Presented by:P.N.V.Sriram 2010231 Swati Jain 2010238 Tushar Manghrani 2010243 Udit Gupta 2010245 Ashikaben Patel 2010270
Suppose we conducted a study to compare two strategies for teaching spelling. Group A had a mean score of 19. The range of scores was 16 to 22, and the standard deviation was 1.5. Group B had a mean score of 20. The range of scores was 17 to 23, and the standard deviation was 1.5. How confident can we be that the difference we found between the means of Group A and Group B occurred because of differences in our reading strategies, rather than by chance?10 9 8 7 6 5 4 3 2 1
2
t-test
12 13 14 15 16 17 18 19 20 21 22 23 24 25
Spelling Test Scores
Tuesday, December 21, 2010
A t-test allows us to compare the means of two groups and determine how likely the difference between the two means occurred by chance. The calculations for a t-test requires three pieces of information: - the difference between the means (mean difference) - the standard deviation for each group - and the number of subjects in each group.
10 9 8 7 6 5 4 3 2 1
3
t-test
12 13 14 15 16 17 18 19 20 21 22 23 24 25
Spelling Test Scores
Tuesday, December 21, 2010
All other factors being equal, large differences between means are less likely to occur by chance than small differences.
10 9 8 7 6 5 4 3 2 1
12 13 14 15 16 17 18 19 20 21 22 23 24 25
Spelling Test Scores10 9 8 7 6 5 4 3 2 1
4
t-test
12 13 14 15 16 17 18 19 20 21 22 23 24 25
Spelling Test Scores
Tuesday, December 21, 2010
The size of the standard deviation also influences the outcome of a t-test. Given the same difference in means, groups with smaller standard deviations are more likely to report a significant difference than groups with larger standard deviations.10 9 8 7 6 5 4 3 2 1
12 13 14 15 16 17 18 19 20 21 22 23 24 25
Spelling Test Scores10 9 8 7 6 5 4 3 2 1
5
t-test
12 13 14 15 16 17 18 19 20 21 22 23 24 25
Spelling Test Scores
Tuesday, December 21, 2010
From a practical standpoint, we can see that smaller standard deviations produce less overlap between the groups Less overlap than larger standard deviations. would indicate that the groups are more different from each other.
10 9 8 7 6 5 4 3 2 1
12 13 14 15 16 17 18 19 20 21 22 23 24 25
Spelling Test Scores10 9 8 7 6 5 4 3 2 1
6
t-test
12 13 14 15 16 17 18 19 20 21 22 23 24 25
Spelling Test Scores
Tuesday, December 21, 2010
The size of our sample is also important. The more subjects that are involved in a study, the more confident we can be that the differences we find between our groups did not occur by chance.16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
12 13 14 15 16 17 18 19 20 21 22 23 24 25
Spelling Test Scores10 9 8 7 6 5 4 3 2 1
7
t-test
12 13 14 15 16 17 18 19 20 21 22 23 24 25
Spelling Test Scores
Tuesday, December 21, 2010
Once we calculate the outcome of the t-test(which produces a t-value), we check that value with the appropriate degrees of freedom on a critical value table to determine how likely the difference between the means occurred by chance.8 t-test Tuesday, December 21, 2010
There are three types of t-tests and each is calculated slightly differently. A correlated (or paired) t-test is concerned with the difference between the average scores of a single sample of individuals who is assessed at two different times (such as before treatment and after treatment) or on two different measures. It can also compare average scores of samples of individuals who are paired in some way (such as siblings, mothers and daughters, persons who are matched in terms of a particular characteristics).
An independent t-test compares the averages of two samples that are selected independently of each other (the subjects in the two groups are not the same people). There are two types of independent t-tests: equal variance and unequal variance.9 t-test Tuesday, December 21, 2010
An equal variance (pooled variance) t-test is used when the number of subjects in the two groups is the same OR the variance of the two groups is similar.
An unequal variance (separate variance) t-test is used when the number of subjects in the two groups is different AND the variance of the two groups is different.
10
t-test
Tuesday, December 21, 2010
Overview Two paired samples: Within-Subject Designs-Hypothesis test -Confidence Interval -Effect Size
Two independent samples: Between-Subject Designs-Hypothesis test -Confidence interval -Effect Sizet-test
11
Tuesday, December 21, 2010
Comparing Two PopulationsUntil this point, all the inferential statistics we have considered involve using one sample as the basis for drawing conclusion about one population.
Although these single sample techniques are used occasionally in real research, most research studies aim to compare of two (or more) sets of data in order to make inferences about the differences between two (or more) populations.
12
t-test
Tuesday, December 21, 2010
Two kinds of studiesThere are two general research strategies that can be used to obtain the two sets of data to be compared: 1. The two sets of data could come from two independent populations (e.g. women and men, or students from
