SESN+9+ASSIGN-1+&+2

Fall 2014-SESSION 9 LECTURE and ASSIGNMENTS-1 & 2

問題 Assignment 1: Read about t-tests in Chi Square and Research Comes Alive found in Session 8 resources. No posting.

問題 Assignment 2. To get an idea of what t actually is let’s enter the data from Chi Square example on page 80. Notice the t test formula and the kinds of information contained in the formula— • x̅ refers to a sample mean. • s refers to the standard deviation of a sample. • s2 refers to the variance of a sample. • n refers to number in the group

Luckily you do not need to put your data into the formula. Quick calcs does it for you and generates __the t statistic__ as you saw in last week’s assignment. The number needs to be large enough to exceed the critical value related to the probability you want and the number of people in your study—or in stat talk, the __degrees of freedom__, which relates to the number of people in your study __minus 1 (repeated measures design) or minus 2 (2 group comparison design)__. In the resource section you will find a __Table of Critical Values__ described in __Chi Square__ so you can see why the data set was considered significant. QuickCalcs actually tells you whether there is __significance__ and also what the __probability__ is that is related to the t.

Enter the data to see if your results align to the one in the book. You will use //**__an unpaired t test__**// this time. //**__ Do you know why? __**// //**__ Post a comment about your results. Did they match (remember, calculation in book was based on rounded off values). __**//

//**__ (Group or individual posting) __**//

.

page 80 .
 * || Group A (Ex) || Group B (Control) ||
 * 1 || 100 || 85 ||
 * 2 || 95 || 85 ||
 * 3 || 95 || 80 ||
 * 4 || 90 || 75 ||
 * 5 || 90 || 75 ||
 * 6 || 100 || 90 ||
 * 7 || 70 || 85 ||
 * 8 || 60 || 75 ||
 * 9 || 85 || 50 ||
 * 10 || 100 || 80 ||
 * 11 || 75 || 80 ||
 * 12 || 75 || 85 ||
 * 13 || 85 || 60 ||
 * 14 || 80 || 70 ||
 * 15 || 75 || 40 ||

問題で言われたので、You will use //**__an unpaired t test__**// this time.

Unpaired //t// test results
The two-tailed P value equals 0.0355 By conventional criteria, this difference is considered to be statistically significant.
 * **P value and statistical significance:**

The mean of Group A (Ex) minus Group B (Control) equals 10.67 95% confidence interval of this difference: From 0.78 to 20.55
 * Confidence interval:**

t = 2.2097 df = 28 standard error of difference = 4.827
 * Intermediate values used in calculations:**

GraphPad's web site includes portions of the manual for GraphPad Prism that can help you learn statistics. First, review the meaning of [|P values] and [|confidence intervals]. Then learn how to interpret results from an [| unpaired] or [|paired]//t// test. These links include GraphPad's popular //analysis checklists//.
 * Learn more:**


 * Review your data:** ||


 * ~ Group ||~ Group A (Ex) ||~ Group B (Control) ||
 * Mean || 85.00 || 74.33 ||
 * SD || 12.25 || 14.13 ||
 * SEM || 3.16 || 3.65 ||
 * N || 15 || 15 ||

=ーー　ここから、我々の答え　ーー=

問題 = You will use //**__an unpaired t test__**// this time. //**__ Do you know why? __**// . According to the site below -- Unpaired t test < http://www.graphpad.com/guides/prism/6/statistics/index.htm?how_the_unpaired_t_test_works.htm > //__says__// "The unpaired t test __compares__ the means of __two unmatched groups__, assuming that the values follow a Gaussian distribution".

On the other hand, Paired or ratio t test < http://www.graphpad.com/guides/prism/6/statistics/index.htm?how_the_unpaired_t_test_works.htm > //__says__// "The paired t test __compares__ the means of __two matched groups__, assuming that the distribution of the before-after differences follows a Gaussian distribution".

P80, we used and compared to two different groups (= __two unmatched groups__ ), so we should use the //**__unpaired__**//  t test.

. 問題 = //**__ Post a comment about your results. Did they match (remember, calculation in book was based on rounded off values). __**// //**__ (Group or individual posting) __**//

//(//**Text p81-83)** ||  ||   || ==Unpaired //t// test results== ||   ||   || df = 28
 * //**__ In book __**//, it //__says__//
 * t = 2.24

p. < 0.05 ||  ||   || **Intermediate values used in calculations:** t = 2.2097 df = 28 standard error of difference = 4.827

The two-tailed P value equals 0.0355 By conventional criteria, this difference is considered to be statistically significant. ||  ||   ||
 * P value and statistical significance:**
 * || Group A (Ex) || Group B (Control) ||  || Group A (Ex) || Group B (Control) ||
 * Mean || 85 || 74.3 || Mean || 85.00 || 74.33 ||
 * SD || 12.25 || 14.12 || SD || 12.25 || 14.13 ||
 * t || t = 2.24 || t = 2.24 ||  || t = 2.2097 || t = 2.2097 ||
 * t || t = 2.24 || t = 2.24 ||  || t = 2.2097 || t = 2.2097 ||
 * t || t = 2.24 || t = 2.24 ||  || t = 2.2097 || t = 2.2097 ||

//**__ Did they match (remember, calculation in book was based on rounded off values) __**// Match most numbers -- some numbers are rounded off, so I assume we can say -- statistically insignificant.

. =ーー　答え　終了ーー=

t tests, Mann-Whitney and Wilcoxon matched pairs test
 * Paired or unpaired? Parametric or nonparametric?
 * Unpaired t test
 * Paired or ratio t test
 * Mann-Whitney or Kolmogorov-Smirnov test
 * Wilcoxon matched pairs test
 * Multiple t tests

---
 * Unpaired t test
 * How to: Unpaired t test from raw data
 * How to: Unpaired t test from averaged data
 * Interpreting results: Unpaired t
 * The unequal variance Welch t test
 * Graphing tips: Unpaired t
 * Advice: Don't pay much attention to whether error bars overlap
 * Analysis checklist: Unpaired t test


 * Paired or ratio t test
 * How to: Paired t test
 * Testing if pairs follow a Gaussian distribution
 * Interpreting results: Paired t
 * Analysis checklist: Paired t test
 * Graphing tips: Paired t
 * Paired or ratio t test?
 * How to: Ratio t test
 * Interpreting results: Ratio t test
 * Analysis checklist: Ratio t test

=Entering data for a t test =

Setting up the data table
From the Welcome (or New Table and graph) dialog, choose the Column tab. If you aren't ready to enter your own data, choose one of the sample data sets. If you want to enter data, note that there are two choices. You can enter raw data or summary data (as mean, SD or SEM, and n).

Entering raw data
[|Enter the data for each group into a separate column]. The two groups do not have be the same size (it's OK to leave some cells empty). If the data are unpaired, it won't make sense to enter any row titles. If the data are matched, so each row represents a different subject of experiment, then [|you may wish to use row titles] to identify each row.

Enter mean and SD or SEM
Prism can compute an unpaired t test (but not a paired t test, and not nonparametric comparisons) [|with data entered as mean, SD (or SEM), and n]. This can be useful if you are entering data from another program or publication. <span class="f_BodyText">From the Column tab of the Welcome dialog, choose that you wish to enter and plot error values computed elsewhere. Then choose to enter mean, n, and either SD, SEM or %CV (coefficient of variation). Entering sample size (n) is essential. It is not possible to compute a t test if you only enter the mean and SD or SEM without n. <span class="f_BodyText">Even though you made your choice on the Column tab of the Welcome dialog, Prism will show you a Grouped data table. Enter your data on the first row of this table.

<span class="f_Heading3">Is it possible to define the two groups with a grouping variable?
<span class="f_BodyText">Some programs expect (or allow) you to enter all the data into one column, and enter a grouping variable into a second column to define which rows belong to which treatment group. Prism does not use this way to organize data. Instead, the two groups must be defined by two columns. Enter data for one group into column A and the other group into column B.

<span class="f_Heading3">Can I enter data in lots of columns and then choose two to compare with a t test?
<span class="f_BodyText">Yes. After you click Analyze, you'll see a list of all data sets on the right side of the dialog. Select the two you wish to compare.

<span class="f_Heading3">Can I enter data as mean, SD (or SEM) and N?
<span class="f_BodyText">Yes. Follow [|this example] to see how. With data entered this way, you can only choose an unpaired t test. It is impossible to run a paired t test or a nonparametric test from data entered as mean, SD (or SEM) and N.

<span class="f_Heading3">Can I enter data for many t tests on one table, and ask Prism to run them all at once?
<span class="f_BodyText">[|Yes!]
 * URL of this page:** @http://www.graphpad.com/guides/prism/6/statistics/index.htm?stat_entering_t_test_data.htm

=<span class="f_Heading1">Analysis checklist: Unpaired t test = <span class="f_BodyText">The unpaired t test compares the means of two unmatched groups, assuming that the values follow a Gaussian distribution. Read elsewhere to learn about [|choosing a t test], and [|interpreting the results].

[[image:http://graphpad.com/guides/prism/6/statistics/check.jpg width="25" height="21"]]<span class="f_Heading3">Are the populations distributed according to a Gaussian distribution?
<span class="f_Bullets">The unpaired t test assumes that you have sampled your data from populations that follow a Gaussian distribution. Prism can perform normality tests as part of the [|Column Statistics] analysis. [|Learn more].

[[image:http://graphpad.com/guides/prism/6/statistics/check.jpg width="25" height="21"]]<span class="f_Heading3">Do the two populations have the same variances?
<span class="f_Bullets">The unpaired t test assumes that the two populations have the same variances (and thus the same standard deviation). <span class="f_Bullets">Prism tests for equality of variance with an F test. The P value from this test answers this question: If the two populations really have the same variance, what is the chance that you would randomly select samples whose ratio of variances is as far from 1.0 (or further) as observed in your experiment? A small P value suggests that the variances are different. <span class="f_Bullets">Don't base your conclusion solely on the F test. Also think about data from other similar experiments. If you have plenty of previous data that convinces you that the variances are really equal, ignore the F test (unless the P value is really tiny) and interpret the t test results as usual. <span class="f_Bullets">In some contexts, finding that populations have different variances may be as important as finding different means.

[[image:http://graphpad.com/guides/prism/6/statistics/check.jpg width="25" height="21"]]<span class="f_Heading3">Are the data unpaired?
<span class="f_Bullets">The unpaired t test works by comparing the difference between means with the standard error of the difference, computed by combining the standard errors of the two groups. If the data are paired or matched, then you should choose a paired t test instead. If the pairing is effective in controlling for experimental variability, the paired t test will be more powerful than the unpaired test.

[[image:http://graphpad.com/guides/prism/6/statistics/check.jpg width="25" height="21"]]<span class="f_Heading3">Are the “errors” independent?
<span class="f_Bullets">The term “error” refers to the difference between each value and the group mean. The results of a t test only make sense when the scatter is random – that whatever factor caused a value to be too high or too low affects only that one value. Prism cannot test this assumption. You must think about the experimental design. For example, the errors are not independent if you have six values in each group, but these were obtained from two animals in each group (in triplicate). In this case, some factor may cause all triplicates from one animal to be high or low.

[[image:http://graphpad.com/guides/prism/6/statistics/check.jpg width="25" height="21"]]<span class="f_Heading3">Are you comparing exactly two groups?
<span class="f_Bullets">Use the t test only to compare two groups. To compare three or more groups, use [|one-way ANOVA] followed by multiple comparison tests. It is not appropriate to perform several t tests, comparing two groups at a time. Making multiple comparisons increases the chance of finding a statistically significant difference by chance and makes it difficult to interpret P values and statements of statistical significance. Even if you want to use planned comparisons to avoid correcting for multiple comparisons, you should still do it as part of one-way ANOVA to take advantage of the extra degrees of freedom that brings you.

[[image:http://graphpad.com/guides/prism/6/statistics/check.jpg width="25" height="21"]]<span class="f_Heading3">Do both columns contain data?
<span class="f_Bullets">If you want to compare a single set of experimental data with a theoretical value (perhaps 100%) don't fill a column with that theoretical value and perform an unpaired t test. Instead, use a [|one-sample t test].

[[image:http://graphpad.com/guides/prism/6/statistics/check.jpg width="25" height="21"]]<span class="f_Heading3">Do you really want to compare means?
<span class="f_Bullets">The unpaired t test compares the means of two groups. It is possible to have a tiny P value – clear evidence that the population means are different – even if the two distributions overlap considerably. In some situations – for example, assessing the usefulness of a diagnostic test – you may be more interested in the overlap of the distributions than in differences between means.

[[image:http://graphpad.com/guides/prism/6/statistics/check.jpg width="25" height="21"]]<span class="f_Heading3">If you chose a one-tail P value, did you predict correctly?
<span class="f_Bullets">If you chose a [|one-tail P value], you should have predicted which group would have the larger mean before collecting any data. Prism does not ask you to record this prediction, but assumes that it is correct. If your prediction was wrong, then ignore the P value reported by Prism and state that P>0.50.
 * URL of this page:** @http://graphpad.com/guides/prism/6/statistics/index.htm?stat_checklist_unpairedttest.htm

=<span class="f_Heading1">Analysis checklist: Paired t test = <span class="f_BodyText">The paired t test compares the means of two matched groups, assuming that the distribution of the before-after differences follows a Gaussian distribution.

[[image:http://graphpad.com/guides/prism/6/statistics/check.jpg width="25" height="21"]]<span class="f_Heading3">Are the differences distributed according to a Gaussian distribution?
<span class="f_Bullets">The paired t test assumes that you have sampled your pairs of values from a population of pairs where the difference between pairs follows a Gaussian distribution. <span class="f_Bullets">While this assumption is not too important with large samples, it is important with small sample sizes. [|Test this assumption with Prism]. <span class="f_Bullets">Note that the paired t test, unlike the unpaired t test, does not assume that the two sets of data (before and after, in the typical example) are sampled from populations with equal variances.

[[image:http://graphpad.com/guides/prism/6/statistics/check.jpg width="25" height="21"]]<span class="f_Heading3">Was the pairing effective?
<span class="f_Bullets">The pairing should be part of the experimental design and not something you do after collecting data. Prism tests the effectiveness of pairing by calculating the Pearson correlation coefficient, r, and a corresponding P value. If the P value is small, the two groups are significantly correlated. This justifies the use of a paired test. <span class="f_Bullets">If this P value is large (say larger than 0.05), you should question whether it made sense to use a paired test. Your choice of whether to use a paired test or not should not be based solely on this one P value, but also on the experimental design and the results of other similar experiments.

[[image:http://graphpad.com/guides/prism/6/statistics/check.jpg width="25" height="21"]]<span class="f_Heading3">Are the pairs independent?
<span class="f_Bullets">The results of a paired t test only make sense when the pairs are [|independent] – that whatever factor caused a difference (between paired values) to be too high or too low affects only that one pair. Prism cannot test this assumption. You must think about the experimental design. For example, the errors are not independent if you have six pairs of values, but these were obtained from three animals, with duplicate measurements in each animal. In this case, some factor may cause the after-before differences from one animal to be high or low. This factor would affect two of the pairs, so they are not independent.

[[image:http://graphpad.com/guides/prism/6/statistics/check.jpg width="25" height="21"]]<span class="f_Heading3">Are you comparing exactly two groups?
<span class="f_Bullets">Use the t test only to compare two groups. To compare three or more matched groups, use repeated measures one-way ANOVA followed by post tests. It is [|not appropriate] to perform several t tests, comparing two groups at a time.

[[image:http://graphpad.com/guides/prism/6/statistics/check.jpg width="25" height="21"]]<span class="f_Heading3">If you chose a one-tail P value, did you predict correctly?
<span class="f_Bullets">If you chose a one-tail P value, you [|should have predicted] which group would have the larger mean before collecting data. Prism does not ask you to record this prediction, but assumes that it is correct. If your prediction was wrong, then ignore the reported P value and state that P>0.50.

[[image:http://graphpad.com/guides/prism/6/statistics/check.jpg width="25" height="21"]]<span class="f_Heading3">Do you care about differences or ratios?
<span class="f_Bullets">The paired t test analyzes the differences between pairs. With some experiments, you may observe a very large variability among the differences. The differences are larger when the control value is larger. With these data, you'll get more consistent results if you perform a [|ratio t test].
 * URL of this page:** @http://graphpad.com/guides/prism/6/statistics/index.htm?stat_checklist_pairedt.htm

Group A (Ex) 100 95 95 90 90 100 70 60 85 100 75 75 85 80 75

Group B (Control) 85 85 80 75 75 90 85 75 50 80 80 85 60 70 40

Just in case.....,

Paired //t// test results
The two-tailed P value equals 0.0211 By conventional criteria, this difference is considered to be statistically significant.
 * **P value and statistical significance:**

The mean of Group A (Ex) minus Group B (Control) equals 10.67 95% confidence interval of this difference: From 1.86 to 19.48
 * Confidence interval:**

t = 2.5968 df = 14 standard error of difference = 4.108
 * Intermediate values used in calculations:**

GraphPad's web site includes portions of the manual for GraphPad Prism that can help you learn statistics. First, review the meaning of [|P values] and [|confidence intervals]. Then learn how to interpret results from an [| unpaired] or [|paired]//t// test. These links include GraphPad's popular //analysis checklists//.
 * Learn more:**


 * Review your data:** ||


 * ~ Group ||~ Group A (Ex) ||~ Group B (Control) ||
 * Mean || 85.00 || 74.33 ||
 * SD || 12.25 || 14.13 ||
 * SEM || 3.16 || 3.65 ||
 * N || 15 || 15 ||

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