Basic STATS Basic Concepts scientific methods and apa
Basic STATS Basic Concepts scientific methods and apa style
Pp # 1 CHAPTER 1 Basic Concepts CHAPTER 2 Describing and Exploring Data Part A 2
§ Behavioral Neuroscience § "The Contribution of Medial Prefrontal Cortical Regions to Conditioned Inhibition" by Heidi C. Meyer and David J. Bucci § Journal of Comparative Psychology § "Dogs (Canis familiaris) Account for Body Orientation but Not Visual Barriers When Responding to Pointing Gestures" by Evan L. Mac. Lean, Christopher Krupeneye, and Brian Hare § Journal of Experimental Psychology: Animal Learning and Cognition § § "Stress Increases Cue-Triggered "Wanting" for Sweet Reward in Humans" by Eva Pool, Tobias Brosch, Sylvain Delplanque, and David Sander Journal of Experimental Psychology: General § "Searching for Explanations: How the Internet Inflates Estimates of Internal Knowledge" by Matthew Fisher, Mariel K. Goddu, and Frank C. Keil § Journal of Experimental Psychology: Human Perception and Performance § "What Can 1 Billion Trials Tell Us About Visual Search? " by Stephen R. Mitroff, Adam T. Biggs, Stephen H. Adamo, Emma Wu Dowd, Jonathan Winkle, and Kait Clark § Journal of Psychological Buletten : http: //www. apa. org/pubs/journals/bul/ Articles on Meta-Analysis 3
APA WRITING STYLE http: //www. apa. org/pubs/highlights/sp otlight/topic-basic. aspx http: //www. apa. org/pubs/highlights/pe eps/index. aspx
Selecting the right research topic requires critical thinking §Describe Your Expectations § You describe your expectations. It is the first step towards creating a hypothesis or a testable prediction of your results. Ex. § You might try to explain the relationship between two (or more) events or variables. You might also predict how changing one variable might affect another. 5
Selecting the right research topic requires critical thinking § Begin by reviewing your topic/hypothesis and research question; § Hypothesis is a Statement/an educated quess or the Topic of a research. Ex. 1 “Relationship between IQ and GPA. § Research Question: Is there a relationship between IQ and GPA? § Ex 2. Hypothesis/Topic: Personality and Preference for Dogs or Cats. § Research Question: Are there differences in personality between people who prefer dogs vs. cats? (descriptive question). 6
Steps in formulating a hypothesis 6 . Identify topic/ Hypothesis theory 5. generate ideas/ 4. develop and elaborate research question 3. knowledge 2. information 1. Describe expectations 7
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What is Statistics? §Set of methods and rules for ORGANIZING SUMMARIZING, and INTERPRETING information (data) 24
Population Sample 25
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Population Sample 27
Population and Sample § Population: § Population is the set of all individuals of interest for a particular study. Measurements related to Population are PARAMETERS such as population mean or standard deviation (i. e. , µ, σ). § Sample: § Sample is a set of individuals selected from a population. Measurements related to sample are STATISTICS such as sample mean and standard deviation (i. e. , M, S). Sample size calculator https: //www. danielsoper. com/statcalc/category. aspx? id=19 28
Sample § The people chosen for a study are its subjects or participants, collectively called a sample. § The sample must be representative. Representativeness refers to the degree to which the sample is similar to the population from which it is drawn. Ex. To select a sample of school children, use random sampling to avoid selecting specific type of students i. e. , only smart, rich, etc. ). Sample size Calculator: § https: //www. surveymonkey. com/mp/sample-sizecalculator/ 29
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Hypothesis educated guess/statement §Selecting a Problem to investigate or a Research Topic §The root of hypothesis is a question, which implemented in a § theory (idea). Ex. Next slide The Effects Of TV Violence On Children 34
Ex. The Effects Of TV Violence On Children Or, The relationship between tv VIOLENCE and aggression in children § Question: § DOES Tv violence CAUSE aggression in children? or § is tv violence related to aggression in children? § Running head: TV Violence and Children § Theory: Tv violence may CAUSE aggression in children or tv VIOLENCE may be related to aggression in children 35
Formulating a hypothesis § Ex. The Effects Of TV Violence On Children § Operational Definitions of Variables § Instruments used § Accuracy of the Instruments- (next slide) determined by Variance, Reliability and Validity § Data Collection § Use of Statistics § Hypothesis reasonable. should be clear, concise and 36
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OPERATIONAL DEFINATIONS § Understanding the scientific process § http: //undsci. berkeley. edu/article/0_0_0/howscienceworks_02 40
Z-score 41
Merriam Webster Dictionary and Thesaurus Definition of Short-Sighted 1. Near sighted or Myopia 2. Lacking Foresight 3. Lacking the power of foreseeing 4. Inability to look forward § My Operational Definition: § 5. person who is able to see near things more clearly than distant ones, needs to wear corrected eyeglasses prescribed (measured) by Ophthalmologist. 42
The American Heritage Dictionary § Definition of Intelligent § § 1. Having or indicating a high or satisfactory degree of intelligence and mental capacity My Operational Definition of Intelligent: § 2. Revealing or reflecting good judgment or sound thought : skillful § And is measured by the IQ score from the Stanford. Binet V IQ Test ( in the Method section of the research paper we write about the reliability and validity of this instrument). You may select other IQ tests i. e. , WAIS or WISC 43
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Hypothesis is a Research Topic § “High Cholesterol May Cause Heart Attack” Experimental Research 46
Hypothesis is a Research Topic § “Heart Attack is Related to High Cholesterol” Correlational Research 47
Hypothesis is a Research Topic § “A Causal Relationship Study of The effect of High Cholesterol on Heart Attack” SEM 48
Hypothesis is a Research Topic §A META ANALYTIC STUDY of Heart Attack and High Cholesterol 49
Hypothesis is a Research Topic Study of Heart Attack and High Cholesterol: A Meta Analysis 50
Key Terms q Measurement: Quantifying an observable behavior or when quantitative value is given to a behavior 52
Key Terms/Concepts § Variable: Any characteristic of a person, object or event that can change (vary). § Independent Variable, IV (manipulate) § Dependent Variable, DV (measure) § Constant (ex. The effect of hunger on learning) § Discrete Numbers: 1, 2 3, 17, 123 § Discrete Variables § Continues Numbers: 2. 6, 3. 5, 1. 7 § Continues Variables: § Intervening Variables § Confounding Variables 53
CONTINUOUS VERSUS DISCRETE VARIABLES § Discrete variables (categorical) § Values are defined by category boundaries § E. g. , gender § Continuous variables § Values can range along continuum § E. g. , height a 54
WHAT IS ALL THE FUSS? § Measurement should be as precise as possible. The precisions of your measurement tools will determine the precession of your research. . § In psychology, most variables are probably measured at the nominal or ordinal level § But—how a variable is measured can determine the level of precision 55
heavy drinkers die at a younger age 56
Confounding Variables § Confounding variables are variables that the researcher failed to control, or eliminate, damaging the internal validity of an experiment. Also known as a third variable or a mediator variable, can adversely affect the relation between the independent variable and dependent variable. § Ex. Next 57
Confounding Variables § Ex: A research group might design a study to determine if heavy drinkers die at a younger age. Heavy drinkers may be more likely to smoke, or eat junk food, all of which could be factors in reducing longevity. A third variable may have adversely influenced the results. 58
Intervening Variables §A variable that explains a relation or provides a causal link between other variables. § Also called “Mediating Variable” or “intermediary variable. ” § Ex. Association between income and longevity Next slide 59
Intervening Variables § Ex: The statistical association between income and longevity needs to be explained because just having money does not make one live longer. § Other variables intervene between money and long life. People with high incomes tend to have better medical care than those with low incomes. § Medical care is an intervening variable. It mediates the relation between income and longevity. 60
extraneous variables § These variables are undesirable because they add error to an experiment. A major goal in research design is to decrease or control the influence of extraneous variables as much as possible. § Ex. In a study examining the effect of postsecondary education on lifetime earnings, some extraneous variables might be gender, ethnicity, social class, genetics, intelligence, age, and so forth.
The Fidelity of Scientific Research Reliability - Dependability, replicability Validity – “True”; It is what we say it is • Internal - Within the study • External - Generalizable to the larger world 62
Reliability and validity of research 63
External & Internal Validity External validity addresses the ability to generalize your study to other people and other situations. Ex. Correlational studies. The association between stress and depression 64
Internal Validity Internal validity addresses the "true" causes of the outcomes that you observed in your study. Strong internal validity means that you not only have reliable measures of your independent and dependent variables But a strong justification that causally links your independent variables to your dependent variables (Ex. Experimental studies. The affect of stress on heart attack). attack 6 5
The Role of Statistics in Quantitative Research
Statistics for quantitative research §Descriptive §VS §Inferential 68
Example of Descriptive Research § https: //www. statistics. com/ § http: //froginapot. org/posts/corona_country_by_country_rev. html § http: //froginapot. org/posts/corona_country_by_c ountry_rev. html 69
Descriptive Stats are § Scales of Measurement § Proportion and percentile § Frequency Distributions and Graphs § Measures of Central Tendency (mean, median, and mode). § Measures of variability; Standard Deviation, Variance, range, semi-interquartile and interquartile range, stem and leaf display, etc. 70
§ Descriptive Statistics Descriptive Stats Describes the distribution of scores and values by using Measures of Central Tendency(Mean, Median, Mode), Variability (Standard Deviation, Variance), frequencies, percentile, etc. § Use in Quantitative or Qualitative research. § Three kinds of Descriptive Research: § 1. Case Study Qualitative Research § 2. Survey (using questioner) Quantitative, or Qualitative, or mixed § 3. Observational Studies Quantitative, Qualitative or Mixed 71
Descriptive Statistics § Descriptive research includes both quantitative and qualitative data and uses these types of data to describe the population being observed. For example, someone interested in why certain groups of trees are dying, while others of the same type and in the same location are thriving, can observe the trees and their surrounding environment to come to a preliminary decision. At its core, this is descriptive research. (or why some students succeed, and some don’t). 72
Descriptive Statistics 73
Descriptive Statistics 74
KEY TERMS §Incidence § Number of cases this year §Prevalence § [ˈpe-v(ə)ləns] widespread presence · generality · 75
Descriptive Statistics 76
Descriptive and Inferential research Descriptive statistics describes data (for example, a chart or graph) and inferential statistics allows you to make predictions (“inferences”) from that data. With inferential statistics, you take data from samples and make generalizations about a population. For example, you might stand in a mall and ask a sample of 100 people if they like shopping at Macy’s. You could make a bar chart of yes or no answers (that would be descriptive statistics) or you could use your research (and inferential statistics) to reason that around 75 -80% of the population (all shoppers in all malls) like shopping at Macy’s. 77
§ inferential statistics There are two main areas of inferential statistics: § Estimating parameters. This means taking a statistic from your sample data (for example, the sample mean) and using it to say something about a population (AU) parameter (i. e. , the population mean). Ex. What is the average Hight of the AU students? § Hypothesis tests. This is where you can use sample data to answer research questions. For example, you might be interested in knowing if a new cancer drug is effective (repeated measures designs). Or if breakfast helps children perform better in schools (independent measures designs). 78
Descriptive Statistics § Let’s say you have some sample data about a potential new cancer drug. You could use descriptive statistics to describe your sample, including: § Sample mean § Sample standard deviation § Making a bar chart or boxplot § Describing the shape of the sample probability distribution 79
A bar graph is one way to summarize data in descriptive statistics. Source: NIH. GOV. 80
Inferential Statistics 81
§ With inferential statistics you take the sample data from a small number of people and try to determine if the data can predict whether the drug will work for everyone (i. e. , the population). There are various ways you can do this, from calculating a z-score (zscores are a way to show where your data would lie in a normal distribution to ANOVA post-hoc (advanced statistics) testing. 82
A hypothesis test can show where your data is placed on a distribution like this one. 83
§ Inferential statistics use statistical models to help you compare your sample data to other samples or to previous research. Most research uses statistical models called the Generalized Linear model and include Student’s t-tests, ANOVA (Analysis of Variance), Regression analysis and various other models that result in straight-line (“linear”) probabilities and results. 84
Inferential Statistics are § § Z Score t-Statistic § ANOVA § Correlations § Regression. . etc. Non-paramedic tests are included. 88
Scales of Measurement/Types of DATA (NOIR) Nominal Scale Qualities Assignment of labels Example Gender— (male or female) Preference— (like or dislike) Voting record— (for or against) What You Can Say Each observation belongs in its own category What You Can’t Say An observation represents “more” or “less” than another observation 89
ORDINAL SCALE Qualities Assignment of values along some underlying dimension (order) Example Rank in college Order of finishing a race What You Can Say One observation is ranked above or below another. What You Can’t Say The amount of one variable is more or less than another 90
INTERVAL SCALE Qualities Equal distances between points “arbitrary zero” Example Number of words spelled correctly on Intelligence test scores Temperature What You Can Say What You Can’t Say One score differs from another on some measure that has equally appearing intervals The amount of difference is an exact representation of differences of the variable being studied 91
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RATIO SCALE Qualities Meaningful and nonarbitrary zero Absolute zero Example Age Weight Time? What You Can Say One value is twice as much as another or no quantity of that variable can exist What You Can’t Say Not much! 93
LEVELS OF MEASUREMENT Level of Measurement Example Quality of Level Ratio Rachael is 5’. 10” and Gregory Absolute zero is 5’. 5” Interval Rachael is 5” taller than Gregory An inch is an inch Ordinal Rachael is taller than Gregory Greater than Nominal Rachael is tall and Gregory is short Different from § Variables are measured at one of these four levels § Qualities of one level are characteristic of the next level up § The more precise (higher) the level of measurement, the more accurate is the measurement process 94
Name the scale of measurement for the ruler. 95
Test your knowledge § Test scores are which scale of measurement? § A. Nominal § B. Ordinal § C. Interval § D. Ratio 96
Frequency Distributions and Graphs Bar 97
Frequency Distributions and Graphs Histogram 98
Histogram of Test Scores 99
Quiz § Frequency distributions of test scores are frequently illustrated by which kind of graph? § a. a histogram § b. a scatterplot § c. a pie chart § d. a bar graph 100
Quiz § Frequency distributions of test scores are frequently illustrated by which kind of graph? § *a. a histogram § b. a scatterplot § c. a pie chart § d. a bar graph 101
Polygon 102
Frequency Distributions and Graphs 103
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Mesokurtic, Normal, Platykurtic, Leptokurtic, 111
Descriptive Statistics Use in descriptive Research Measures of Central Tendency 112
Measures of Central Tendency § Mean---- Interval or Ratio scale Polygon § The sum of the values divided by the number of values-often called the "average. " § μ=ΣX/N N=ΣX/μ ΣX=μ. N Add all of the values together. Divide by the number of values to obtain the mean. § Example: X X² 7 49 10 100 9 81 6 36 8 64 § ΣX= 40 ΣX²= 330 What is difference between ΣX² and (ΣX)²=1600 113
Descriptive Statistics The Sample Mean is: M or (x ) and μ=Population Mean μ=ΣX/N= 40/5=8 (7 + 9+10+6+8) / 5 = 8 114
The Characteristics of Mean § 1. Changing a score in a distribution will change the mean § 2. Introducing or removing a score from the distribution will change the mean § 3. Adding or subtracting a constant from each score will change the mean § 4. Multiplying or dividing each score by a constant will change the mean § 5. Adding a score which is same as the mean will not change the mean 115
Measures of Central Tendency § Median Middle Ordinal Scale Bar/Histogram § Divides the values into two equal halves, with half of the values being lower than the median and half higher than the median. § Sort the values into ascending order. § If you have an odd number of values, the median is the middle value. § If you have an even number of values, the median is the arithmetic mean (see above) of the two middle values. § Example: The median of the same five numbers (7, 12, 24, 20, 19) is ? ? ? . 116
Measures of Central Tendency § The median is 19. § Mode Nominal Scale Bar/Histogram § The most frequently-occurring value (or values). § Calculate the frequencies for all the values in the data. § The mode is the value (or values) with the highest frequency. § Example: For individuals having the following ages -- 18, 19, 20, 20, 21, and 23, the mode is ? ? 117
CHARACTERISTICS OF MODE § Nominal Scale § Discrete Variable § Describing Shape 118
WHEN TO USE WHICH MEASURE Measure of Central Tendency Level of Measurement Use When Examples Mode Nominal Data are categorical Eye color, party affiliation Median Ordinal Data include Rank in class, extreme scores birth order, income Mean Interval and ratio You can, and the data fit Speed of response, age in years
WHITEBOARD PRACTICE § To access and use the Whiteboard 120
WHITEBOARD PRACTICE § 1. Calculate the Mean, Median, and Mode, for the following scores 6, 5, 10, 21, 5, and 14. § 2. Calculate the Mean, Median, and Mode, for the following scores 8, 8, 19, 21, 8, 19, and 15 § 3. Calculate the Mean, Median, and Mode, for the following scores 2, 3, 2, 1, 17, 43, 16, 3, and 3 § 4. Calculate the Mean, Median, and Mode, for the following scores 22, 23, 21, 54, and 22 § 5. Calculate the Mean, Median, and Mode, for the following scores 11, 1, and 32 § 6. Calculate the Mean, Median, and Mode, for the following scores 13, 61, 8, 32, and 13 121
§Frequency Distributions 122
Frequency Distributions §Frequency Distributions(ƒ)is the number of frequencies, Or when a score repeat itself in a group of scores. 123
Frequency Distributions §Frequency Distributions (ƒ) 2, 4, 3, 2, 5, 3, 6, 1, 1, 3, 5, 2, 4, 2 Σƒ=n=14 Ρ=ƒ/n Proportion Probability %=P (100) μ=ΣƒX/Σƒ mean for frequency distribution only 124
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Frequency Distribution Table X f f. X Probability % P=f/n Px 100 Cumulative %
Frequency Distribution Table Probability % X f f. X P=f/n Px 100 Cumulative % 1 2 2 2/14=. 14 14% 2 4 8 4/14=0. 29 29% 43% 3 3 9 3/14=0. 21 21% 64%
Frequency Distribution Table Probability % X f f. X P=f/n Px 100 Cumulative % 4 2 8 2/14=. 14 14% 78% 5 2 10 2/14=0. 14 14% 92% 6 1/14=0. 07 7% 99% almost 100%
Frequency Distributions § μ=ΣƒX/Σƒ § X=2, f=4, N=14 § Ρ=ƒ/N P=4/14=. 29 § %=P x 100= 29% § X=3, f=4, N=14 § P=3/14=. 21 § Probability or %= 21% 129
How do you Calculate Cumulative Percent ? § Add each new individual percent to the running tally of the percentages that came before it. § For example, if your dataset consisted of the four numbers: 100, 200, 150, 50 then their individual values, expressed as a percent of the total (in this case 500), are 20%, 40%, 30% and 10%. § The cumulative percent would be: 1. Proportion 2. percentage § 100/500=0. 2 x 100: 20% § 200: (i. e. 20% from the step before + 40%)= 60% § 150: (i. e. 60% from the step before + 30%)= 90% § 50: (i. e. 90% from the step before + 10%) = 100% 130
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Stem-and-Leaf Displays § Stem-and-Leaf Displays is another method for displaying data with at least two significant digits. § Leading Digit are the most significant digits (Stems). § Trailing Digits are the less significant digit (Leaves). 132
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Stem-and-Leaf Displays §A stem-and-leaf display is a device for presenting quantitative data in a graphical format, similar to a histogram, to assist in visualizing the shape of a distribution. A stem-andleaf display is often called a Stemplot (popular in 70 s and 80 s). Ex. Score on a test 134
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Stem-and-Leaf Displays § Can be useful for comparing two different distributions. Such as comparing scores from men and women. § Just like frequency distribution raw data can be breakdown into smaller intervals (see p. 25 -26 text or next slide). 136
Stem plot Data can be breakdown into smaller intervals 137
Starbucks 138
SPSS 139
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S tatistical P ackage for the S S ocial ciences 144
Frequency Distributions §Frequency Distributions (ƒ) 2, 4, 3, 2, 5, 3, 6, 1, 1, 3, 5, 2, 4, 2 145
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§End of Stats for quiz 1 § Please take the quiz one on Blackboard and do your SPSS assignment 151
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