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19.11.2014
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The width of the confidence interval tells us more about how certain (or uncertain) we are about the true figure in the population.
Population size: this does not usually affect the CI but can be a factor if you are working with small and known groups of people.
Sample Size: the smaller your sample, the less likely it is you can be confident the results reflect the true population parameter. A 0% confidence level means you have no faith at all that if you repeated the survey that you would get the same results. The confidence coefficient is the confidence level stated as a proportion, rather than as a percentage. In general, the higher the coefficient, the more certain you are that your results are accurate. The fashion industry has come a long way in terms of how it views plus size models, but that's not to say there isn't still work to be done.
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No.10 Avoid your pocketsThe first tip on my list of the top 10 tips to show confidence with body language is to keep your hands out of your pockets.
No.8 Keep your eyes forwardKeeping your eyes level might be one of the trickiest ways to show confidence in body language. No.7 Stand up straight with your shoulders backStanding up straight is one of the most important of our top 10 tips to project confidence through body language.
No.5 Firm handshakesAnother of my top 10 tips for showing confidence with body language has to do with the firm handshake.
No.4 Proper groomingImagine yourself walking into a room, maybe there are lots of beautiful women there or maybe the room is filled with respected colleagues. Get the Understanding Islam, Muslim and Quran widget and many other great free widgets at Widgetbox! While line and bar graphs are a very common medium for presenting data in psychology, currently they rarely present information that the reader would like to know: which means are statistically significant from one another.
Standard deviation is useful when the absolute magnitude of the within group variance is of interest (see Figure 1a).
In contrast to standard deviations, standard error bars (see Figure 1b) do make use of the sample size. Third, standard error bars are not the appropriate error information for within subjects designs (see Estes (1997) and Loftus and Masson (1994) for a detailed exposition of this issue). In contrast to standard error bars, confidence intervals solve the first of the three problems with standard error bars (see Figure 1c). These last two problems can be addressed using modified confidence intervals that are based on pooled variance and are appropriate for within subjects designs (see Loftus and Masson (1994) for a presentation of these modified confidence intervals).
Pooled standard errors or pooled confidence intervals are not usually given in standard statistical package outputs, and thus do not provide a practical definition.
Occasionally, authors prefer not to use error bars for interaction line graphs because the error bars from one line obscure the data points from the other line, creating a cluttered display.
As a third issue, occasionally the difference in slope rather than the pairwise means comparisons are of interest in an interaction graph.
As a related issue, there has been recent debate whether significance testing should be banned entirely because of the many logical errors that it produces (Cohen, 1994; Loftus, 1993). An alternative scheme to using SSBs is to include markings (symbols or coloring) indicating which means are statistically different from other means. In considering various kinds of error bars, Estes (1997) argues against the use of confidence intervals and other constructs which incorporate statistical criteria tied to particular a levels. At the beginning of this paper, I listed several commonly mentioned reasons for not including error bars in graphs. We are eternally grateful to everyone who had supported the site over the years, from vendors, content editors and developers, to our fantastic users — you made our passion a reality. A 100% confidence level means there is no doubt at all that if you repeated the survey you would get the same results.
For example, if you had a confidence level of 99%, the confidence coefficient would be .99.
Shouldn’t it be that if the survey were conducted over and over, that the results would fall between 38-3=35% and 38+3=41% in 95% of the survey instances? All rights reserved.Your Privacy RightsThe material on this site may not be reproduced, distributed, transmitted, cached or otherwise used, except with the prior written permission of Fashion Times. Also, recognize that putting your hands in your pockets encourages slouching, which isn’t good.
A man who can’t keep still, is a man who is worried, tense and certainly not confident.
It can be a challenge especially if you’ve been a sloucher all your life, but get over it. Try this as an experiment: smile at someone as you pass them on the street or walking around the office. Don’t be afraid to pat a buddy or a colleague on the back when he or she delivers a perfectly timed punch line or nails the big presentation.
I present a new kind of error bar, statistical significance bars (SSBs), that allows the reader to more directly and easily infer whether any two means in the graph are statistical significant from one another.
First, most line and bar graphs display no error bars at all.1 This lack of error bars can be readily seen by examining current psychology journals. From the coding of the 1998 journal articles, when authors did use error bars, the most common type was standard error bars. A survey given to faculty at my own psychology department found a variety of reasons for not presenting error bars in journal articles (in decreasing order of frequency): not being required to include error bars by editors, not knowing how to add error bars in their graphing package, not knowing which type of error bar to use, believing that error bars are irrelevant to their purposes, aesthetics, adding error bars requires too much effort, and worrying that the error bars they know how to add make the effects look less reliable than they actually are. Comparison of standard deviation, boxplots, standard error, 95% confidence intervals, root mean square error, and statistical significance bars for assessing distribution information (range and homogeneity of variance), effect size, absolute location of the population means, pairwise statistical significance of differences between means, and applicability to repeated measures designs. A psychologist runs a study with three conditions and displays the resulting condition means in a line graph.3 The readers of the psychologist's article will want to know which condition means are statistically significantly different from one another.
In this section, I will step through the various existing types of error bars that can be used, demonstrating why they are inappropriate for the task of determining the statistical significance of pairwise means comparisons. They are quite useful for examining group variance, but quite impractical for assessing statistical significance of means comparisons. Specifically, the standard error is equal to standard deviation divided by the square root of n.


Thus, to properly assess statistical differences, the graphically displayed variance should also be a pooled variance estimate. For within subject designs, the variability within conditions (which standard error bars convey) is irrelevant. An example graph displaying A) standard deviation bars, B) standard error bars, C) 95% Confidence intervals, and D) .05 Tukey HSD statistical significance bars. However, confidence intervals, including these modified confidence intervals, have an important additional problem: confidence intervals are not for comparing pairs of condition means. A statistical significance bar is an error bar that displays pairwise statistical significance between means using the visual overlap test.
For between subjects designs, SSB is simply the (pooled) confidence interval divided by, or the (pooled) standard error multiplied by a criterion value (usually a t-statistic with given degrees of freedom and a level) and then divided by . For example, for binary data, a corresponding SSB may be constructed from the logistic regression. Table 2 presents the results of an ANOVA applied to sample data taken from Loftus and Masson (1994). The example graph from Figure 1D (with .05 Tukey HSD statistical significance bars) with the scales expanded. The relationship between SSBs and SE bars will vary from situation to situation, which is exactly why one cannot rely on SE bars to determine statistical significance. In this case, authors should plot mean differences between conditions, with SSBs derived from the error term for the interaction effect. In psychology, our dependent measures are often continuous, our independent measures are often discrete values, and our goal is determine the pairwise statistical significance of differences between means.
It might be argued that the use of SSBs would further support poor use of reasoning about a levels.
Specifically, Estes raises the issue that lower a levels give wider bands, seemingly giving less confidence in the location of a point. By error bars, I mean all visual display constructs that are used to convey variance information, including standard deviation bars, standard error bars, confidence intervals, interquartile range bars, and boxplots. This included all issues of 1998 for each journal, producing 26 Psychological Review articles, 17 JEP:G articles, and 79 Psychological Science articles. There is some debate regarding when to use line graphs versus bar graphs relating to issues of avoid unwarranted interpolation, ease of reading, and aesthetics.
Of course, in some cases it is important to display the full range of the scale rather than magnify the effect.
What a 95 percent confidence level is saying is that if the poll or survey were repeated over and over again, the results would match the results from the actual population 95 percent of the time. In reality, you would never publish the results from a survey where you had no confidence at all that your statistics were accurate (you would probably repeat the survey with better techniques). It’s extremely rare to see a coefficient of 1 (meaning that you are positive without a doubt that your results are completely, 100% accurate).
The point we’re trying to make is that grooming is an essential component of communicating confidence through body language. This method works for both with and between subjects designs and is based directly upon standard statistical tests that the authors would normally use for pairwise means comparisons. However, simply knowing which points are above or below other points is not typically sufficient in determining the effects of variables.
Specifically, 22% of graphs contained standard error bars, 2% contained standard deviation bars, 1% displayed confidence interval, and 6% did not describe which error bars were displayed. Moreover, the current APA publication manual (APA, 1994) provides no guidance on this issue of whether to use error bars in graphs, and if so, which ones are most appropriate. Table 1 presents a summary of various information one might seek from an error bar and how well each type of error bars conveys that information. To determine this information, the reader would normally have to refer to the text in which the results of an ANOVA and pairwise posthoc contrasts are described. This overview will serve to enumerate concretely the desirable features of an appropriate type of error bar. As another example, when criteria are to be used to separate groups in clinical settings, the within group variance is also important to assess the reliability of the criterion. Unfortunately, most graphing packages default to displaying condition specific standard error bars (which will vary in size from condition to condition).
Instead it is the information about the variability in the difference between conditions that is important.
It turns out that such an error bar is quite easy to calculate using information readily available in an ANOVA table. In general, whatever test the author would use to test the pairwise significance between points can be applied to create an SSB. The same formulas described above are used, except that the value for k in the equation is the number of cells in the interaction. This difference score plot with SSBs will allow the reader to quickly determine whether the effect of one variable is the statistically different across conditions of the other variable.
However, there is nothing inherently illogical in the appropriate use of significance testing (Dixon, 1998). For example, by including information about degrees of freedom, the authors clarify the kinds of aggregation that was used in the statistics.
Since the same error bars can be used in either case, this debate will not be discussed further here.
In this case, you would expect the results to be 35 (38-3) to 41 (35+3) percent, 95% of the time. Keep your chin up and your eyes forward, even when you’re walking down the street by yourself. Because the researcher has typically gathered only a small subset of all possible data, there is a question of statistical significance: how certain are we that the true population means actually differ? As I will shortly explain, none of these error bars are appropriate for the task of easily judging the statistical significance of differences between means.
The function of this paper is to introduce a new kind of error bar that is the best choice for one of the most common goals of data analysis in psychology: assessing the statistical significance of pairwise comparisons between means. In this case, the graph itself is in effect potentially misleading, because apparently significant differences are not significant, or at least ambiguous.
However, standard deviations are not appropriate variance estimates for assessing statistical significance between means because they do not reflect the sample size.
However, standard errors do not convey information regarding the criterion associated with an a level.
Note: if the difference in variance across conditions is very large, then pooled variance is inappropriate both for the display and for the statistical tests. Unfortunately, the confidence intervals that authors typically use suffer from the other two problems with standard error bars. To understand this feature in the current context, one must think about the typical habits of an individual reading a line or bar graph. To test whether two points are significantly different, a normal confidence interval is too small by a factor of (as described above).


The goal of including SSBs is to have the figure match the inferential statistics as closely as possible. The independent measure, manipulated within participants, is the exposure time to each word: 1, 2, or 3 seconds per word. In a within subjects design, SSBs can be much smaller or even larger than the SE bars, depending on the consistency of the within subjects effect. Moreover, there is nothing in particular about SSBs that would support less logical thinking about significance testing.
Instead, the current proposal is to augment the in-text inferential statistics by having the line and bar graphs clearly indicate the results of the inferential statistics. Here, A and C can be significantly different from one another, and yet there are no statistically significant differences between A and B or between B and C. On the communication of information by displays of standard errors and confidence intervals. A picture is worth a thousand p values: On the irrelevance of hypothesis testing in the microcomputer age. Here again, line graphs and bar graphs have the potential of being more informative than tables.
In a historical analysis of the journal JEP:LMC, Estes (1997) found a similar dearth in the use of error bars in graphs (contrasting sharply with a recent rise in the presentation of variance information in tables). A much more desirable state of affairs would be for the reader to be able to determine more directly and easily from the graph which means are significantly different from one another. As the sample size increases, the variance (as reflected in the standard deviation) will remain stable, whereas the variance in the estimate of the mean decreases. This measure is appropriate for within subjects designs and is a pooled measure of variance. First, they reflect the variance within each condition rather than the pooled variance that is used in the statistical tests. When confronted with a graph containing error bars, a likely activity is for the reader to look for overlapping error bars. In the presented example, the effect was very consistent across participants (producing the small SSBs) but the absolute performance levels across participants was quite variable (producing large SE bars).
For example, if the author wishes to convey information about the distribution of a variable, either within or across groups, then boxplots should be used. SSBs merely allow one to visual determine whether a given a level criterion has been met, which is what the text that accompanies figures currently indicates.
Also, most readers do not have the appropriate post hoc criteria memorized.6 Finally, each paper implicitly adopts a given a level for determining what is statistically significant and what is not. By now using appropriate error bars, statistically significant differences will continue to look significant.
In a glance, most people can discern if we’re apprehensive or outgoing, relaxed or aggressive. By adding the appropriate error bars to the graph, simple visual comparisons may be used to determine how likely it is that the differences between sample means can be attributed to noise. If this were possible, then the reader would not need to navigate the clumsy text or appendices outlining the results of all pairwise contrasts. Thus, to begin to assess statistical significance using standard deviation bars, the reader must know the ns of each point, and scale the standard deviations bars appropriately. Since the statistics are typically a complex function of the degrees of freedom and an a level, a reader cannot easily estimate statistical significance with only an estimate of variance.
Second, they are also not appropriate for within subjects designs, for exactly the same reasons.
When the error bars for two means overlap, the reader will assume the means do not differ from one another.
However, this will produce a result in which points are significantly different from one another if one point is not inside the error bars of the other. If the effect had been less consistent across participants or if there had been less variance in absolute performance levels across participants, the SSBs may have become as large or even larger than the SE bars. If effect size is the more desirable information, standard deviation bars are more helpful. With more than three points, more complicated patterns of statistical significance are possible. With a little practice, we can learn the tips to show confidence through body language so that we always appear confident, capable and ready.
Try it in front of the mirror -- you’ll be surprised how much more confident it makes you look. This computation is no trivial task, especially in complex experimental designs with uneven ns. For example, are two means significantly different when their difference is more than 1.5, 2, 2.5, or 3 times the size of the standard error?
To be able to accurately judge statistical significance, a reader armed only with confidence intervals would need a ruler and a calculator (assuming a reader even knew that this was required). If the error bars do not overlap, the reader will assume the means do differ from one another. To move to a situation in which one uses the overlap of the bars (rather than the overlap of a point within a bar), one must divide the bars in half. In this case, the error term is the Block by Participant interaction, and so the MSE is 0.615. Thus, there will be no confusion about the precision of the data from varying a levels because the a levels will not typically vary.
This excuse is equivalent to not reporting accurate reaction times because of not knowing how to use data collection software (Gillan et al., 1998). Unfortunately for the reader, all existing error bars do not accurately support this inference procedure. Since most psychology papers use .05, it will probably be best to use this convention in graphing as well. Currently there are many readily available and inexpensive graphing packages that easily allow the addition of use-specified error bars to line and bar graphs. That is, for a good type of error bar, when any two bars overlap, the two means should never be statistically different from one another, and when any two bars do not overlap, the two means should always be statistically different from one another. With these other excuses removed, perhaps editors of journals will also begin to require the inclusion of error bars in graphs. This scale is unusually large for Figure 1d, but was selected to accommodate the large standard deviation bars.




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