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Population and Sample 4. (Population (Definition (Formal (Set of Similar…

- - - - Set of Similar items or events which is of Interest for some question or experiment.
    - - Read: population of Interest. All individuals
        considered interesting to find smth out
    - - All the people we would
        ideally like to involve
  - - - Kid
        
        Le persone che alla fine riesci a contattare
      - Formal
        
        A relatively small part of the population
        
        A Subset of the Population
        
        Equals or minor the memebers in the Samplig Frame
      - Personal
        
        Le persone o eventi che vengono effettivamente consultati
- - - - the Ideal sample is Representative
        of the population
        
        Random sample
        
        Normal Random sample
        
        All individuals have equal chance
        to be chosen
        
        gives the Highest Generality
        for the results
        
        Definition:
        Randomly choose from population
        
        When:
        
        Litlle informarton bt Population
        
        Difficult to divide in Salient Subgroups
        
        Stratified random sample
        
        Examples
        
        GPA of Students:
        
        select relevant Stratum (subgroup) -> major
        
        randomly pick from different strata
        
        Average Grades of Uni Students:
        Possible subgroups (Strata):
        
        Socioeconomic class
        
        Conscentiousness Trait
        
        IQ scores +/- 100 (avrg.)
        
        When:
        
        Heterogeneous population
        
        Easily broken in Salient Subgroups
        
        Salient Subgroups (Stratum/a)
        
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        Pro:
        
        Salient Subgroups are Represented
        
        Systematic random sample
        
        Ex. Every 7th individual of sampling frame
        
        the Sampling Frame must be
        organized Randomly
        
        Cluster sample
        
        Population divided in clusters
        
        First-stage
        
        all individuals of the cluster are sampled
        
        Second-stage
        
        Further sampling of the cluster subpopulation
        
        Clusters
        
        cluster should be as homogenous (similar) as possible
        
        Subpopulation within each cluster
        should be as heterogeneous as possible
        
        Ex. a Region of Norway
        among all regions
        
        Nonrandom sample
        
        Most common in psychology
        
        Highly Specific subpopulation
        
        Mostly: College students
        Ex.: ca. 80% for soc-psych.
        
        Pros:
        
        easy
        
        save time
        
        save money
        
        Cons:
        
        little generality
        
        not know the chance
        of being chosen
      - Problems
        
        Reduced Sampling Frame
        
        Response Rate: those who actually respond
        
        Selective Refusal: bias in ppl responding?
- - - - characteristics of the Population
        
        ex. mu = avrg. in a Pop.
      - Population
        
        contains All the Possible Scores
        
        Not considered a Group,
        but a theoretical Distribution
        from which our Sample is Drawn
        
        Observed Score = True Score +
        Systematic E. + Unsystematic E.
    - - characteristics of the Sample
        
        ex. x = avrg. in a Sample
    - - makes Assumptions about characteristics of the Population
        based on those of the Sample
      - we have Info from a Sample
        and we try to Say smth bt the Population
  - - - All the Averages we Could have found
        if we did the Study Many times
        
        Law of the Big Numbers
        
        the Average in a Sample will get Closer
        to the Average of the Pop. when N Observations Increase
        
        the Bigger the Sample, the Closer we get
        to the Average of the Pop.
        
        Central Limit Theorem
        
        when the Sample Increases its Size its Shape gets closer
        to that of a Normal Distribution (IF diff. indiepndent causes)
        
        gives us info bt the Uncertainty of the Samples Averages (Samples Means)
        Compared to the Population Average (Actual Mean)
        
        tell us how Far from the Samples Averages
        is the Pop. Average
        
        Standard Error
        
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        by Increasing the Amount of Samples (or the Sample Size)
        for a Sampling Distribution:
        
        the Sample(s) Mean will get Closer to the Actual Mean
        
        the Sampling Distribution will acquire the shape of a Normal Distribution
        
        Independently on the Shape
        ot their/its Original Distribution
      - A Sampling Distribution of a Mean
        
        can be based on:
        
        One single Sample and its Mean
        (A Sample and Its Mean)
        
        Many Diff. Samples and their Means (A Sample of Sample Means)