Introduction & Basic Concepts
description
Transcript of Introduction & Basic Concepts
![Page 1: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/1.jpg)
Introduction & Basic ConceptsPSYC 2101
![Page 2: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/2.jpg)
What is Measurement?• Strict definition: “any method by which a
unique and reciprocal correspondence is established between all or some of the magnitudes of a kind and all or some of the numbers...”– Magnitude: a particular amount of an
attribute– Attribute: a measurable property
![Page 3: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/3.jpg)
Example
length |---Y---Y--Y----Y--------------->numbers<---|---+---+--+----+---------------> 0 2 4 5½ 8
![Page 4: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/4.jpg)
Loose Definition: • “the assignment of numerals to objects or
events according to rules” (presumably any rules). A numeral is any symbol other than a word.
![Page 5: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/5.jpg)
The Nominal Scale of Measurement
• The function of nominal scales is to classify - are arbitrarily assigned to name.
• Does not meet the criteria of the strict definition of measurement.
• Given two measurements, I can determine whether they are the same or not.
• Write you Banner ID on your paper money and put it in this bag.
![Page 6: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/6.jpg)
Ordinal Scale of Measurement
• the objects/events are arranged in serial order with respect to the property measured, that order is identical to the order of the measurements.
• Given ordinal data on two objects, we can state whether they have equal amounts of the attribute measured or, if not, which has the greater amount.
![Page 7: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/7.jpg)
• The most common type of ordinal scale is that of rank order.
• I throw those bills out the window. My associate, outside, my associate, outside, ranks the students in order of how long it took them to retrieve their money, where rank 1 belongs to the student who most quickly retrieved her money.
![Page 8: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/8.jpg)
Ranks are Ordinal Data
Minutes | 1 3 4 7 12 TIME |-Y---Y-Y-----Y---------Y----->RANK | 1 2 3 4 5• For the ranks, we can say that 3 represents
more time than 1, but we cannot honestly say that the difference between rank 3 and rank 1 (3 minutes) is the same as the difference between rank 5 and rank 3 (8 minutes).
![Page 9: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/9.jpg)
Interval Scale of Measurement
• The “Minutes” data on the previous slide. • a change of 1 unit on the measurement
scale corresponds to the same change in the measured attribute, no matter where on the measurement scale the change is.
• We can make statements about (a-b) versus (c-d).
![Page 10: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/10.jpg)
Ratio Scale of Measurement
• a true zero point – a score of 0 means that the object/event has absolutely none of measured attribute.
• With nonratio data we cannot make meaningful statements about the ratio of two measurements, but with ratio data we can.
![Page 11: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/11.jpg)
• we cannot say that 20 degrees Celsius (interval scale) is twice as hot as 10 degrees Celsius
• we can say that 300 degrees Kelvin (ratio scale) is twice as hot as 150 degrees Kelvin
![Page 12: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/12.jpg)
![Page 13: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/13.jpg)
![Page 14: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/14.jpg)
![Page 15: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/15.jpg)
Variables• A variable is a quantity that can take on
different values. A constant is a quantity that is always of the same value.
• Discrete variable - one for which there is a finite number of potential values which the variable can assume between any two points on the scale. Number of light bulbs in a warehouse; number of items correctly answered on a true-false quiz.
![Page 16: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/16.jpg)
Continuous Variable• one which theoretically can assume an
infinite number of values between any two points on the scale.
• Example: Weight of an object in pounds.• Can you find any two weights between
which there is no intermediate value possible?
![Page 17: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/17.jpg)
Categorical Variable• similar to discrete variable, but usually
there are only a relatively small number of possible values.
• Also called a grouping variable or classification variable.
• The categories may be nominal (female, male; red, green, blue, other) or they may be ordinal (final grade of A, B, C, D, or F).
![Page 18: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/18.jpg)
Bivariate Experimental Research
![Page 19: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/19.jpg)
Light Switch Experiment• Experimental Units / Subjects =
classrooms• Manipulated IV = position of light switch• Randomly assign to groups• DV = brightness of room• IV effect on DV = signal to be detected• EV cause noise in DV
![Page 20: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/20.jpg)
Coin Size Experiment• IV = size of coin tossed in pool• DV = height of wave produced• EV = rowdy youngsters in pool• Noise may obscure the IV DV signal• Confound: EV entangled with IV
![Page 21: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/21.jpg)
Tacker’s Educational Experiment
• IV = method of instruction, traditional or new
• DV = student performance on exams• Two classes, no random assignment• New method significantly > old method• Confounding variable:• Time of class
![Page 22: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/22.jpg)
Nonexperimental Research• Observational research• “Correlational” is a confusing term best
avoided.• No variable is manipulated.• Best not to use the terms “independent
variable” and “dependent variable”• Better to use “grouping variable” and
“criterion variable.”
![Page 23: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/23.jpg)
Alcohol and Reaction Time Observation
• Participants = folks randomly sampled in downtown Greenville in evening.
• Grouping variable = have been drinking or not.
• Criterion variable = score on reaction time task.
• We cannot make a causal inference.
![Page 24: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/24.jpg)
Third Variable Explanation
![Page 25: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/25.jpg)
Alcohol and Reaction Time Experiment
• Randomly assign participants to groups.• One group drinks alcohol, the other not.• IV = alcohol consumption• DV = score on reaction time task• We can make a causal inference.
![Page 26: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/26.jpg)
Causal Inference
To infer that X is a cause of Y• Show that X precedes Y.• Show that X and Y and correlated.• Rule out noncausal explanations.
– establish prior equivalence of treatment groups
– treat groups differently (manipulate IV)– demonstrate that groups differ on DV
![Page 27: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/27.jpg)
More Definitions• Data - numbers or measurements
collected as a result of observations. This word is plural. The single is “datum.”
• Population – in applied statistics, a population is a complete and well defined collection of measurements, aka scores. A population is often considered to be composed of an infinite number of cases.
![Page 28: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/28.jpg)
• An example of a finite population is the amounts spent on lunch today by all students at ECU.
• Sample - a subset of population. For example, the amounts spent on lunch today by members of my classes is a sample from that the population defined above.
![Page 29: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/29.jpg)
• Parameter - a characteristic of a population. These are typically symbolized with Greek symbols, such as y for the population mean of variable Y.
• Statistic - A characteristic of a sample. These are typically symbolized with Roman letters. For example, the sample mean of variable Y can be symbolized as MY or
Y
Y
![Page 30: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/30.jpg)
• Statistics are also called estimators, as these are typically used to estimate the value of population parameters.
• Descriptive Statistics - procedures for organizing, summarizing, and displaying data, such as finding the average weight of students in your statistics class or preparing a graph showing the weights.
![Page 31: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/31.jpg)
• Inferential Statistics - methods by which inferences are made to a larger group (population) on the basis of observations made on a smaller group (sample). For example, estimating the average weight at ECU by finding the average weight of a randomly selected sample of ECU students.
![Page 32: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/32.jpg)
• Real Limits - a range around any measure taken of a continuous variable equal to that measure plus or minus one half the (smallest) unit of measurement. For example, 5.5 seconds means between 5.45 and 5.55 seconds.
• Upper case Greek sigma means sum. Y = Y1 + Y2 + ..... + Yn
![Page 33: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/33.jpg)
Rounding
• If the first (leftmost) digit to be dropped is less than 5, simply drop all unwanted digits.
• If the first digit to be dropped is greater than 5, increase the preceding digit by one.
![Page 34: Introduction & Basic Concepts](https://reader035.fdocuments.net/reader035/viewer/2022062316/5681694a550346895de0e07e/html5/thumbnails/34.jpg)
• If the first digit to be dropped is 5– and any non-zero digits appear anywhere to
the right of the 5, increase the preceding digit by one.
– and no non-zero digit appears anywhere to the right of the 5• if the preceding digit is even, simply drop all
unwanted digits• if the preceding digit is odd, increase it by one.