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You will see descriptions of two scientific research papers and we ask you to indicate your personal guess on several features of these studies sample size, p-value, ….
It is important that you give your personal and intuitive estimates. You must not be shy in delivering your estimates, even if you are not sure at all. We are aware that this may be a difficult task for you — yet, please try.
In this study researchers investigated the influence of warmth on social distance. The hypothesis was that warmth leads to social closeness.
There were two groups to investigate this hypothesis:. Participants of group 1 held a warm drink in their hand before filling in a questionnaire. Participants of group 2 held a cold drink in their hands before they filled in the same questionnaire. Participants were told to think about a known person and had to estimate their felt closeness to this person. The closeness ratings of the participants of group 1 were then compared to the closeness ratings of group 2.
Previous studies have shown that body movements can influence cognitive processes. For instance, it has been shown that movements like bending an arm for pulling an object nearer go along with diminished cognitive control.
Likewise, participants showed more cognitive control during movements pushing away from the body. In this study, the influence of movement of the complete body stepping forward vs. The hypothesis was that stepping back leads to more cognitive control, i. There were two conditions in this study: In the first condition participants were taking four steps forwards, and in the second condition participants were taking four steps backwards.
Directly afterwards they worked on a test capturing attention in which their responses were measured in milliseconds. The mean reaction time of the stepping forward-condition was compared to the mean reaction time of the stepping backward-condition.
Researchers found a statistically significant [non-significant] effect in this study. Reprints and Permissions. The significance fallacy in inferential statistics. BMC Res Notes 8, 84 Download citation. Hence a sample statistic has a distribution of its own which is known as the sampling distribution , and this is an important concept in inferential statistics. Sampling distributions of sample statistics from random samples have these properties:.
Before proceeding to the next section, test your understanding of inferential statistics by choosing the best answer for the following question:. Suppose a researcher is interested in cholesterol levels in a population. If they recruit a sample randomly from the population, they can estimate the cholesterol level of the whole population using the actual cholesterol level they calculated directly from the sample.
In this case:. While point estimates are useful, often it is preferable to estimate a population parameter using a range of values, so that the likely variation between the sample and population statistics is taken into account.
This is where confidence intervals come in A confidence interval gives a range of values as an estimate for a population statistic, along with an accompanying confidence coefficient. For another way of interpreting confidence intervals, think back to the sampling distribution of a sample statistic and consider that you could calculate a confidence interval for each possible sample of the same size. Before calculating a confidence interval for a population you should ensure that the following assumptions are valid:.
Assumption 1: The sample is a random sample that is representative of the population. Assumption 2: The observations are independent, i. Assumption 3: The variable is normally distributed, or the sample size is large enough to ensure normality of the sampling distribution. Finally, it is important to remember that the population parameter is fixed and it is the sample mean and interval that change from sample to sample.
Once the interval is calculated then the unknown population value is either inside or outside of the interval, and we can only state the certainty with which we believe the interval to contain the population value. If you would like to practise calculating and interperting confidence intervals, have a go at one or both of the following activities.
Hypothesis testing involves formulating hypotheses about the population in general based on information observed in a sample. These hypotheses can then be tested to find out whether differences or relationships observed in the sample are statistically significant in terms of the population. In order to do this, two complementary, contradictory hypotheses need to be formulated; the null hypothesis and the alternative hypothesis or research hypothesis.
Definitions of these are as follows:. Null hypothesis: This hypothesis always states that there is no difference or relationship between variables in a population.
Alternative hypothesis: Also known as the research hypothesis, this hypothesis always states the opposite of the null hypothesis; i. Both hypotheses can be written using either words or symbols, often in a few different ways. For example if we want to test whether a new drug has significantly reduced the mean blood pressure of a population of patients, some example hypotheses are:.
If you would like to practise writing hypotheses, have a go at formulating null and alternative hypotheses for the following activity:. Once the hypotheses have been formulated they can be tested to evaluate statistical significance, as explained in the following section. It is also important to keep in mind practical significance at this point as well, as explained in the subsequent section.
In order to evaluate statistical significance an appropriate test needs to be conducted, some common examples of which are covered in later sections of this page.
This will produce a test statistic , which compares the value of the sample statistic for example, the sample mean change in blood pressure in our blood pressure example with the value specified by the null hypothesis for the population statistic i. Therefore a large test statistic indicates that there is a large discrepancy between the hypothesised value and the sample statistic - although note that the test statistic is not simply equal to the difference between them, and that the sample standard deviation and sample size are also involved in its calculation.
This is evidence to reject the null hypothesis, and hence of statistical significance. Note that if:. It is important to note here that confidence intervals can also be used to decide whether a difference or relationship is statistically significant or not. For example, based on data collected in the sample for our blood pressure example, a confidence interval can be calculated giving the range of values we expect the difference in mean blood pressure to lie between for the population.
Confidence intervals are good because not only do they tell us about statistical significance, but they also tell us about the magnitude and direction of any difference or relationship. If you would like to test your understanding of this concept, have a go at this activity:. It is important to note here that because hypothesis testing involves drawing conclusions about complete populations from incomplete information, it is always possible that an error might occur when deciding whether or not to reject a null hypothesis.
In particular there are two types of possible errors, and details of these including how to mitigate against them are provided below:. Type I error: This occurs when we reject a null hypothesis that is actually correct. Type II error: This occurs when we do not reject a null hypothesis that is actually incorrect.
To minimise the risk of a Type II error a power analysis is often used to determine an appropriate sample size - where the power of a particular statistical test is the probability that the test will find an effect if one actually exists. The power of a test depends on three main factors:. You can use this information to calculate the power of a test using software, for example using SPSS software Version 27 or above.
If you would like to test your understanding of the different error types, have a go at the following activity:. A slight issue with statistical significance is that it is influenced by sample size; meaning that in a very large sample, very small differences may be statistically significant, and in a very small sample, very large differences may not be statistically significant.
For this reason it is a often a good idea to measure practical significance as well, which is determined by calculating an effect size. The effect size provides information about whether the difference or relationship is meaningful in a practical sense i.
Details on how to calculate effect size are covered for each of the tests outlined in subsequent sections. Different inferential statistical tests are used depending on the nature of the hypothesis to be tested, and the following sections detail some of the most common ones. First, though, it is important to understand that there are two different types of tests:.
Parametric tests: These require at least one continuous variable, which must be normally distributed. Non-parametric tests: These don't require any continuous variables to be normally distributed, and indeed don't require any continuous variables at all.
So just like the mean is typically the go-to measure of central tendency over the median, so too are parametric tests over non-parametric tests. Trading Basic Education. Advanced Technical Analysis Concepts. Financial Analysis. Actively scan device characteristics for identification. Use precise geolocation data. Select personalised content.
Create a personalised content profile. Measure ad performance. Select basic ads. Create a personalised ads profile. Select personalised ads. Apply market research to generate audience insights. Measure content performance. Develop and improve products. List of Partners vendors. Your Money. Personal Finance. Your Practice. Popular Courses. Financial Analysis How to Value a Company. What Is Statistical Significance? Key takeaways Statistical significance refers to the claim that a result from data generated by testing or experimentation is likely to be attributable to a specific cause.
If a statistic has high significance then it's considered more reliable. The calculation of statistical significance is subject to a certain degree of error. Statistical significance can be misinterpreted when researchers do not use language carefully in reporting their results. Article Sources. Investopedia requires writers to use primary sources to support their work. These include white papers, government data, original reporting, and interviews with industry experts. We also reference original research from other reputable publishers where appropriate.
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