Chapters 1-6: Intro, Frequency Dist., Central Tendency, Variability, Z-Scores, Probability

Statistics

___________ - a set of mathematical procedures for:

1) Organizing + summarizing info → describe

2) Interpreting information (help answer questions) → inferences

Population

____________ - the set of all individuals of interest in a particular study

• Ex: Chinese Americans over 65

Sample

__________ - A set of individuals selected from a population intended to represent the population in a research study

• Ex: 200 Chinese American participants over 65

Random sample

___________ - a sample where everyone in a population has an equal chance of being picked to better represent a population

Variable

__________ - a characteristic or condition that changes or has different values for different individuals

Data

___________ - measurements or observations

Data Set

____________ - a structured collection of measurements or observations

• Ex: A chart of height and weight of kittens

Datum

___________ - a single measurement or observation, commonly called a score or a raw score

Parameter

_________ - a characteristic that describes a population

• Ex: The average running speed of 11-year-old girls in Saskatchewan

Statistic

_________ - A characteristic that describes a sample

• Ex: The average speed of thirty 11-year-old males in a study

Descriptive statistics

____________ - statistical procedures used to summarize, organize, and simplify data

• Ex: Averaging, tables, graphs

Inferential statistics

__________ - consist of techniques that allow us to study samples and then make generalizations about populations from which they were selected

Representative sample

_________ - a sample that reflects general population, used in inferential statistics to better make generalizations about a population

Sampling error

___________ - the naturally occurring discrepancy that exists between a sample statistic and the corresponding population parameter

AKA margin of error

When inferring, you do not have every individual accounted for

• Ex: A population with an average IQ of 100 but a sample with an average IQ of 107

• Why we use n-1 in variance formula

Constructs

_________ - internal attributes or characteristics that cannot be directly observed but are useful for describing and explaining behaviour

• Ex: Self-esteem or hunger

Operational definition

____________ - identifies a measurement procedure for measuring external behaviour and used the resulting measurements as a definition and a measurement of a hypothetical construct

• Ex: Heart rate while giving a speech to measure anxiety levels

Discrete variable

____________ - consists of separate indivisible categories. No values can exist between two neighbouring categories

• Ex: Number of students in a class (there can't be half a student) or majors of students

Continuous variable

___________ - when there are an infinite number of possible values that fall between two observed values.

• Ex: Time

Real limits

___________ - the boundaries of intervals for scores that are represented on a continuous number line. Located halfway between scores

• Ex: 49.5 and 50.5 are the limits for what counts as a score of 50

• Upper ______: the highest to round (50.5)

• Lower _______: the lowest to round (49.5)

Nominal scale

___________ - a set of categories that have different names. Measurements on this scale label categories as observations but do not make any quantitative distinctions between observations

• Ex: Hair color

Ordinal scale

___________ - consists of a set of categories that are organized in an ordered sequence. Measurements on an ________ rank observations in terms of size and magnitude

• Ex: First, second, third

Interval scale

__________ - consists of ordered categories that are all intervals of exactly the same size. Zero point on an interval scale is arbitrary and does not indicate a 0 amount being measured

• Ex: Temperature

Ratio scale

__________ - An interval scale with an absolute 0 point representing nothing/an absolute zero. Ratios of numbers reflect ratios of magnitude

Correlational method

____________ - two different variables are observed to set whether there is a relationship between them

• Does NOT determine causation

Frequency distribution

_________- an organized tabulation of the number of individuals located in each category on the scale of measurement

Proportion + percentage

__________ - are two other measures besides frequency distribution that describe distribution of scores and can be incorporated into the table

Proportion

_________- the fraction of the total group associated with each score

Parts of a whole— can be described as fractions, decimals or percentages

• p= f/n

Percentage formula

% = p(proportion)100

Percentile rank

__________ - a particular score is defined as the percentage of individuals in the distribution with scores at or below the particular value

• Ex: A rank of 80th percentile means the student scored better than 80% of other test-takers, while only 20% scored higher.

Percentile

_____________- specific value or score— when a score is identified by its percentile rank

• Ex: A score of 9 is within the 95th percentile

Cumulative frequency

_____________ - the accumulation of individuals as you move up the scale, listed as cf

• Sum of all frequency counts of scores up to an including the upper real limit of a given scores

Cumulative percentage

____________ - shows the percentage of individuals as you move up the scale, listed as c%

• The percentage of all frequency counts of scores in a freq. dist. up to and including the upper real limit of a giving score

Cumulative percentage formula

c%= cf/N(100%)

Real limits

___________ - Frequency distribution uses ________ when using continuous data because because it measures in intervals

• Ex: X=8 could be 7.5 - 8.5

Abscissa

____________ - another name for the X axis

Ordinate

__________- another name for the Y axis

Measurement scales

__________ - how variables (x values) are categorized, counted, or measured

• NOIR: Nominal, ordinal, interval, ratio

Histograms + polygons

___________ - Two graphing options for data using interval or ratio scale

Characteristics of a histogram

__________ - Made of bars, no spaces between bars

Informal histogram

__________ - Instead of bars the graph consists of stacked blocks.

Characteristics of a polygon

_____________ - Dots representing data, are placed through each score with a line going through, the line is ended by drawing it down to the x axis

Bar graph

_________ - What graph can be used for nominal or ordinal data?

Characteristics of a bar graph

__________ - For nominal scale, there are spaces between bars to indicate separate categories

For ordinal, it is because you can't assume the categories are the same size

Smooth curves

____________ - What graphs can be used for population distribution? (Interval or ratio scale)

Normal curve

_________ - a smooth curve graph with a single wide slope that is symmetrical on both sides

• Ex: IQ scores

• Cannot be bimodal

Symmetrical distribution

____________ - the scores tend to pile up toward the middle parts of the scale and taper off gradually at the other ends

• Also applies to bimodal

Positively skewed

__________ - tail moving towards the right, body to the left

• Ex: It is positive if you’re drunk and closer to the wall

Negatively skewed

___________ - tail going toward the left, body to the right

• Ex: It is negative if you’re not close to the wall

Central tendency

__________ - statistical measure to determine a single score that defines the center of a distribution of scores

• Goal is to find the most typical or representative value!

• Mean, median, & mode are most used

  • Mean esp.

Mean

Central tendency

__________ - the sum of scores divided by the number of scores

• Represented by— M, Xbar or mu

• Associated w. interval or ratio data

Median

Central tendency

_________ - the score corresponding to the point having 50% of the observations below it [and 50% above] when the observations are arranged in numerical order, does not always change when adding or dropping a score

When is the median preferred?

Central tendency

___________ - Ordinal data or continuous data that is skewed

Mode

Central tendency

__________ - the most commonly occurring score in a sample or population does not always change with new score or change in score

• People in the population/sample MUST have this as a score

When is the mode preferred?

Central tendency

_________ - for nominal scale, discrete variables

• The mode is also useful for describing shape when used along with the mean

3 measures of central tendency

Central tendency

_________- Mean, Median, Mode

Examples of mean

Central tendency

__________ - examples include: report card, sports

Examples of median

Central tendency

__________ - examples include: household income, salary

Examples of mode

Central tendency

__________ - examples include: retail sales, election voting

Variability

_________- a group of quantitative measures of the differences between scores + describes the degree to which the scores are spread out or clustered together

• Includes: Range, IQR, variance, standard deviation

• GREATLY affected by outliers

Two purposes of variability

Variability

__________-

1. Describes the distribution of scores

2. Helps determine how representative a score is to the entire distribution

Range

Variability

________ - distance covered by scores in a distrbution. Determined by only the most extreme high and low scores in a distribution— doesn’t cover all scores, so it is not the most accurate

• Crude and unreliable measure of variability

• Not really used in formal descriptions cuz of this

Range formula

Variability

________ - For this class, focuses on these two formulas:

For discrete variables:

• Xmax - Xmin + 1

For continuous variables:

• XmaxURL (upper real limit) - XminLRL (lower real limit)

Simple ______ is Xmax-Xmin

Interquartile range (IQR)

Variability

________ - the range of scores that make up the middle 50% of a dist. Based on quartiles, a type of percentile rank. Bottom and top 25% of distribution are excluded

For semi ______, simply divide the _____ by half.

• Q1 = 25th percentile (25% of scores fall below it)

• Q2 = 50th percentile

• Q3 = 75th percentile

• Q4 = 100th percentile (highest score)

IQR formula

Variability

__________ - Q3 - Q1

• For semi ______, simply divide the _____ by half/2

Deviation

Variability

______- the distance of a score from the mean

• For populations, deviation score = X - μ

• For samples, Deviation score = X - M

Sum of Squares (SS)

Variability

__________ - the sum of the squared deviation scores

• Represented by the symbol, SS, SS =Σ(X -μ)²

Variance

Variability

___________ - the average squared [raised to the second power] distance from the mean, represented by σ² or s²— measures how spread out a set of numbers is from its average (mean), calculated as the average of the squared differences from the mean

• Population: SS/n

• Sample: SS/n -1

Standard devation

Variability

_________ - the square root of the variance and provides a measure of the average distance from the mean

• Represented by σ or s

Standard deviation formula

Variability

o= sqrt Sum(X-M)^2/N

Degrees of freedom

___________- The number of scores in the sample that are independent & free to vary

Z-score

__________ - a measure of how many standard deviations you are away from the average/mean. Used to describe a location within a distribution using a single number.

• Allows for comparisons between distributions w/ diff means and std. deviations

• Comparisons are based on the equivalent magnitude of differences from the mean

Z-score formula

_________- z = (X - μ)/σ

Standardized (z) distribution

__________- a symmetrical distribution composed of scores that have been transformed to create predetermined values for μ & σ.

Probability

___________ - for a situation in which several diff, outcomes are possible, the __________ for any specific outcome is defined as a fraction or a proportion of all possible outcomes.

• If possible outcomes are identified as A, B, C, D and so on then

probability of A = number of outcomes classified as A / total number of possible outcomes

• Told in fractions or decimals (not percentages unless asked)

Random sampling w/ replacement

_________ - requires random sampling (each individual has an equal chance of being selected) also that the probability of being selected stays constant from one selection to the next if more than one individual is selected

Items are returned to the pool after selection, allowing duplicates and keeping probabilities constant

• Can also simply be called random samples or independent random sampling

• Ex: Looking for an Ace of Hearts = 1/52

  • Pulled a Deuce of Spades, keeping that card in. Still probability(Ace of Hearts) = 1/52

Random sampling WITHOUT replacement

___________ - requires random sampling (each individual has an equal chance of being selected) also that the probability of selected items being removed (not constant) preventing repeats and changing probabilities w/ each draw

• Samples = unique, draws dependent

• Ex: Looking for an Ace of Hearts = 1/52

  • Pulled a Deuce of Spades, taking that card out. Now probability(Ace of Hearts) = 1/51

History

________- in this order:

1. Florence Nightingale (1820-1910)

2. Francis Galton (1822-1911)

3. Karl Pearson (1857-1936)

4. Sir Ronald Fisher (1890-1962)

5. Freudians and Behaviourists (1920s)

6. Trait theorists (1940s)

7. Decline of behaviourism (1950s)

8. Statistics and psychology

9. Quantitative vs qualitative

1) Florence Nightingale

History

___________ - revolutionized statistics by using data visualization, particularly her "rose diagram," to show that sanitation, not battle wounds, caused most soldier deaths in the Crimean War, advocating for public health reforms and establishing data collection standards for comparable hospital statistics, making her a pioneer in data-driven healthcare and a foundational figure in statistical graphics. 

2) Francis Galton

History

___________ -

• Suffered a breakdown in anticipation of the honors exams which resulted in his graduating without a distinguished degree

• First to demonstrate that the "normal distribution" could be applied to human psychological attributes, including intelligence

• Coined the term "eugenics" and the phrase "nature versus nurture"

• Discovered that fingerprints were an index of personal identity

• First to utilize the survey as a method for data collection

3) Karl Pearson

History

___________ -

• Argued successfully to have the University regulations changed so that attendance was no longer compulsory at divinity lectures or at the chapel — and then continued to attend

• Galton's Natural Inheritance in 1889 prompted him to explore statistical analyses to explain heredity and evolution: regression, correlation, and the chi-square test

• Correlation, demonstrating the relation of two variables

• Cannot determine cause and effect

• Pearson was a co-founder, with Weldon and Galton, of the statistical journal Biometrik

4) Sir Ronald Fisher

History

___________ -

• After leaving Cambridge, Fisher had no means of financial support and worked for a few months on a farm in Canada

• Pearson offered him the post of chief statistician at the Galton laboratories but he instead became chief statistician at the Rothamsted Agricultural Experiment Station

• Experimental method

• Random assignment

• Independent variable

• Dependent variable

• Small samples

5) The rest of history

History

___________ -

• 1920’s Freudians and Behaviorists

• 1940’s Trait theorists

• 1950’s Decline of Behaviorism

• Statistics as the language of psychology

• Quantitative vs. Qualitative

Variable

_________- a characteristic or condition that can or does change between individuals in a sample

• Participant + Enviornmental

• IV vs DV

• Quasi-independent ______

• Discrete and continuous _____

Constant

__________ - a characteristic or condition that is fixed and cannot change between individuals in a sample

Experimental method

__________- determine if one variable causes another variable to change, by manipulating one variable and controlling the research situation

• Contains manipulation and control

• IV and DV

• Control and experimental conditions

Participant + enviornmental variables

Variables

___________ -

Participant: individual differences — age, gender, intelligence, education, etc.

Environmental: Time of day, weather, termperature, colour of walls, etc.

IV vs DV

Variables

___________ -

IV: stays same throughout experiment (ex: group category, sex)

• Can be quasi-independent

DV: changes dependent on the research, specficially the experimental condition

Quasi-experimental/nonexperimental design

__________ - experiments where you cannot manipulate the IV and control of other extraneous variables

• Ex: Comparing depression rates in North Central vs Wascana

Control condition

Experimental method

__________- there is NO experimental treatment

• Ex: Placebo

Experimental condition

Experimental method

__________- there is an experimental treatment

• Ex: Actual drug

Outliers

_________ - scores that are substantially distant from the other scores in a sample

• Ex: Elon Musk’s wealth compared to everyone else

Descriptive research

__________ - involved measuring one or more seperate variables for intent of simply describing the individual variables

Grouping

________ - collapsing of scores into mutually exclusive classes defined by grouping intervals

• Less cumbersome, greater comprehension

• Info can be lost when categories/data are combined

• Categories can be arbitrary

Cummulative proportion

________ - the proportion of all frequency counts of scores in a freq. dist. up to and including the upper real limit of a given score

Kurtosis

_________ - a statistical measure describing the "tailedness" or outliers in a probability distribution, indicating how heavy or light its tails are compared to a normal distribution

• How tall a distribution is, gives idea into variability

Weighted mean

M = ∑X1 + ∑X2 / n1 + n2

Research design

________ - Statistics are important but the research design is far more important

• Statistics cannot fix a poor research design

• Causality is determined by the research design, not by the statistical analysis

Skewness

__________ - measures the asymmetry or lack of symmetry in a data distribution, indicating if data points are clustered more on one side of the mean than the other, unlike a perfect bell-shaped normal distribution where mean, median, and mode align