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Psychological Statistics Midterm Exam, Exams of Statistics

A.T. Still University of Health Sciences (ATSU)Statistics

Psychological Statistics Midterm Exam

Typology: Exams

2023/2024

Available from 04/01/2024

DrShirleyAurora
DrShirleyAurora 🇺🇸

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Psychological Statistics Midterm Exam
Statistics -
- Mathematical procedures for organizing, summarizing, and interpreting data/information
Population -
- Entire group of interest
- the set of all the individuals of interest in a particular study
Sample -
- Subset of individuals selected from population
- Usually intended to represent the population in a research study
- subset of population exposed to treatment
- Results of sample are used to estimate what would happen to entire population if treated
Variable -
- Characteristic that has different values
Data -
- Measurements or observations
Parameter -
- Characteristic/Value that describes a population
- A value, usually a numerical value, that describes a population.
- Is usually derived from measurements of the individuals in the population
Statistic -
- Characteristic/Value that describes a sample
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Psychological Statistics Midterm Exam

Statistics -

  • Mathematical procedures for organizing, summarizing, and interpreting data/information Population -
  • Entire group of interest
  • the set of all the individuals of interest in a particular study Sample -
  • Subset of individuals selected from population
  • Usually intended to represent the population in a research study
  • subset of population exposed to treatment
  • Results of sample are used to estimate what would happen to entire population if treated Variable -
  • Characteristic that has different values Data -
  • Measurements or observations Parameter -
  • Characteristic/Value that describes a population
  • A value, usually a numerical value, that describes a population.
  • Is usually derived from measurements of the individuals in the population Statistic -
  • Characteristic/Value that describes a sample
  • is a value, usually a numerical value, that describes a sample and is usually derived from measurements of the individuals in the sample Descriptive Statistics -
    • Summarize, organize, and simplify data
  • Tables and Graphs: Frequency Distributions, Histograms
  • Measures of Central Tendency: Mean, Median, Mode
  • Measures of Variability: Range, Variance, Standard Deviation Inferential Statistics -
    • Uses samples to make inferences about populations
  • consist of techniques that allow us to study samples and then make generalizations about the populations from which they were selected Sampling Error -
    • Discrepancy (or error) between a sample statistic and the corresponding population parameter
  • the naturally occurring discrepancy, or error, that exists between a sample statistic and the corresponding population parameter Correlational method -
    • Relationships Between Variables
  • Variables are measured
  • "Correlation does not imply causation"
  • Correlation does NOT provide explanation for WHY relationship exists Experimental Methods (Comparing Groups) -
    • Independent Variable (IV)
  • Dependent Variable (DV)
  • Control Condition
  • Psychological "process" or "mechanism"
  • Cannot be observed directly
  • Assumed to cause observable behavior or "symptoms" Operational Definition -
    • Procedures for measuring construct
  • Uses observable behaviors/symptoms
  • Defines construct in terms of how it will be measured Discrete Variable -
    • Separate, indivisible categories
  • No values can exists between categories
  • Examples: Occupation (teacher, lawyer, doctor) and major (psychology, biology, math) Continuous Variable -
    • Infinite number of possible values between any two observed values
  • Examples: Time, height, weight, and distance Nominal Scale -
    • Categories that have different names
  • No quantitative distinction between categories Ordinal Scale -
    • Categories organized in ordered sequence
  • No information about distance between categories A researcher is interested in the texting habits of high school students in the United States. If the researcher measures the number of text messages that each individual sends each day and calculates the average number would be an example of a _____________ -
  • parameter Interval Scale -
  • Categories are intervals of exactly the same size
  • Zero point is arbitrary Ratio Scale -
  • Interval scale with absolute zero Variable Notation -
  • Variables are usually noted with an alphabetical letter
  • Example: X, Y Number of scores -
  • N = number of scores in population
  • n = number of scores in sample Summation Notation -
  • Ʃ
  • ƩX
  • Greek Letter sigma (capital)
  • Indicates scores should be added together A researcher is interested in how watching a reality television shows featuring fashion models influences the eating behavior of 13-year-old girls a) A group of 30 13-year-old girls is selected to participate in a research study. The group of 30 13-year- old girls is an example of a ____________. b) In the same study, the amount of food eaten in one day is measured for each girl and the researcher computes the average score for the 30 13-year-old girls. The average score is an example of a _____________. -
  • Graph of frequency distribution Bar Graph -
  • use for noncontinuous categorical data Symmetrical Distribution -
  • One side is mirror image of other Skewed Distribution -
  • Scores pile up at one end and are "skewed" at the other
  • Tail :Section where scores tend to "taper off" toward one end of a distribution Positive Skew -
  • Tail on right side Negative Skew -
  • Tail on left side Central Tendency -
  • Single score that defines the center of a distribution
  • Single score that is most typical or representative of the entire group Measure of Central Tendency -
  • Mean
  • Median
  • Mode The Mean: Mean definition, Population mean calculation, Sample mean calculation -
  • Mean = sum of scores, divided by number of scores
  • Population Mean (u): u = ƩX/N
  • Sample Mean: M = ƩX/n
  • Dividing the Total Equally
  • Mean as Balance Point The Median: definition, when n is odd, when n is even -
    • Median = scores are listed in order of magnitude
  • Median is middle score in distribution
  • When n is odd the middle score that separates the bottom half of scores from the top half of scores
  • When n is even the median = mean of the middle two scores The mode: definition, bimodal, multimodal -
    • Mode = the score/category with the greatest frequency
  • Identify using frequency distribution
  • Bimodal = Distribution with 2 modes
  • Multimodal = Distribution with more than 2 modes Selecting Measures of Central Tendency: The Mean, Median, Mode -
    • The Mean:
  • preferred; uses every score in distribution
  • The Median:
    • skewed distributions, undetermined scores, open-ended distributions, ordinal data
  • The Mode:
    • nominal data, discrete variables Shapes of Distributions: Mean, Median, Mode -
    • Symmetrical Distributions:
    • Right side is mirror of left side
  • Both mean and median are at center point

Raw Score -

  • Score on measurement instrument using original scale of measurement Standard Score -
  • Identify and describe exact location of each score a distribution
  • Relative to other scores
  • Single value indicates how score compares to other scores (similar to percentiles) z-score -
  • Specifies precise location of each score in a distribution sign -
  • +/- indicates if score is above or below the mean Numerical Value -
  • Distance of score from mean in Standard Deviation Units
  • How many standard deviations score is from mean
  • Example: z-Score of 1 = Score is 1 Standard Deviation above the Mean Standard Distributions: z-score -
  • Standard Distribution
  • Transforming entire distribution of Raw Scores into - z-Scores
  • Used to make dissimilar distributions comparable
  • Shape
  • Will be exactly the same as distribution of raw scores
  • Mean
  • will always be zero z = (Mean - Mean) / SD
  • Standard Deviation
  • Will always be 1

Probability -

  • When several outcomes are possible, the probability for any given outcome is defined as a fraction or proportion of all possible outcomes
  • Probability = Proportion
  • Probability and proportions are equivalent
  • Proportion of individuals in a distribution indicates the probability of randomly selected those individuals Random Sample -
  • Each individual in population has equal chance of being selected
  • Required for probability formula to work Independent Random Sample -
  • Each individual in population has equal chance of being selected; and that probability of being selected remains constant across selections (if multiple selections occur)
  • "Sampling with Replacement" Sampling Distribution -
  • A distribution of statistics obtained by selecting all possible samples of a specific size from a population Distribution of Sample Means -
  • Collection of sample means for all possible random samples of a particular size that can be obtained from a population
  • A.K.A the "Sampling Distribution of the Mean"
  • All possible samples means from population if null-hypothesis is true Central Limit Theorem -
  • The distribution of sample means will approach a normal distribution as n approaches infinity
  • State Hypothesis
  • Set Criteria for Decision
  • Compute Sample statistic and Compare to Hypothesis
  • Make a Decision Null Hypothesis (Ho) -
  • Treatment has no effect Alternative Hypothesis (H1) -
  • Treatment has an effect Sample Means likely if Ho is True -
  • Sample mean should be close to population mean Sample Means likely if Ho is False -
  • Sample means should be far from population mean Alpha Level (a) -
  • Boundary that separates high-probability samples (if Ho is true) from low probability samples (if Ho is true)
  • Probability of obtaining data in critical region if Ho is true
  • a = Probability of Type I Error Critical Region -
  • Sample means that are unlikely if null-hypothesis is true z-Score for Sample Mean -
  • Indicates how far sample mean is from population mean

Reject Ho (null-hypothesis) -

  • If z-score for sample mean is located in critical region
  • Unlikely that result occurred by "chance" (i.e. sampling error) if Ho is true
  • Reject Ho: Assume treatment had an effect Fail to Reject Ho -
  • If z-Score for Sample Mean is NOT located in critical region
  • Likely that result occurred by "chance" (i.e. sampling error) if Ho is true
  • Fail to Reject Ho: Assume treatment had NO effect Type I Error -
  • Reject Ho when Ho is true
  • Falsely conclude that treatment has effect Type II Error -
  • Fail to reject Ho when Ho is false
  • Falsely conclude that treatment has no effect Selecting Alpha Level -
  • Minimize Risk of Type I Errors
  • Common Values
  • a = 0.
  • a = 0.
  • a = 0.
  • "Social Convention" p-value -
  • Exact probability of obtaining result if Ho is true
  • Ho: u with treatment = u without treatment
  • H1: Scores do increase (or decrease)
  • H1: u with treatment > u without treatment Critical Region for Directional Tests -
  • Resides in 1 tail of distribution; where sores are unlikely to occur if direction prediction is true Statistical Power -
  • Probability that hypothesis test will correctly reject a false null-hypothesis
  • Probability test will correctly detect a true treatment Problem with z-scores -
  • requires population variance to compute
  • t-statistic does not require population variance OR population mean
  • the sample variance is used as an estimate of the population variance Degrees of Freedom -
  • The number of scores in a sample that are independent and free to vary
  • Sample mean places restriction on the value of 1 score
  • Degree of Freedom df = n- Estimated Standard Error -
  • Sample variance as estimate for population variance Hypothesis Test with t statistic -
  • State Hypotheses
  • Set Criteria for Decision
  • Compute Test Statistic
  • Make a Decision

Assumptions for t-Test -

  • Independent Observations
  • Normal Distribution (Population)
  • Probabilities (and critical region) for sampling distribution do not apply if distribution is skewed