Bidin Yatim, PhD

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Data Analysis with SPSS

• Bidin Yatim, PhD
• Applied Statistics, Exeter University
• Industrial Mathematics, Aston University
• Mathematics Statistics, Notingham University

Topic 3
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Testing hypothesis about two population means

• Investigate assumptions required for small sample
  tests
• Perform hypothesis tests concerning the different
  in means of two dependent populations
• Perform hypothesis tests concerning the
  difference in means of two independent
  populations

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Review of Tests Weve Learned So Far

• One-sample t-tests
• Used to compare one sample mean to a population
  mean or some other known value.
• More common Compare two (or more) sample means
  to each other
• Two general research strategies
• Two completely separate (independent) samples
• Two related (dependent) samples

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Introducing the Independent Samples t-test

• To be considered independent, we must have no
  reason to believe that the observation in one
  sample could effect or be affected by the
  observations in the other.
• Did mental imagery raise scores or are the
  differences due to chance (sampling error)?
• Or, do the samples come from the same population?

Pop1 µ?
Pop2 µ?
Sample1 Rote Memory M19
Sample2 Imagery M25
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Setting the Statistical Hypothesis for Ind.
Samples

• For Two-Tailed Tests
• H0
• H0 µ1 µ2 0 Or H0 µ1 µ2
• H1
• H1 µ1 µ2 ? 0 Or H1 µ1 ? µ2

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Two Sample T-Test Example

• Group1 Rote Group2 Imagery
• 24 13 18 31
• 23 17 19 29
• 16 20 23 26
• 17 15 29 21
• 19 26 30 24

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Two Sample T-Test Example

• Research Question Does mental imagery change
  memory scores?
• State Statistical Hypothesis
• H0 µ rote µ imagery
• H1 µ rote ? µ imagery

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Directional Test (one-tailed)

• Mental imagery improves memory scores.
• H0 µ1gtµ2 or H0 µ1-µ2gt0
• H1 µ1ltµ2 or H1 µ1-µ2lt0
• Mental imagery decreases memory scores.
• H0 µ1ltµ2 or H0 µ1-µ2lt0
• H1 µ1gtµ2 or H1 µ1-µ2gt0
• Where µ1Rote Group and µ2Imagery Group

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Assumptions of the Independent Samples t-test

• Independent Observations
• Normality
• Homogeneity of Variance

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Hey! Lets get our hands dirty Using SPSS.

• FilegtOpengtDatagtStudents file

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Assumptions Independent, normality, equal
variances

• Equal variances is not actually required. SPSS
  will handle it.
• Normality, t-test is reliable as long as the
  sample suggest symmetric n bell shaped.

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Checking normality GraphgtInteractivegtHistogram

• Drag Height and place it
• Drag gender and place it
• Click OK
• Reasonably symmetrical,
• bell shaped, suitable for t-test

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Visualize using box-plotGraphgtInteractivegtBoxplot

• Drag Height and place it
• Drag Gender and place it
• Click OK and
• Roughly symmetrical,
• Comparable variances, median
• line suggests average are
• different hence t-test

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AnalyzegtCompare MeansgtIndependent-Samples T Test
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AnalyzegtCompare MeansgtIndependent-Samples T
TestgtOk

• Recall, were testing one-sided hypothesis
• Equal or unequal variances
• P-value is very small, reject null hypothesis

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Introducing the Dependent Samples t-test

• The type of t-test you use is determined by the
  research design employed.
• Use a one sample t-test if you wish to compare a
  single sample mean to a hypothesized population
  mean value.
• Use a independent samples t-test if you have two
  independent sample means that you wish to
  compare.
• Use a dependent samples t-test if you 1) measure
  the same participants on a dependent variable at
  two different times, or 2) have two separate
  groups of participants that have been matched
  based on some characteristic.

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Dependent Samples t-testResearch Strategies
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Dependent Samples t-test Repeated Measures
Design Example

• Research Question Is clinical depression
  affected by new pharmaceutical treatment?
• State Statistical Hypothesis (two-tailed)
• H0 µ before µ after or µ D 0
• H1 µ before ? µ after or µ D ? 0

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Dependent Samples t-test Example

• Before After 72 64
  
• 68 60
• 60 50
• 71 66
• 55 56

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Dependent Samples t-test Matched Design Example

• Research Question Does hypnosis decrease
  cigarette smoking?
• State Statistical Hypothesis (one-tailed)
• H0 µ hypnosis gt µ no hypnosis or µ D gt 0
• H1 µ hypnosis lt µ no hypnosis or µ D lt 0

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Dependent Samples t-test Example

• No Hypnosis Hypnosis 19 13
  
• 35 37
• 20 14
• 31 25

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Hey! Lets get our hands dirty Using SPSS.

• FilegtOpengtDatagtSwimmers2
• This file contains swimming meet results for high
  school swim team. Each swimmer competed in one or
  more events, for each event, the file contains
  the time for the swimmers first n last heat.

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Dependent sample t-testAnalyzegtCompare
MeansgtPaired-Sample T Test

• Choose the two variables related to the 100 meter
  free-style and click OK
• After selecting the two variables, click here

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On average, swimmers improve their times by
5.9931 seconds, the p-value is approximately 0
hence But what if we treat the data as
independent? Dont just sit there, do something
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Exercises DIY

• Swimmer2
• Do individual swimmers significantly improve
  their performance between the first and second
  recorded times in the 50-meter freestyle?
• In their second times, do swimmers who compete in
  the 50-meter freestyle swim faster than they do
  in the 50-meter backstroke?

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End of Part ThreeSee U LaterPlease Dont Go
Away What if the data is not normal?