Statistics Variable Anything that can have more than one value ie. Height, weight, sex, IQ, video games Constant Anything that remains the same ie. Study on females (females remains constant) Statistics cont. Utilizes the organization of raw data that has already been collected Expressed in different ways: 1. Histogram (Bar graph) x axis (abscissa) - horizontal y axis (ordinate) - vertical 2. Pie Chart 3. Polygon (Line graph) Which class performed better? Class A Class B 90 90 75 85 60 45 % on test % on test 80 30 15 75 0 Ss 1 Ss2 Ss3 Ss4 Ss1 Ss2 Ss3 Ss4 Measurement Scales Nominal Scale: numbers are used to name or categorize (ie. Sports uniforms, gender,driver’s licence) Ordinal Scale: numbers represent serial position (ie. Finish in a race, rankings, level of aggression) Measurement Scales cont. Interval Scale: consistent units if measurement and equal spacing between units (no true zero point) ie. Celcius Ratio Scale: Same as interval, but has absolute zero point ie. Weight, height, time, distance Types of Statistics Descriptive Statistics - A statistic to describe behaviour - ie. SAT scores Inferential Statistics - A statistic that explains behaviour - Bandura’s Bobo doll experiment on aggression - example: t-test or ANOVA (analysis of variance) Measures of Central Tendencies A single score that represents a whole set of scores Mode: Most frequently occurring score Median: Middle score (half above and below) Mean: Arithmetic average (most widely used) Skewed statistics When the data is not distributed evenly, atypical scores can mislead the data Always be aware of the measure of central tendency that people are reporting Income data $20,000 $22,000 $23,000 $28,000 What is the Mode? $34,000 $38,000 $41,000 What is the Median? $42,000 $44,000 $85,000 $90,000 What is the Mean? $210,000 $210,000 Normal Curve (Bell Curve) Theoretical or hypothetical frequency of scores 68% between 1 and -1 SD 95% between 2 and -2 SD 99% between 3 and -3 SD Examples: height, weight, IQ Variability The amount of variability between scores tells us the reliability of the data The lower the variability the more reliable the results Basketball player example Range: The gap between the lowest and the highest score Crude estimate of variability based on extreme scores Standard Deviation - Standard measurement of how the scores in a distribution deviate from the mean - Better way to assess level of variability between scores - Represented by lower case s - ie. UBC vs. Kwantlen entrance marks who has the smaller SD? When is an observed difference reliable? 1. Representative vs. Biased Sample Is it random and large enough? 2. Less variable observations are more reliable 3. More cases are better ie. Assessing which school is better? Statistical Significance - Statistical statement of how likely it is that an obtained result occurred by chance - p<.05 - “beyond a reasonable doubt” - indicates the likelihood the result will happen by chance - Does not indicate IMPORTANCE of result - ie. IQ between first born and second born Reliability & Validitiy Reliability is the extent to which an experiment, test, or any measuring procedure yields the same result on repeated trials. Validity refers to the degree to which a study accurately reflects or assesses the specific concept that the researcher is attempting to measure. Reliability & Validity While reliability is concerned with the accuracy of the actual measuring instrument or procedure, validity is concerned with the study's success at measuring what the researchers set out to measure. Reliability & Validity Correlation Coeffiecient Measures relationship between two variables - data must be interval or ratio Pearson Product-Moment Correlation is represented by small case r remember… If anything is paid attention to in our schools, colleges, and universities, thinking must be it. Unfortunately, thinking can be lazy. It can be sloppy….It can be fooled, misled, bullied... Students possess great untrained and untapped capacities for logical thinking, critical analysis, and inquiry, but these are capacities that are not spontaneous: They grow of wide instruction, experience, encouragement, correction, and constant use. Experiment Information: The Nestle Inc. authoritatively states that Smarties are 25% pink, 20% green, 15% brown,15% yellow, 15% orange, and 10% purple. This distribution is important for “quality control”. Is this true? Are they that accurate? Sample Three random boxes of mini Smarties. All boxes are still originally sealed and have not been tampered with. Design a data sheet and complete your data collection. (Ensure that you complete your data before premature subject mortality occurs!) Convert raw data into percentages Hypothesis Develop a hypothesis based on the distribution of the data you collected Proving your hypothesis Join up with two other classmates and integrate your data. Is your hypothesis still right? Do you have a new hypothesis?
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