What is Statistics?  Set of methods and rules for organizing summarizing, and interpreting information 2

Population Sample Population Sample 3

Population and Sample  Population:  Population is the set of all individuals of interest for a particular study. Measurements related to Population are PARAMETERS.  Sample:  Sample is a set of individuals selected from a population. Measurements related to sample are STATISTICS. 4

Statistics  The people chosen for a study are its subjects or participants, collectively called a sample –The sample must be representative 5

Role of Statistics in Research  Selecting a Problem (Is the hypothesis clear, concise and reasonable?)  Operational Definitions of Variables  Ex. The Effects Of Watching Tv Violence On Children  Instruments  Accuracy of the Instruments  Large Variance, Good Reliability and Validity  Data Collection  Use of Statistics 6

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 MMMMy Operational Definition: 5555. person who is able to see near things more clearly than distant ones, needs to wear corrected eyeglasses prescribed (measured) by Ophthalmologist. 7

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). Or select WAIS or WISC 8

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S tatistical P ackage for the S ocial S ciences 11

Key Terms  Constant I.e. temp in learning and hunger  Variable: Any characteristic of a person, object or event that can change (vary).  IV  manipulate  DV  measure  Discrete Numbers 1, 2, 3, 14  Continues Numbers 1.3,

Key Terms  Measurement: Quantifying an observable behavior or when quantitative value is given to a behavior Quantifying an observable behavior or when quantitative value is given to a behavior 14

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 15

Hypothesis is a Research Topic  “High Cholesterol Can Cause Heart Attack” Experimental Research 16

Hypothesis is a Research Topic  “Heart Attack is related to High Cholesterol” Correlational Research 17

Key Terms  Variable: Any characteristic of a person, object or event that can change (vary).  Independent Variable, IV  Dependent Variable, DV  Constant  Discrete Numbers  Continues Numbers  Confounding Variable  Intervening Variables 18

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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 20

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. 21

Intervening Variables  A variable that explains a relation or provides a causal link between other variables.  Also called “Mediating Variable” or “intermediary variable.”  Ex. Next slide 22

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. intervening variable. It mediates the relation between income and longevity. 23

CONTINUOUS VERSUS DISCRETE VARIABLES  Discrete variables (categorical) –Values are defined by category boundaries –E.g., gender  Continuous variables –Values can range along a continuum –E.g., height 24

Role of Statistics in Research  Descriptive  VS  Inferential 25

Descriptive & Inferential Statistics  Descriptive Describes the distribution of scores and values by using Mean, Median, Mode, Standard Deviation, Variance, and Covariance Describes the distribution of scores and values by using Mean, Median, Mode, Standard Deviation, Variance, and Covariance  Inferential Infer or draw a conclusion from a sample. Infer or draw a conclusion from a sample. by using statistical procedures such as Correlation, Regression, t-test, ANOVA..etc by using statistical procedures such as Correlation, Regression, t-test, ANOVA..etc 26

Descriptive & Inferential Statistics  Scales of Measurement  Frequency Distributions and Graphs  Measures of Central Tendency  Standard Deviations and Variances  Z Score  t-Statistic  Correlations  Regressions………etc. 27

Scales of Measurement (NOIR) Scales of Measurement (NOIR) Nominal Scale QualitiesExampleWhat You Can Say What You Can’t Say labels Assignment of labels Gender— male or (male or female) female) Preference— (like or dislike) Voting record—(for or against) belongs in its own category Each observation belongs in its own category “more” or “less” An observation represents “more” or “less” than another observation 28

ORDINAL SCALE QualitiesExampleWhat You Can Say What You Can’t Say (order) Assignment of values along some underlying dimension (order) Rank in college Order of finishing a race above or below One observation is ranked above or below another. amount that one variable is more or less The amount that one variable is more or less than another 29

INTERVAL SCALE Qualities ExampleWhat You Can Say What You Can’t Say Equal distances between points “arbitrary zero” Number of words spelled correctly on Intelligence test scoresTemperature One score differs from another One score differs from another on some measure that has equally appearing intervals The amount of difference is an exact The amount of difference is an exact representation of differences of the variable being studied 30

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RATIO SCALE QualitiesExampleWhat You Can Say What You Can’t Say non- arbitrary zero Meaningful and non- arbitrary zero Absolute zero AgeWeightTime? One value is twice as much One value is twice as much as another or no quantity of that variable can exist Not much! 32

LEVELS OF MEASUREMENT  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 Level of Measurement For Example Quality of Level Ratio Rachael is 5 ’ 10 ” and Gregory is 5 ’ 5 ” Absolute zero Interval Rachael is 5 ” taller than Gregory An inch is an inch is an inch Ordinal Rachael is taller than Gregory Greater than Nominal Rachael is tall and Gregory is short Different from 33

CHAPTER 2  Frequency Distributions 34

Graphs/Charts 

Frequency Distributions and Graphs Bar 36

Frequency Distributions and Graphs Histogram 37

Polygon 38

Frequency Distributions and Graphs 39

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Mesokurtic, Normal, Platykurtic, Leptokurtic, 46

Frequency Distributions  Frequency Distributions (ƒ) FD is the number of frequencies, FD is the number of frequencies, Or when a score repeat itself in a group of scores. 47

Frequency Distributions  Frequency Distributions (ƒ) 2, 4, 3, 2, 5, 3, 6, 1, 1, 3, 5, 2, 4, 2 2, 4, 3, 2, 5, 3, 6, 1, 1, 3, 5, 2, 4, 2 Σƒ=N=14 Σƒ=N=14 Ρ=ƒ/N  Proportion Ρ=ƒ/N  Proportion %=P x 100 μ=ΣƒX/Σƒ mean for frequency distribution only %=P x 100 μ=ΣƒX/Σƒ mean for frequency distribution only 48

Frequency Distributions  Frequency Distributions (ƒ) X f fX Ρ=ƒ/N %=P x 100 Cum% X f fX Ρ=ƒ/N %=P x 100 Cum% /14=.07 7% /14=.07 7%

Frequency Distribution Table X ffX P=f/n %= px100 Cumulative % 6161/14=.077% 52102/14=.1414%21% 4282/14=.1414%35%

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=0.2x100: 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% 51

Frequency Distributions  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  %= 21% 52