Transcript of The Independent- Samples t Test Chapter 11. Independent Samples t-Test >Used to compare two means in...
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- The Independent- Samples t Test Chapter 11
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- Independent Samples t-Test >Used to compare two means in a
between-groups design (i.e., each participant is in only one
condition)
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- Distribution of Differences Between Means
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- Hypothesis Tests & Distributions
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- Steps for Calculating Independent Sample t Tests >Step 1:
Identify the populations, distribution, and assumptions. >Step
2: State the null and research hypotheses. >Step 3: Determine
the characteristics of the comparison distribution. >Step 4:
Determine critical values, or cutoffs. >Step 5: Calculate the
test statistic. >Step 6: Make a decision.
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- Population 1: People told they are drinking wine from a $10
bottle. Population 2: People told they are drinking wine from a $90
bottle. The distribution: a distribution of differences between
means (rather than a distribution of mean difference scores).
Assumptions: The participants were not randomly selected so we must
be cautious with respect to generalizing our findings. We do not
know whether the population is normally distributed. Step 1:
Identify the populations, distribution, and assumptions.
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- Null hypothesis: On average, people drinking wine they were
told was from a $10 bottle give it the same rating as people
drinking wine they were told was from a $90 bottle. H 0 : 1 = 2
Research hypothesis: On average, people drinking wine they were
told was from a $10 bottle give it a different rating than people
drinking wine they were told was from a $90 bottle. H 1 : 1 2 v
Step 2: State the null and research hypotheses.
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- Calculate the pooled variance and then the standard deviation
of the difference. Step 3: Determine the characteristics of the
comparison distribution.
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- Formulae
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- Additional Formulae
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- Step 4: Determine critical values, or cutoffs.
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- Step 5. Calculate the test statistic
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- Step 6: Make a Decision.
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- >t(df) = tcalc, p .05 if there is no difference between
means Use p t(7) = -2.44, p
- Beyond Hypothesis Testing >Just like z tests, single-sample
t tests, and paired-samples t tests, we can calculated confidence
intervals and effect size for independent-samples t tests
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- Steps for Calculating CIs >Step 1. Draw a normal curve with
the sample difference between means in the center. >Step 2.
Indicate the bounds of the CI on either end, writing the
percentages under each segment of the curve. >Step 3. Look up
the t values for lower and upper ends of the CIs in the t table.
>Step 4. Convert the t values to raw differences. >Step 5.
Check the answer.
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- A 95% Confidence Interval for Differences Between Means, Part
I
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- A 95% Confidence Interval for Differences Between Means, Part
II
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- A 95% Confidence Interval for Differences Between Means, Part
III
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- Effect Size >Used to supplement hypothesis testing
>Cohens d:
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- Effect Size
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- Data Transformations 1. Transform a scale variable to an
ordinal variable. 2. Use a data transformation such as square root
transformation to squeeze the data together to make it more normal.
>Remember that we need to apply any kind of data transformation
to every observation in the data set.
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- >When would you use a z test over a t test? >When would
you use an independent sample t test? Think of a specific study.
>When would you use a paired sample t test? Think of a specific
study. Stop and Think