This document discusses the independent t-test, which is used to evaluate mean differences between two independent samples from different populations. It describes the key characteristics of an independent-measures design, including that it uses separate samples without prior knowledge of the population parameters. The t-test follows four steps: stating hypotheses; finding critical values; computing the test statistic, which compares the sample mean difference to the standard error; and making a decision about whether to reject the null hypothesis of no mean difference. It also notes the importance of the homogeneity of variance assumption and alternatives if it is violated.
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Linearity concept of significance, standard deviation, chi square test, students T- test, ANOVA test , pharmaceutical science, statistical analysis, statistical methods, optimization technique, modern pharmaceutics, pharmaceutics, mpharm 1 unit i sem, 1 year m
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The one-sample t-test is used to determine whether a sample comes from a population with a specific mean. This population mean is not always known, but is sometimes hypothesized.
linearity concept of significance, standard deviation, chi square test, stude...KavyasriPuttamreddy
Linearity concept of significance, standard deviation, chi square test, students T- test, ANOVA test , pharmaceutical science, statistical analysis, statistical methods, optimization technique, modern pharmaceutics, pharmaceutics, mpharm 1 unit i sem, 1 year m
pharm, applications of chi square test, application of standard deviation , pharmacy, method to compare dissolution profile, statistical analysis of dissolution profile, important statical analysis, m. pharmacy, graphical representation of standard deviation, graph of chi square test, graph of T test , graph of ANOVA test ,formulation of t test, formulation of chi square test, formula of standard deviation.
The one-sample t-test is used to determine whether a sample comes from a population with a specific mean. This population mean is not always known, but is sometimes hypothesized.
Marketing Research Project on T test and Sample Designing, Detail Analysis of all the aspect of T test and usage of all the tools for finding out the different variants.
Marketing Research Project on T test and Sample Designing, Detail Analysis of all the aspect of T test and usage of all the tools for finding out the different variants.
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The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
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Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
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2. 2
Independent-Measures Designs
• The independent-measures hypothesis test
allows researchers to evaluate the mean
difference between two populations using the
data from two separate samples.
• The identifying characteristic of the
independent-measures or between-subjects
design is the existence of two separate or
independent samples.
• Thus, an independent-measures design can be
used to test for mean differences between two
distinct populations (such as men versus
women) or between two different treatment
conditions (such as drug versus no-drug).
3.
4. 4
Independent-Measures Designs (cont.)
• The independent-measures design is used in
situations where a researcher has no prior
knowledge about either of the two populations
(or treatments) being compared.
• In particular, the population means and standard
deviations are all unknown.
• Because the population variances are not
known, these values must be estimated from the
sample data.
5. 5
Hypothesis Testing with the
Independent-Measures t Statistic
• As with all hypothesis tests, the general purpose
of the independent-measures t test is to
determine whether the sample mean difference
obtained in a research study indicates a real
mean difference between the two populations (or
treatments) or whether the obtained difference is
simply the result of sampling error.
• Remember, if two samples are taken from the
same population and are given exactly the same
treatment, there still will be some difference
between the sample means..
6. 6
Hypothesis Testing with the
Independent-Measures t Statistic (cont.)
• This difference is called sampling error
• The hypothesis test provides a
standardized, formal procedure for
determining whether the mean difference
obtained in a research study is
significantly greater than can be explained
by sampling error
7. 7
Hypothesis Testing with the
Independent-Measures t Statistic (cont.)
• To prepare the data for analysis, the first
step is to compute the sample mean and
SS (or s, or s2) for each of the two
samples.
• The hypothesis test follows the same four-
step procedure outlined in Chapters 8 and
9.
8. 8
Hypothesis Testing with the
Independent-Measures t Statistic (cont.)
1.State the hypotheses and select an α level. For
the independent-measures test, H0 states that
there is no difference between the two
population means.
2.Locate the critical region. The critical values for
the t statistic are obtained using degrees of
freedom that are determined by adding together
the df value for the first sample and the df value
for the second sample.
9. 9
Hypothesis Testing with the
Independent-Measures t Statistic (cont.)
3. Compute the test statistic. The t statistic for the
independent-measures design has the same structure as
the single sample t introduced in Chapter 9. However, in
the independent-measures situation, all components of
the t formula are doubled: there are two sample means,
two population means, and two sources of error
contributing to the standard error in the denominator.
4. Make a decision. If the t statistic ratio indicates that the
obtained difference between sample means (numerator)
is substantially greater than the difference expected by
chance (denominator), we reject H0 and conclude that
there is a real mean difference between the two
populations or treatments.
10.
11. 11
The Homogeneity of Variance
Assumption
• Although most hypothesis tests are built on a set of
underlying assumptions, the tests usually work
reasonably well even if the assumptions are violated.
• The one notable exception is the assumption of
homogeneity of variance for the independent-
measures t test.
• The assumption requires that the two populations from
which the samples are obtained have equal variances.
• This assumption is necessary in order to justify pooling
the two sample variances and using the pooled variance
in the calculation of the t statistic.
12. 12
The Homogeneity of Variance
Assumption (cont.)
• If the assumption is violated, then the t statistic
contains two questionable values: (1) the value
for the population mean difference which comes
from the null hypothesis, and (2) the value for
the pooled variance.
• The problem is that you cannot determine which
of these two values is responsible for a t statistic
that falls in the critical region.
• In particular, you cannot be certain that rejecting
the null hypothesis is correct when you obtain an
extreme value for t.
13. 13
The Homogeneity of Variance
Assumption (cont.)
• If the two sample variances appear to be
substantially different, you should use
Hartley’s F-max test to determine whether
or not the homogeneity assumption is
satisfied.
• If homogeneity of variance is violated, Box
10.3 presents an alternative procedure for
computing the t statistic that does not
involve pooling the two sample variances.
14.
15. 15
Measuring Effect Size for the
Independent-Measures t
• Effect size for the independent-measures t
is measured in the same way that we
measured effect size for the single-sample
t in Chapter 9.
• Specifically, you can compute an estimate
of Cohen=s d or you can compute r2 to
obtain a measure of the percentage of
variance accounted for by the treatment
effect.