “level of stress.” So, What is variable? What is valueS? and What is Variable?  VARIABLE VALUES SCORE A variable is a condition or A value is just a It is the particular characteristic that can have number, such as 4, – persons value. different values, it can vary. 81, or 367.12. Example: In our example, the variable A value can also be Bermudo – 8 was level of stress, which a category, such as Glinoga- 7 can have the values of 0 male or female, or a Samper- 9 through 10. Height is a psychiatric diagnosis variable, social class is a —major depression, variable, post-traumatic stress score on a creativity test is a disorder—and so variable, type of forth. Levels of Measurement: 1. Numeric Variable 2. Equal-Interval Variable 3. Ratio Scale 4. Rank-Order Variable 5. Nominal Variable 6. Discrete Variable 7. Continuous Variable Numeric Variable  Numeric variable- variable whose values are numbers (as opposed to a nominal variable).Also called quantitative variable.  There are several kinds of numeric variables. In psychology research the most important distinction is between two types: equal- interval variables and rank-order variables. Types of Numeric Variable An equal-interval - A rank-order variable, is a variable is a variable in variable in which the which the numbers stand for approximately equal numbers stand only for amounts of what is being relative ranking. (Rank-order measured. variables are also called So, for example, a ordinal variables.) difference between stress ratings of 4 and 6 means A student’s standing in his or about as much as the her graduating class is an difference between 7 and 9. example. From its word EQUAL A rank-order variable INTERVAL provides less information than an equal-interval variable. Nominal Variable  The term nominal comes from the idea that its values are names. (Nomi-nal variables are also called categorical variables because their values are categories.) Examples are Gender (Male and Female) Psychiatric diagnosis ( PTSD, Schizophrenia, OCD) Nominal Variable  The term nominal comes from the idea that its values are names. (Nomi-nal variables are also called categorical variables because their values are categories.) Examples are Gender (Male and Female) Psychiatric diagnosis ( PTSD, Schizophrenia, OCD) Discrete Variable  A discrete variable is one that has specific values and cannot have values between the specific values. For example: The number of daily admission to a general hospital. The number of time you visited dentist in a year. Continuous Variable A continuous variable, there are in theory an infinite number of values between any two values. So, even though we usually answer the question “How old are you?” with a specific age, such as 19 or 20, you could also answer it by saying that you are 19.26 years old. Height, weight, and time are examples of other continuous variables. Knowledge Check: 15 minutes 1. A father rates his daughter as a 2 on a 7-point scale (from 1 to 7) of crankiness. In this example, (a) what is the variable, (b) what is the score, and (c) what is the range of values? 2. What is the difference between a numeric and a nominal variable? 3. Give the level of measurement of each of the following variables: (a) a person’s nationality (Mexican, Chinese, Ethiopian, Australian, etc.), (b) a person’s score on a standard IQ test, (c) a person’s place on a waiting list (first in line, second in line, etc.). 4. What is the difference between a discrete and a continuous variable? Frequency Table Frequency – number of times the students appear in the raw score. Frequency Table- It is the systematic listing of the numbers od scores of e ach value in the group studied. Why would a researcher want to make a Frequency table? Simply because, a frequency table makes it easy to see the pattern in a large group of scores. But how to do a frequency table then?.. Follow the steps next to this slide How to make a Frequency Table ❶ Make a list down the page of each possible value, from lowest to highest. ❷ Go one by one through the scores, making a mark for each next to its value on your list. ❸ Make a table showing how many times each value on your list is used. That is, add up the number of marks beside each value. ❹ Figure the percentage of scores for each value by using the formula Frequency/Total number of scores x 100 Make sure that the percentage on the table is equivalent to 100 and Frequency is equivalent to total number of population Board work Let us try to make our own frequency table: In the scale of 1-10 where 10 is the highest How stress are you right now academically ? Frequency Tables for NOMINAL Variable You will be using the same process BUT the variable is not listed as numbers but LABEL instead. *** Remember: Nominal variable has NO intrinsic order or ranking but has name or label** Group Frequen cy Table: It is a frequency table that uses Knowledge Check: 15 minutes 1. What is a frequency table? 2. Why would a researcher want to make a frequency table? 3. Make a frequency table for the following scores: 5, 7, 4, 5, 6, 5, 4. 4. What does a grouped frequency table group? Let us Check: 1. A frequency table is a systematic listing of the number of scores (the frequency) of each value in the group studied. 2. A frequency table makes it easy to see the pattern in a large group of scores. 3 4. A grouped frequency table groups the frequencies of adjacent values into intervals. Histogram It is a bar like graph of a frequency distribution in which the values are plotted along the horizontal axis and the height of each bar is the frequency of that value; the bars are usually placed next to each other without spaces, giving the appearance of a city skyline. Histogram Histogram Why researchers make histogram? Simply to show the pattern visually in the frequency table. As we can see Histogram is different from bar graph because Histograms are put next to each other with no spaces in between How to Make a Histogram ❶ Make a frequency table (or grouped frequency table). ❷ Put the values along the bottom of the page, from left to right, from lowest to highest. If you are making a histogram from a grouped frequency table, the values you put along the bottom of the page are the interval midpoints. The midpoint of an interval is halfway between the start of that interval and the start of the next highest interval ❸ Make a scale of frequencies along the left edge of the page that goes from 0 at the bottom to the highest frequency for any value. ❹ Make a bar above each value with a height for the frequency of that value. For each bar, make sure that the middle of the bar is above its value. Knowledge Check: 15 minutes 1. Why do researchers make histograms? 2. When making a histogram from a frequency table, (a) what goes along the bottom, (b) what goes along the left edge, and (c) what goes above each value? 3. Make a histogram based on the following frequency table:  4. How is a histogram based on a nominal variable different from one based on a numeric equal- interval variable? Shapes of Frequency Distribution 1. If the DISTRIBUTION has only one point or one high tower it is UNIMODAL DISTRIBUTION. 2. If a distribution has two FAIRLY equal high points, it is a BIMODAL DISTRIBUTION. 3. If the distribution has more than one peak it is known as MULTIMODAL DISTRIBUTION 4. A distribution with values of all about the same frequency is a RECTANGULAR DISTRIBUTION. Symmetrical and Skewed Distribution 1. If the pattern of the frequencies on the left and right side are mirror image, it is SYMMETRICAL DISTRIBUTION. 2. A distribution that clearly is not symmetrical is called a SKEWED DISTRIBUTION. A skewed distribution has one side that is long and spread out, somewhat like a tail. Skewed Distribution A distribution that is skewed to the right is also called POSITIVELY SKEWED. A distribution skewed to the left is also called NEGATIVELY SKEWED. When many scores pile up at the low end because it is impossible to have a lower score, the result is called a floor effect. Skewed Distribution A distribution that is skewed to the right is also called POSITIVELY SKEWED. A distribution skewed to the left is also called NEGATIVELY SKEWED. If it is peak of flat, it is compared to a normal curve, or NO SKEW. When many scores pile up at the low end because it is impossible to have a lower score, the result is called a floor effect. Ceiling effect on the other hand occurs when too large a percentage of participants achieve the highest score on a test. Kurtosis Kurtosis is how much the shape of a distribution differs from a normal curve in terms of whether its curve in the middle is more peaked or flat than the normal curve. 1997). Kurtosis comes from the Greek word kyrtos, “curve.” Kurtosis describes the “fatness” of the tails found in probability distributions.  Kurtosis Categories 1. Mesokurtic (normal) 2. Platykurtic (less than normal) 3. Leptokurtic (more than normal). Knowledge Check: 15 minutes 1. Describe the difference between a unimodal and multimodal distribution in terms of (a) a frequency graph and (b) a frequency table. 2. What does it mean to say that a distribution is skewed to the left? 3. What kind of skew is created by (a) a floor effect and (b) a ceiling effect? 4. When a distribution is described as peaked or flat, what is it being compared to?  Wrap Up: Before you go home, you should master the following: ✤ The Two Branches of Statistical Methods ✤ Some Basic Concepts ✤ Frequency Tables ✤ Histograms ✤ Shapes of Frequency Distributions ✤ Frequency Tables and Histograms