A Bar graph is a visual representation of data using bars of different heights or lengths to show the frequency or value of different categories.
A Histogram is a graphical representation that organizes a group of data points into user-specified ranges, showing the frequency of data within each range.
A Frequency distribution table is a summary of how often each different value occurs in a dataset, displaying the number of observations within specified intervals.
The distribution of all possible outcomes of a sampling design.
A probability distribution describes the likelihood of different outcomes for a continuous variable, indicating that the probability of the variable being exactly a particular value is zero.
The area A under the standard normal distribution curve represents the probability that a standardized random variable falls between negative infinity and 1.48, which is 0.9306.
The histogram of a sample of data from a population can be taken as an approximation of the population PDF curve.
The critical value of the test statistic (e.g., z or t) is the value that separates the region of rejection from the region of non-significance in the sampling distribution.
Memory score (%) represents the percentage of individuals who achieved specific scores on a memory test, summarized in a frequency distribution.
The area under the PDF curve over a specified interval represents the probability that a continuous random variable falls within that interval.
The alpha level is the criterion for statistical significance (e.g., 5%) that should be preset before conducting a study.
If the p value is no more than alpha (α), the null hypothesis is rejected, indicating that the results are statistically significant and the research hypothesis is supported.
Statistical significance means that if the null hypothesis is true, it is unlikely that the sample results would have turned out as observed.
A statistical test used to determine if the mean of a single sample is significantly different from a known or hypothesized population mean.
The total area of A and B is equal to 1, meaning that A and B jointly cover all values of the standardized random variable.
A probability distribution describes how the probabilities are distributed over the values of a random variable, indicating the likelihood of each outcome.
t score = (sample mean – hypothetical mean) / [ s / √N ], where s is the sample standard deviation and N is the sample size.
The observed difference is calculated as the sample mean minus the expected mean, which in this case is 40.58 - 38.76 = 1.82.
The phenomenon where the moon appears larger when it is near the horizon compared to when it is at the zenith.
The sampling distribution of the mean is the distribution of sample means over repeated sampling from a population. According to the central limit theorem, if a population’s scores are normally distributed, the sampling distribution of the mean will also be normally distributed regardless of sample size. If the population is not normally distributed, the sampling distribution will approach a normal distribution as the sample size increases.
A probability distribution that has a mean of 0 and a standard deviation of 1, used to describe the distribution of standardized scores.
Critical values of t are specific points on the t-distribution that correspond to a particular significance level, used in hypothesis testing to determine whether to reject the null hypothesis.
A probability distribution summarizes and represents a sizeable or infinite population of observations in terms of the probability or relative frequency of occurrence of a variable’s values.
The sample mean is a sample statistic obtained from a random sample, and its distribution across many samples approximates the sampling distribution.
The sampling distribution of the mean is the probability distribution of all possible sample means from a population.
Statistical significance refers to the determination of whether the p value of a sample's test statistic is less than or equal to alpha (α), leading to the rejection of the null hypothesis and support for the research hypothesis.
The probability that a standard normal variable z is less than 1.17, calculated from the cumulative distribution function.
A ratio of 1 implies that there is no illusion, meaning the perceived size of the moon is the same at both the horizon and the zenith.
If the p value is more than alpha (α), the null hypothesis is not rejected, meaning the research hypothesis is not supported by the results.
A statistical test used to determine if the mean of a single sample is significantly different from a known or hypothesized population mean, especially when the population standard deviation is unknown.
A statistical method used to determine whether there is enough evidence to reject a null hypothesis based on sample data.
The p-value is the probability of obtaining the observed test statistic value or a more extreme value if the null hypothesis is true.
It indicates that the observed value is beyond the critical range of ±1.96, suggesting that the occurrence probability is below 5%, leading to the rejection of the null hypothesis.
It is used when the population standard deviation is unknown, which is common in most research situations.
A statistical test used to determine if the mean of a single sample is significantly different from a known or hypothesized population mean.
The anticipated ratio of different categories (e.g., men and women) in random samples drawn from a population.
The sampling distribution is the distribution expected for a sample statistic (e.g., sample mean) if we drew an infinite number of random samples of the same size from a population and calculated the statistic on each sample.
A p value corresponds to the probability of observing the test statistic value (2.08) or a more extreme value if the null hypothesis is true.
Standard error is the standard deviation of the sampling distribution of the sample mean, indicating how much sample means are expected to vary from the true population mean.
For a one-sample t test, the degrees of freedom (df) is calculated as N - 1, where N is the sample size.
Sampling error refers to the deviation of a sample's statistic (e.g., sample mean) from the population value (e.g., population mean) due to the specific units or observations included in the sample. It does not indicate carelessness or mistakes.
A Normal Distribution is a probability distribution that is symmetric about the mean, where most of the observations cluster around the central peak and probabilities for values further away from the mean taper off equally in both directions.
A probability density function (PDF) formally describes the probability distribution of a continuous random variable, indicating the probability of the variable being close to a specified value.
A bell-shaped probability density curve does not necessarily represent a normal distribution; it may indicate other types of distributions that also exhibit a similar shape.
The z score of the sample mean is calculated as the observed difference (1.82) divided by the standard error (0.875), resulting in a z score of 2.080.
A statistical test used to determine if the mean of a single sample is significantly different from a known or hypothesized population mean.
38.76.
The probability that a standardized random variable is greater than 1.48, represented as area B under the standard normal distribution curve, is 0.0694.
These z-values represent the critical values for a two-tailed test at the 5% significance level, indicating the threshold beyond which the null hypothesis can be rejected.
The critical value to be used for a t test depends on the degrees of freedom (df) value.
A and B represent the specified values between which the probability of the random variable X is being calculated.
The average value of the sample, which is 1.463 in this case.
Instead of a dichotomous accept-reject decision, it is better to report an actual p-value or a confidence interval.
The probability of rejecting the null hypothesis when it is actually true, commonly set at 0.05 in many tests.
A probability distribution that has a mean of 0 and a standard deviation of 1, used to describe the distribution of standardized scores (z-scores).
The probability density of a normal distribution is precisely defined by a mathematical formula, which describes the shape of the distribution curve.
The probability that a standard normal variable z falls between negative infinity and 0.50.
The t distribution is a probability distribution that varies with its degrees of freedom (df) and is used in statistical analyses, particularly for one-sample t tests.
A Standard Normal Distribution is a special case of the normal distribution where the mean is 0 and the standard deviation is 1.
The number of observations in the sample being analyzed, which in this case is 10.
6.31, assumed to be the same as the main population’s SD.
Whether self-efficacy scores differ across the intervention participants and non-participants.
C and D represent the specified values between which the scores of the random variable Y are being calculated.
The sampling distribution is a probability distribution of all possible sample means from a population, which is normally distributed with a mean equal to the population mean if the null hypothesis is true.
The intervention makes a difference in self-efficacy.
The Central Limit Theorem states that the distribution of the sample means approaches a normal distribution as the sample size increases, regardless of the population's distribution.
The standard error (SE) is calculated as 6.31 divided by the square root of 52, which equals 0.875.
The distribution of the t statistic, which is used in hypothesis testing when the population standard deviation is unknown and is different from a normal distribution.
It is calculated by subtracting P(z < -1) from P(z < 0.8), resulting in P(z < 0.8) - P(z < -1) = 0.7881 - 0.1587 = 0.6294.
The research hypothesis is not true; the observed difference arises from sampling errors only.
40.58.
The number of observations in the sample being analyzed, which in this example is 10.
Degrees of freedom, calculated as the sample size minus one (N - 1), which in this example is 9.
The expected mean of the sampling distribution is 38.76 according to the central limit theorem and the aforementioned assumptions.
A statistical test used to determine if the mean of a single sample is significantly different from a known population mean.
H0: μ = 1 (no illusion); H1: μ ≠ 1 (there is an illusion), where μ represents the population mean.
It implies that the mean self-efficacy score of the intervention participant population is significantly greater than that of the non-participant population.
H0 represents the null hypothesis, which posits that there is no effect or no difference, and in this context, it states that the intervention participant population has a mean of 38.76.
To reject H0 means to conclude that the sample population difference is statistically significant, indicating that the alternative hypothesis H1 is supported by the data, typically when the probability is less than 0.05.
The average value of the sample data, which in this example is 1.463.
It represents the null hypothesis stating that the population mean is equal to 1.
The significance level used is alpha = 0.05.
The expression 'accept the null hypothesis' should be avoided because it can be misleading; it is more accurate to discuss failing to reject the null hypothesis.
Random sampling is a method where each unit/observation of the population has an equal probability of being included in the sample, and the selection of one unit/observation is independent of the selection of every other unit/observation.
In the context of t-distribution, df stands for degrees of freedom, which is a parameter that influences the shape of the t-distribution.
t = (sample mean - hypothetical mean) / [s / √N], where s is the sample standard deviation and N is the sample size.
A sample is a subset of the units/observations of a population selected to represent the population for research.
The standard deviation (SD) quantifies the amount of variation or dispersion in a set of values, which is crucial in determining how likely a sample mean is to occur under the null hypothesis.
The Central Limit Theorem states that if a population’s scores are normally distributed, the sampling distribution of the mean will be exactly a normal distribution, regardless of the sample size (N).
For populations that are not normally distributed, as the sample size (N) increases, the sampling distribution of the mean approaches a normal distribution, regardless of the shape of the population’s distribution.
The probability that a standard normal variable z is less than 0.8, which is approximately 78.81%.
The conservative approach involves using the table row of the next lower df number when the exact df is not available, which may lead to less accurate critical values.
The conclusion is that the mean ratio of the perceived moon size is significantly greater than 1, supporting the existence of the moon illusion.
A statistical test used to determine if the mean of a single sample is significantly different from a known or hypothesized population mean.
An effect-size estimate should always be provided when reporting a p-value.
A p-value of .000 should be reported as 'p < .001' instead of 'p = .000'.
Results should not be described as 'almost significant', 'close to significant', or 'marginally significant' if the p-value is slightly above the alpha level.
It indicates the likelihood of obtaining a sample mean that deviates from the population mean under the null hypothesis.
It means that there is sufficient evidence to conclude that the sample mean is significantly different from the hypothesized population mean, in this case, supporting the existence of the moon illusion.
The critical t value defines the threshold at which the null hypothesis can be rejected, based on the chosen significance level (α) and degrees of freedom (df).
Very small p-values (e.g., p = 0.002) should not be described as 'highly significant'.
A measure of the amount of variation or dispersion in a set of sample values, which in this example is 0.341.
The population is the entire collection of units/observations to which a researcher's conclusions are intended to apply.
The probability that a standard normal variable z is less than -1, which is approximately 15.87%.
A sample mean of 40.85 is considered far off from the population mean of 38.76, and its likelihood of occurrence under the null hypothesis can determine whether to reject H0.
True random sampling is rarely feasible in practice, particularly for large populations, leading researchers to often take samples of convenience.
It indicates that the sample mean is significantly different from the hypothesized mean, as it falls outside the critical range of ±2.262.
A decision-making process in which hypotheses are evaluated statistically.
A more accurate critical t value can be obtained using reliable software or websites, such as the Excel formula '= TINV(0.05, 39)' for a significance criterion of 5%.
Reporting guidelines are standards that recommend how to present statistical results, emphasizing clarity and accuracy, such as providing p-values and effect size estimates.
