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BHS 307 Statistics for the Behavioral Sciences

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Variable a characteristic or property that can take on different values. ... How many people show a characteristic, have a given value or are members of a category. ... – PowerPoint PPT presentation

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Title: BHS 307 Statistics for the Behavioral Sciences


1
BHS 307 Statistics for the Behavioral Sciences
  • Chapter 1

2
What is Statistics
  • A tool for discovering relationships and patterns
    in data.
  • A way of describing and comparing behavior of
    groups.
  • A way of presenting and supporting arguments
    empirically.

3
Two Kinds of Statistics
  • Descriptive statistics tools for organizing and
    summarizing observations.
  • Tables, graphs, averages
  • Inferential statistics tools for generalizing
    beyond the actual observations.
  • Hypothesis tests (t-test, ANOVA)

4
Two Types of Data
  • The type of statistic used depends on whether
    data consist of numbers or words (or codes).
  • Qualitative any single observation is a class
    or category.
  • Quantitative any single observation is an
    amount or a count.

5
What is a Variable
  • Variable a characteristic or property that can
    take on different values.
  • Observations in a data set that have different
    values are a variable because they vary (are
    different).
  • Constant an observation that has only one value
    or stays the same.
  • Score -- any single observation in a data set. A
    score is a constant.

6
Two Kinds of Variables
  • Numeric Variables scores are numbers,
    quantitative data.
  • Nominal variables scores are words or names of
    categories.
  • Also called categorical variable.
  • Sex, hair color, religion

7
Numeric Variables
  • Continuous (scale) scores can be any number on
    the number scale.
  • Equal-interval (discrete or interval) scores
    increase in equal increments.
  • Most counts, rounded off continuous values,
    rating scales
  • Rank-order (ordinal) scores stand for relative
    rankings.

8
Numerical Codes
  • When data consists of classes or categories,
    often numbers can be used to replace category
    names.
  • Male 1, Female 2
  • Yes 1, No 2
  • Doing this does not make the variable
    quantitative.
  • This is a convenience for entering data or using
    software like SPSS.

9
Variables in Research
  • Independent variable the variable manipulated
    by the investigator.
  • May be used to define groups.
  • Used to test hypotheses about causation.
  • Dependent variable the variable measured,
    counted, or recorded by the investigator.
  • The outcome.
  • Confound an uncontrolled variable that varies
    with the independent variable.

10
Multiple Dependent Variables
  • Sometimes variables of interest cannot be
    manipulated (e.g., sex, poverty) but only
    measured.
  • Correlation studies -- studies with multiple
    dependent variables.
  • Goal is to identify relationships among the
    dependent variables measured.
  • Often used in observational research.
  • Called multivariate research.

11
Multiple Independent Variables
  • Sometimes an experimental study wishes to explore
    the effects of different influences on behavior.
  • Such studies manipulate several causes of change
    (factors) forming multiple groups to be compared.
  • Goal is to identify the influence of changing the
    IV on each group.
  • Called factorial studies.

12
Frequency Distributions
  • One of the simplest forms of measurement is
    counting
  • How many people show a characteristic, have a
    given value or are members of a category.
  • Frequency distributions count how many
    observations exist for each value for a
    particular variable.

13
Frequency Table
  • A frequency table is a collection of
    observations
  • Sorted into classes
  • Showing the frequency for each class.
  • A class is a group of observations.
  • When each class consists of a single observation,
    the data is considered to be ungrouped.

14
Creating a Table
  • List the possible values.
  • Count how many observations exist for each
    possible value.
  • The text uses a simple method using hash-marks
    and crossing off each value.
  • Figure out the corresponding percent for each
    class by dividing each frequency by the total
    scores.

15
Example
16
When to Create Groups
  • Grouping is a convenience that makes it easier
    for people to understand the data.
  • Ungrouped data should have lt20 possible values or
    classes (not lt20 scores, cases or observations).
  • Identities of individual observations are lost
    when groups are created.

17
Guidelines for Grouping
  • See pgs 9-10 in text.
  • Each observation should be included in one and
    only one class.
  • List all classes, even those with 0 frequency (no
    observations).
  • All classes with upper lower boundaries should
    be equal in width.

18
Optional Guidelines
  • All classes should have an upper and lower
    boundary.
  • Open-ended classes do occur.
  • Select an interval (width) that is natural to
    think about
  • 5 or 10 are convenient, 13 is not
  • The lower boundary should be a multiple of class
    width (245-249).
  • Aim for a total of about 10 classes.

19
Gaps Between Classes
  • With continuous data, there is an implied gap
    between where one boundary ends and the other
    starts.
  • The size of the gap equals one unit of
    measurement the smallest possible difference
    between scores.
  • That way no observations can ever fall within
    that gap.
  • Class sizes account for this.

20
Relative Frequency
  • Relative frequency frequency of each class as a
    fraction () of the total frequency for the
    distribution.
  • Relative frequency lets you compare two
    distributions of different sizes.
  • Obtain the fraction by dividing the frequency for
    each group by the total frequency
  • Total 1.00 (100)

21
Relative Frequency (Percent) and Cumulative
Frequency
22
Cumulative Frequency
  • Cumulative frequency the total number of
    observations in a class plus all lower-ranked
    classes.
  • Used to compare relative standing of individual
    scores within two distributions.
  • Add the frequency of each class to the
    frequencies of those below it.

23
Cumulative Proportion (Percent)
  • The cumulative proportion or percent is the
    relative cumulative frequency.
  • Percent proportion x 100
  • It allows comparison of cumulative frequencies
    across two distributions.
  • To obtain cumulative proportions divide the
    cumulative frequency by the total frequency for
    each class.
  • Highest class 1.00 (100)

24
Percentile Ranks
  • Percentile rank percent of observations with
    the same or lower values than a given
    observation.
  • Find the score, then use the cumulative percent
    as the percentile rank
  • Exact ranks can be found from ungrouped data.
  • Only approximate ranks can be found from grouped
    data.

25
Qualitative Data
  • Some categories are ordered (can be placed in a
    meaningful order)
  • Military ranks, levels of schooling (elementary,
    high school, college)
  • Frequencies can be converted to relative
    frequencies.
  • Cumulative frequencies only make sense for
    ordered categories.

26
Interpreting Tables
  • First read the title, column headings and any
    footnotes.
  • Where do the data come from, source?
  • Next, consider whether the table is
    well-constructed does it follow the grouping
    guidelines.
  • Finally, look at the data and think about whether
    it makes sense.
  • Focus on overall trends, not details.
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