Data Analysis

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Data Analysis

• Statistics

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Levels of Measurement

• Nominal Categorical no implied rankings among
  the categories. Also includes written
  observations and written responses from
  qualitative interviews or open-ended survey
  questions.
• Ordinal Categorical data with implied rankings
  or data obtained through respondent ranking of
  categories. In some cases, a ranking process may
  be set up for a particular variable.
• Interval No fixed zero point. Data is
  numerical, not categorical. Rank order among
  variables is explicit with an equal distance
  between points in the data set -2, -1, 0, 1,
  2
• Ratio Fixed zero point otherwise the same as
  interval.

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In general, type of data can be inferred using
the following the criteria

• Nominal Categorical no implied rankings among
  the categories. Also includes written
  observations and written responses from
  qualitative interviews or open-ended survey
  questions.
• Ordinal Categorical data with implied rankings
  or data obtained through respondent ranking of
  categories. In some cases, a ranking process may
  be set up for a particular variable.
• Interval No fixed zero point. Data is
  numerical, not categorical. Rank order among
  variables is explicit with an equal distance
  between points in the data set -2, -1, 0, 1,
  2
• Ratio Fixed zero point otherwise the same as
  interval.
• Any categorical data is either nominal or
  ordinal.
• All qualitative data is nominal.
• All scores on standardized scales are either
  interval or ratio. (Note almost all the scales
  we use in social work, except IQ scores are
  ratio).
• The level of measurement determines what
  statistical method we can use.

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In some cases, we can covert a variable into
another level of measurement

• We can change a variable from ratio to either
  ordinal or nominal

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Coverting Data (Use Recode in SPSS)
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Advantages of using ratio data

• We can covert it to another level of data we
  cant do this with nominal data.
• People can simply write down information about
  how they fit a particular attribute (age,
  income).
• We have more statistical options with ratio data.
  Inferential statistics requires that dependent
  variables always be ratio.

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Primary types of data analysis are

• Qualitative
• Descriptive. Used to describe the distribution of
  a single variable or the relationship between two
  nominal variables (mean, frequencies,
  cross-tabulation)
• Inferential (Used to establish relationships
  among variables assumes random sampling and a
  normal distribution)
• Nonparametric (Used to establish causation for
  small samples or data sets that are not normally
  distributed)

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Much of what you will use in your research will
be descriptive statistics.

• For example, the most basic type of descriptive
  statistic is the frequency. Frequencies are the
  number of times a specific value or data within a
  specific category occurs.
• Most often we convert frequencies to percentages
  Formula is f/n, where f frequency and n the
  total number of values in a data set. For
  example, the if the age 25 occurs 5 times in a
  data set of 50 5/50 10.

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Examples of use of frequency data

• 40 of respondents are male.
• The mean level of income was 35,000
• 40 of all female voters cast their vote for
  Arnold compared to 52 of the male voters.
• Note the other descriptive statistic we use is
  the standard deviation. It describes the degree
  to which data points vary from the mean of a
  distribution. In a research article, you will see
  the standard deviation included with the mean.

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Application of Standard Deviation (SD)

• Mean income was 35,000 with SD 5,000
• M 23,000, SD 500
• This is interpreted as there being less
  variability in income among members of the second
  data set. That is scores are grouped more tightly
  around the mean.

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Normal Distribution

• Meanmedianmode
• Bell shape curve
• 50 of scores fall below and 50 fall above the
  mean.
• Data set can be assessed in terms of how much
  data falls within one, two or three standard
  deviations from the mean.
• Generally is unimodal although some distributions
  may be bimodal or trimodal.
• Theoretically, at least, inferential statistics
  may only be used when a set of scores conform to
  a normal distribution. However, this assumption
  is often violated.

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Frequencies used in almost all types of data
analysis. Frequency tables can be formatted in a
variety of ways. (Some analysis add value and
cumulative percent)
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We can also use tables to determine if there is a
relationship between two nominal variables,
although we can not assess the strength of the
relationship. This is called a cross-tabulation
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Categories in both Qualitative Analysis must be

• Mutually exclusive (no overlap)
• Exhaustive (all possible categories should be
  included)

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Cross-tabulation is the basis for chi-square.
Chi-square

• Measures the strength of the relationship between
  the two variables in the table.
• Is not technically a inferential statistic does
  not require a normal distribution but is often
  grouped with inferential statistics.
• Usually requires a random sample although data
  collected from everyone in a population group is
  usually considered sufficient for a chi-square
  analysis.

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Means can also be used to make comparisons among
groups.
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You may use means on your project

• If your variables include ratio data
• If you want to compare groups on a ratio variable
• If you want to summarize scores on a standardized
  instrument or a likert scale

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Some inferential statistics look at the strength
of the relationship between mean scores on ratio
level variables and membership in particular
demographic group

• T-tests (two group comparisons)
• Analysis of variance (compares three or more
  groups)
• Answers question Is the difference in means
  between the two (or more) groups large enough to
  be statistically significant?

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We also use correlations to measure the strength
of a relationship between two variables.
Correlations can only be used

• To assess the strength of two ratio level
  variables.
• To measure associations rather than cause and
  effect relationships.
• With data sets in which there are 30 or more
  observations.

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Inferential statistics commonly used include

• Independent T-test (compares two groups on one
  variable). (Test statistic T)
• Paired sampled t-test (compares ratio level
  scores on pre and post test data). (Test
  statistic T)
• ANOVA compares three or more groups on ratio
  data (Test statistic F)
• Correlation measures the association between
  two ratio level variables (Test statistic R)
• Regression analysis (dependent ratio variable
  can include more than one independent variable
  (can be a combination of ratio, ordinal, and
  nominal data in the regression model). (Test
  statistic is R2, F, or partial correlation
  coefficients)

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Inferential Statistics require that we assess the
probability that there is actually a causal
relationship between two variables.

• We state the research null hypotheses.
• State the degree to which we will risk being
  wrong about whether or not a relationship
  actually exists between two variables (level of
  significance usually under .10)
• Choose an appropriate statistical test and
  compute it.
• Compare the probability level on your computer
  print out to the level of significance. If the p.
  value is lower than your confidence level, then
  reject the null hypothesis. If the p value is
  higher than the confidence level, accept the null
  hypothesis.

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For example

• There is a positive relationship between scores
  on the self-esteem scale and depression. Level of
  significance is .05. R .75, p .01. Reject
  Null Hypothesis and accept the Research
  Hypothesis.
• Women will have higher test scores than men.
  Level of significance .10. T .30, p. .60.
  Accept the Null Hypothesis and Reject the
  Research Hypothesis.

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Other info

• Chi-square is interpreted in the same way as
  inferential statistics.
• Most statistics books contain tables that let you
  determine p values if you calculate test
  statistics by hand.
• SPSS print outs always contain p values for
  inferential statistics.
• Theoretical assumptions are often violated in
  research articles.
• Sample size determines if a relationship between
  two or more variables is large enough to be
  statistically significant.
• Relationships between two variables can be either
  positive or negative. High positive relationships
  are close to 1.00 and high negative
  relationships are close to 1.00.