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Overview

  • Syllabus declaration
  • Interests
  • Chapter 1-2
  • TYK 1
  • HW 1 due next class

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Test 1 Topics

  • Chapter 1 and 2 - Easy stuff, why study statistics, types of variables, ect.
  • Chapter 3 and 4 - Averages and variability
  • Chapter 5 - Standardized scores/z-scores

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Overview

  • 1.1 WHY STUDY STATISTICS?
  • 1.2 WHAT IS STATISTICS?
  • 1.3 MORE ABOUT INFERENTIAL STATISTICS
  • 1.4 THREE TYPES OF DATA
  • 1.5 LEVELS OF MEASUREMENT
  • 1.6 TYPES OF VARIABLES

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1.1 WHY STUDY STATISTICS?�

  • To Understand
    • News sensationalize
      • Diet coke causes cancer?
      • N of 2
      • Dire wolves

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1.1 WHY STUDY STATISTICS?�

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1.1 WHY STUDY STATISTICS?�

  • Which analysis?
  • How to conduct analysis?
  • How to report the analysis?

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1.2 WHAT IS STATISTICS?�

  • Variability
  • Descriptive - simple statistics that describe situation
  • Inferential - generalizing from a sample to a population

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1.3 MORE ABOUT INFERENTIAL STATISTICS

  • Population
    • complete collection of observations or potential observations
  • Sample
    • smaller collection of actual observations drawn from a population
  • Random Sampling
    • a sample should be randomly selected from a population in order to increase the likelihood that the sample accurately represents the population.
    • Convenience sample - WEIRD
  • Random Assignment
    • Random assignment signifies that each person has an equal chance of being assigned to any group in an experiment.

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1.4 THREE TYPES OF DATA

  • Qualitative
    • A set of observations where any single observation is a word, letter, or numerical code that represents a class or category.
  • Ranked
    • A set of observations where any single observation is a number that indicates relative standing.
  • Quantitative
    • A set of observations where any single observation is a number that represents an amount or a count.

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1.4 THREE TYPES OF DATA

  • Type Description Example

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  • Qualitative Categories/Labels Gender, Ethnicity
  • Ranked Ordered Finishing place in race
  • Quantitative Numeric values/intervals Height, Test scores

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1.5 LEVELS OF MEASUREMENT

  • Nominal
    • Words, letters, or numerical codes of qualitative data that reflect differences in kind based on classification.
  • Ordinal
    • Relative standing of ranked data that reflects differences in degree based on order.
  • Interval/Ratio
    • These should have a true zero and equal intervals

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1.5 LEVELS OF MEASUREMENT

  • Nonphysical
    • Is the difference between 130 and 140 in weight the same as the difference between 60 and 70?
    • What about for IQ?

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1.4 THREE TYPES OF DATA

  • Level Example Suitable Stats

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  • Nominal Eye color Frequencies, Chi-square
  • Ordinal Rank in contest Median, Spearman correlation
  • Interval Depression t-tests, ANOVA

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1.6 TYPES OF VARIABLES

  • Discrete
    • A variable that consists of isolated numbers separated by gaps
  • Continuous
    • A variable that consists of numbers whose values, at least in theory, have no restrictions
  • Approximate
    • Rounding

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1.6 TYPES OF VARIABLES

  • Independent Variables
    • treatment manipulated by the investigator.
  • Dependent Variables
    • variable is believed to have been influenced by the independent variable

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1.6 TYPES OF VARIABLES

  • Independent Variables
    • Drug or placebo
  • Dependent Variables
    • measurement of anxiety, depression, ect
  • The DV “depends” on the IV

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1.6 TYPES OF VARIABLES

  • Observational Studies
  • Confounds
    • An uncontrolled variable that compromises the interpretation of a study.

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Overview

  • TABLES (FREQUENCY DISTRIBUTIONS)
  • 2.1 FREQUENCY DISTRIBUTIONS FOR QUANTITATIVE DATA
  • 2.2 GUIDELINES
  • 2.3 OUTLIERS
  • 2.4 RELATIVE FREQUENCY DISTRIBUTIONS
  • 2.5 CUMULATIVE FREQUENCY DISTRIBUTIONS
  • 2.6 FREQUENCY DISTRIBUTIONS FOR QUALITATIVE (NOMINAL) DATA
  • 2.7 INTERPRETING DISTRIBUTIONS CONSTRUCTED BY OTHERS

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Overview

  • GRAPHS
  • 2.8 GRAPHS FOR QUANTITATIVE DATA
  • 2.9 TYPICAL SHAPES
  • 2.10 A GRAPH FOR QUALITATIVE (NOMINAL) DATA
  • 2.11 MISLEADING GRAPHS
  • 2.12 DOING IT YOURSELF

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2.1 FREQUENCY DISTRIBUTIONS FOR QUANTITATIVE DATA

  • Frequency Distribution
    • A collection of observations produced by sorting observations into classes and showing their frequency (denoted by the letter f) of occurrence in each class.
  • Ungrouped Data
  • Grouped Data

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FREQUENCY DISTRIBUTION (UNGROUPED DATA)�

  • TABLE 2.1 (Imagine all numbers are present for ungrouped data)

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  • WEIGHT f
  • 245 1
  • 244 0
  • 243 0
  • 135 2
  • 134 0
  • 133 1
  • Total 53

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  • WEIGHT f
  • 240–249 1
  • 230–239 0
  • 220–229 3
  • 210–219 0
  • 200–209 2
  • 190–199 4
  • 180–189 3
  • 170–179 7
  • 160–169 12
  • 150–159 17
  • 140–149 1
  • 130–139 3
  • Total 53

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2.2 GUIDELINES

  • Essential
    • Each observation should be included in one, and only one, class.
    • List all classes, even those with zero frequencies.
    • All classes should have equal intervals.
    • Book doesn’t mention – List in order from most to least
      • So “1” would be at the bottom and “10” would be at the top

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2.2 GUIDELINES

  • Optional (do them if at all possible)
    • All classes should have both an upper boundary and a lower boundary.
    • Select the class interval from convenient numbers, such as 1, 2, 3, … 10, particularly 5 and 10 or multiples of 5 and 10.
    • The lower boundary of each class interval should be a multiple of the class interval (130 is divisible by 10 which is the class interval).
    • Aim for a total of approximately 10 classes.

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2.2 GUIDELINES

  • Constructing Frequency Distributions
    • Range (245-133 is 112)
    • Class interval (112/10 is 11.2)
    • Round (11.2 to 10)
    • Lowest Class begin and end (not 133 instead 130)
    • Work upward (lowest number on bottom)
    • Tally then replace with f
    • Headings

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2.3 OUTLIERS

  • Check for accuracy
  • Maybe segregate

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2.4 RELATIVE FREQUENCY DISTRIBUTIONS

  • Constructing Relative Frequency Distributions
    • A frequency distribution showing the frequency of each class as a fraction of the total frequency for the entire distribution.

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  • WEIGHT f RELATIVE f
  • 240–249 1 .02
  • 230–239 0 .00
  • 220–229 3 .06
  • 210–219 0 .00
  • 200–209 2 .04
  • 190–199 4 .08
  • 180–189 3 .06
  • 170–179 7 .13
  • 160–169 12 .23
  • 150–159 17 .32
  • 140–149 1 .02
  • 130–139 3 .06
  • Total 53 1.02*

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2.5 CUMULATIVE FREQUENCY DISTRIBUTIONS

  • Cumulative Frequency Distributions
    • A frequency distribution showing the total number of observations in each class and all lower-ranked classes.
  • Percentile Ranks
    • Percentage of scores in the entire distribution with equal or smaller values than that score.

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  • WEIGHT f CUMULATIVE f CUMULATIVE PERCENT
  • 240–249 1 53 100
  • 230–239 0 52 98
  • 220–229 3 52 98
  • 210–219 0 49 92
  • 200–209 2 49 92
  • 190–199 4 47 89
  • 180–189 3 43 81
  • 170–179 7 40 75
  • 160–169 12 33 62
  • 150–159 17 21 40
  • 140–149 1 4 8
  • 130–139 3 3 6
  • Total 53

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  • WEIGHT f CUMULATIVE f CUMULATIVE PERCENT
  • 240–249 1 53 100
  • 230–239 0 52 98
  • 220–229 3 52 98
  • 210–219 0 49 92
  • 200–209 2 49 92
  • 190–199 4 47 89
  • 180–189 3 43 81
  • 170–179 7 40 75
  • 160–169 12 33 (21+12) 62
  • 150–159 17 21 (4+17) 40
  • 140–149 1 4 (3+1) 8
  • 130–139 3 3 6
  • Total - 53

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  • WEIGHT f CUMULATIVE f CUMULATIVE PERCENT
  • 240–249 1 53 100
  • 230–239 0 52 98
  • 220–229 3 52 98
  • 210–219 0 49 92
  • 200–209 2 49 92
  • 190–199 4 47 89
  • 180–189 3 43 81
  • 170–179 7 40 75
  • 160–169 12 33 (21+12) 62 (33/53)
  • 150–159 17 21 (4+17) 40 (21/53)
  • 140–149 1 4 (3+1) 8 (4/53)
  • 130–139 3 3 6 (3/53)
  • Total - 53

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2.6 FREQUENCY DISTRIBUTIONS FOR QUALITATIVE (NOMINAL) DATA

  • FACEBOOK PROFILE SURVEY

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  • Response f
  • Yes 56
  • No 27
  • Total 83

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2.6 FREQUENCY DISTRIBUTIONS FOR RANKED DATA

  • RANK f PROPORTION CUMULATIVE PERCENT
  • General 311 .004* 100.0
  • Colonel 13,156 .167 99.6
  • Major 16,108 .204 82.9
  • Captain 29,169 .370 62.5
  • Lieutenant 20,083 .255 25.5
  • Total 78,827

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Distributions

  • Positively Skewed Distribution
    • A distribution that includes a few extreme observations in the positive direction (to the right of the majority of observations).
  • Negatively Skewed Distribution
    • A distribution that includes a few extreme observations in the negative direction (to the left of the majority of observations).

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2.9 TYPICAL SHAPES

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2.10 A GRAPH FOR QUALITATIVE (NOMINAL) DATA

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Real World Example - NEU Acceptance Rates

Year Percentage Accepted

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1980 90

1990 88.3

2002 61.3

2010 37.9

2020 20.5

2024 5.2

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APA Style

  • Your final grade will be highly reflective of you precision and usage of APA style. This includes:
    • Rounding
    • p values
    • leading and following zeros

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Rounding

  • Almost all stats in this class will be rounded to two decimal places
  • .054 will round to .05
  • .055 will round to .06
  • .0545 will round to .05
    • We look at the third number to round the second
    • We don’t round the fourth number then they third number

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p values

  • p > .05 - fail to reject the null/not significant
  • p < .05 - reject the null (do not say accept the alternative)/this is significant
  • Examples:
  • p = .06
  • .06 > .05 - fail to reject the null (not significant)
  • Example 2:
  • p = .04
  • .04 < .05 - reject the null (significant)

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p values

  • p values are listed two ways. One is the exact number to three decimal places. Example:
    • If SPSS lists the p value as .003, we can write it up as p = .003
    • The equal sign is key
  • If you see a p value is listed as “<”, it can be written up one of three ways:
    • p > .05
    • p < .05
    • p < .01
    • p < .001

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p values

  • SPSS lists a p value as .002. The quiz has the following:
    • “p = _____”
    • You fill in the blank with .002.
    • “p < _____”
    • You fill in the blank with .01.

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Leading Zero

  • "If the statistic can be greater than 1, use a leading 0 (0.24 in)
  • If the statistic cannot be greater than 1, do not use a leading 0 (p = .04)"

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  • Values for p, r, R squared, eta squared, and partial eta squared can never exceed 1, so they do not have a leading zero. Some people will put a leading zero in front of a p-value, but from an APA-style point of view, it is not needed.

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Leading Zero

  • The essential part – means and standard deviations should have a 0 before the decimal if appropriate.
  • Something that is a proportion/percentage (it can’t go above 1) should not have a leading zero.
  • If SPSS lists the mean as .86, we write it up as 0.86 (a mean can exceed 1.00)
  • The proportion for the chance of rain tomorrow is .86 (this can not exceed 1.00)
  • Your grades on the tests will heavily depend on your precision and on your understanding of this slide

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Following Zero

  • If SPSS lists the mean as .7, we write it up as 0.70 (a mean can exceed 1.00)
  • If SPSS lists the mean as 2, we write it up as 2.00 (a mean can exceed 1.00)
  • These are called following zeros. We are taking the number out two decimal places even if the numbers are zeros.
  • Your grades on the tests will heavily depend on your precision and on your understanding of this slide

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Upcoming

  • TYK1
  • HW1
  • Syllabus declaration
  • 3, 4, 5 - Averages, Variability, Standardized Scores

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