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The T-Test

The T-Test
« PreviousHomeNext » The t-test assesses whether the means of two groups are statistically different from each other. This analysis is appropriate whenever you want to compare the means of two groups, and especially appropriate as the analysis for the posttest-only two-group randomized experimental design. Figure 1 shows the distributions for the treated (blue) and control (green) groups in a study. What does it mean to say that the averages for two groups are statistically different? This leads us to a very important conclusion: when we are looking at the differences between scores for two groups, we have to judge the difference between their means relative to the spread or variability of their scores. The formula for the t-test is a ratio. The top part of the formula is easy to compute -- just find the difference between the means. Remember, that the variance is simply the square of the standard deviation. The final formula for the t-test is shown in Figure 5: Related:  High School Field Ecology Course

Independent Groups t-test: Chapter 10 Independent Groups t-test: Chapter 10 Strength of the Relationship (10.3) - For the example we computed in class, we found a statistically significant difference – there is a “statistically significant relationship” between test-taking strategy (fake v. honest) and personality test scores. - Our next question is: since a relationship exists, how strong is this relationship? - Question addresses the issue of “practical significance” or “real-world significance” - One way to address question is to try to interpret the difference between means directly. - We know our best estimate of this difference is 5.300, in raw-score units. - May be o.k. when have implicit knowledge of distribution (e.g., income) of DV - Problem with most DVs – we are not informed of distribution - What is the meaning of a 5.3 unit difference in personality scores? - Another way of judging how strongly the IV and DV are associated, or related, to one another is to compute “eta-squared” (eta2 or where df = n1 + n2 – 2 to

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ONE-WAY ANOVA Analysis of variance (ANOVA) for comparing means of three or more variables. Use this test for comparing means of 3 or more samples/treatments, to avoid the error inherent in performing multiple t -tests Background. If we have, say, 3 treatments to compare (A, B, C) then we would need 3 separate t -tests (comparing A with B, A with C, and B with C). If we had seven treatments we would need 21 separate t -tests. Ideally, for this test we would have the same number of replicates for each treatment , but this is not essential. An important assumption underlies the Analysis of Variance: that all treatments have similar variance . Procedure (see worked example ) Don't be frightened by this! Assume that we have recorded the biomass of 3 bacteria in flasks of glucose broth, and we used 3 replicate flasks for each bacterium. Step 1 . Step 2 . , S x 2 , and S d 2 ( click here for method ) Step 3 . Step 4 . Step 5 . and call the sum B . Step 6. Step 7. Step 8 . Step 9 . Step 10 . Step 11 . Step 12 .

Welcome to the NASA Star and Exoplanet Database Standard deviations and standard errors Douglas G Altman (, professor of statistics in medicine1, J Martin Bland, professor of health statistics2 Author Affiliations Correspondence to: Prof Altman The terms “standard error” and “standard deviation” are often confused.1 The contrast between these two terms reflects the important distinction between data description and inference, one that all researchers should appreciate. The standard deviation (often SD) is a measure of variability.

Connecting the Dots: From Christmas Cookies to Climate Just before Christmas 2014, MongaBay, one of the most widely read and well-respected forest-climate online publications, released an editorial by ADP founder Jeff Horowitz elucidating how the groceries we buy contribute to the destruction of forests. Actor/Conservationist Harrison Ford doing a bit of field research in a local supermarket. (Scene from Showtime’s Emmy Award wining climate change series “Years of Living Dangerously”) Harrison Ford checking out everyday products to see which ones contain palm oil? Not exactly the high-octane activity we associate with an adventurer like Ford…so what gives? Ford cares about the ingredients used to make these products because our high demand for these everyday consumer goods is directly tied to high rates of deforestation and climate change. You may not know that for all his success as an actor, Harrison Ford’s personal passion is nature conservation. Ford and many other well-known individuals, including Dr. Deforestation in Borneo, Indoneisa.

Stats: Two-Way ANOVA The two-way analysis of variance is an extension to the one-way analysis of variance. There are two independent variables (hence the name two-way). Assumptions The populations from which the samples were obtained must be normally or approximately normally distributed. Hypotheses There are three sets of hypothesis with the two-way ANOVA. The null hypotheses for each of the sets are given below. The population means of the first factor are equal. Factors The two independent variables in a two-way ANOVA are called factors. Treatment Groups Treatement Groups are formed by making all possible combinations of the two factors. As an example, let's assume we're planting corn. The data that actually appears in the table are samples. Main Effect The main effect involves the independent variables one at a time. Interaction Effect The interaction effect is the effect that one factor has on the other factor. Within Variation The Within variation is the sum of squares within each treatment group. F-Tests

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The standard error of the mean We saw with the sampling distribution of the mean that every sample we take to estimate the unknown population parameter will overestimate or underestimate the mean by some amount. But what's interesting is that the distribution of all these sample means will itself be normally distributed, even if the population is not normally distributed. The central limit theorem states that the mean of the sampling distribution of the mean will be the unknown population mean. The standard deviation of the sampling distribution of the mean is called the standard error. Ok, so, the variability of the sample means is called the standard error of the mean or the standard deviation of the mean (these terms will be used interchangeably since they mean the same thing) and it looks like this. Standard Error of the Mean (SEM) = The symbol σ sigma represents the population standard deviation and n is the sample size. The standard deviation tells us how much variation we can expect in a population.

Frogs that Thrive and Dive in Vernal Pools : The National Wildlife Federation Blog In honor of Save the Frogs Day, April 30th, we’re celebrating species of frogs that depend on a very unique habitat – vernal pools. Vernal pools are shallow depressional wetlands that appear seasonally in meadows and woodlands and serve as important breeding grounds for amphibians like frogs. The seasonal wetlands and pools of the prairie pothole region are also vernal pools. Since vernal pools are usually not filled with water year-round, fish cannot inhabit them. Wood Frog Wood frogs come in varying shades of brown and red, with black marks over their eyes that resemble a robber’s mask. The wood frog ranges from New England, the Appalachians and the Great Lake states to as far north as the Arctic Circle. During cold winter months, they cease breathing, their heart stops, and nearly 70% of their body water turns to ice. As the weather warms in early spring, the frogs thaw out and head to vernal pools to find mates, sometimes even before the ice has fully melted. Spring Peeper