T test
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T-Test. The purpose of t test (Gosset, 1908) is to compare two means. It assesses whether two means are statistically different. It can assess the difference between two groups or two variables. Limitations.

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T-Test

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T test

T-Test

  • The purpose of t test (Gosset, 1908) is to compare two means.

  • It assesses whether two means are statistically different.

  • It can assess the difference between two groups or two variables.


Limitations

Limitations

  • It assumes that the data are normally distributed (e.g., Wilk-Shapiro normality test)

  • It assumes that there is equality of variances between groups (e.g., F test, or more robust Levene's test)

  • It is highly sensitive to sample sizes (need n>30)

  • It only can be used to compare two groups. If used to compare more than 2 groups, we may incur a type-I error.


T test models

T-Test Models

  • Independent-samples t test (independent means): Compares the means of one variable for two groups.

  • Paired-samples t test (dependent means): Compares the means of two variables for a single group.


Independent samples t test

Independent-samples t test

  • It compares means for two groups of cases.

  • Used in survey studies with different groups (e.g., teachers and administrators) to assess whether there are differences in responses or scores between the two groups.


Example independent samples

Example - Independent Samples

  • Used in experimental studies, in which subjects are randomly assigned to two groups (treatment and control), to assess whether differences are found between groups before the intervention (equivalence)

  • Question: Are the two groups of students (treatment and control) the same on key characteristics (e.g., reading pre-test score) before the intervention?


Procedures

Procedures

  • Analyze

    Compare means

    Independent-samples t test

    Test variables: select the variables

    Grouping variable: select the group variable

    Define groups: type codes

    (e.g., control=0, treatment=1)

    Click Continue, then OK


An example

An example

  • Dataset: Survey3ED.sav (Pallant)

  • Use t test to assess whether there are significant differences between males and females on their self-esteem levels

  • The grouping variable will be: Gender.

  • Check data (Ns for each group, missing data? Coding?)

  • Check assumptions (e.g., Levene’s test for equality of variances)


Survey3ed example continued

Survey3ED example (continued)

  • Assess differences between groups

  • Calculate effect sizes

  • Present results


Are we having fun

Are we having fun?

  • Based on your research interests, what research questions would require an independent samples t-test?

  • Try it out!


Paired samples t test

Paired-samples t test

  • It is commonly used in quasi-experimental or "pre-post" design.

  • Pre-post designs consists of two measurements taken on the same subjects, one before and one after the introduction of a treatment or intervention.

  • If the treatment had no effect, the average difference between the measurements is equal to 0 and the null hypothesis holds.

  • If the treatment had an effect (intended or unintended!), the average difference is not 0 and the null hypothesis is rejected.


Example paired samples

Example Paired-Samples

  • Used in experimental studies, in which subjects are randomly assigned to two groups (treatment and control), to assess whether differences are found between groups after the intervention (pre-post impact)

  • Research Question: Will students randomly assigned to the reading intervention improve their reading outcomes significantly more than students randomly assigned to the control group?


Procedures1

Procedures

  • Analyze

    Compare Means

    Paired-Samples T Test

    Paired variables: Select pre-post variables

    Options:

    Confidence interval: 95%

    Missing values: exclude cases analysis by analysis


An example1

An example

  • Dataset: experim3ED.sav (Pallant)

  • Use t test to assess whether there are significant differences between students’ confidence in their ability to successfully complete a statistics course following the intervention.

  • The grouping variable will be: Time.

  • Check data (Ns for each group, missing data? Coding?)

  • Check assumptions (e.g., Levene’s test for equality of variances, plus difference between scores are normally distributed, n>30)


T test

Experim3ED example (cont.)

  • Determine overall significance (p<.05)

  • Compare mean values – which is higher? T1 or T2?

    • Limitation: No treatment/control groups

    • PCVs – Potentially confounding variables

  • Calculate effect size

  • Present results


Are we still having fun

Are we (still) having fun?

  • Based on your research interests, what research questions would require a paired samples t-test?

  • Try it out!


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