Flashcards in Chapter 4 and 5 Deck (71):
What three measures does central tendency refer to?
Central tendency refers to three slightly different ways to describe what is happening in the center of a distribution of data: the mean, the median, and the mode.
Explain the term "Central Tendency"?
Central tendency refers to the descriptive statistic that best represents the center of a data set, the particular value that all the other data seem to be gathering around.
Explain what the mean of a dataset is?
The mean is the arithmetic average of a group of scores. It is calculated by summing all the scores in a data set and then dividing this sum by the total number of scores.
What is a Statistic?
A statistic is a number based on a sample taken from a population; statistics are usually symbolized by Latin letters.
What is a Parameter?
A parameter is a number based on the whole population; parameters are usually symbolized by Greek letters.
What is the formula for calculating the Mean of a set of scores?
The formula for the mean is: M= ∑X ÷ N To calculate the mean, we add up every score, and then divide by the total number of scores.
Explain what is the Median of a set of scores?
The median is the middle score of all the scores in a sample when the scores are arranged in ascending order. If there is no single middle score, the median is the mean of the two middle scores.
What is the Mode of a set of scores.
The mode is the most common score of all the scores in a sample.
What is the most common indicator of central tendency?
The mean is the most common indicator of central tendency, but it is not always the best. When there is an outlier or few observations, it is usually better to use the median.
What does the Central Tendency describe?
The central tendency of a distribution is the one number that best describes what is typical in that distribution (often its high point).
What are the three measures of Central Tendency?
The three measures of central tendency are the mean (arithmetic average), the median (middle score), and the mode (most frequently occurring score).
What is the most common measure of central tendency?
The mean is the most commonly used measure of central tendency, but the median is preferred when the distribution is skewed.
What meanings do symbols convey in statistics?
The symbols used in statistics have very specific meanings; changing a symbol even slightly can change its meaning a great deal.
Variability is indicated by?
4.3: Variability is the second most common concept (after central tendency) to help us understand the shape of a distribution. Common indicators of variability are range, variance, and standard deviation.
What is variability?
Variability is a numerical way of describing how much spread there is in a distribution.
What is Range?
The range is a measure of variability calculated by subtracting the lowest score (the minimum) from the highest score (the maximum).The formula for the range is: range = Xhighest – Xlowest, We simply subtract the lowest score from the highest score to calculate the range.
Want is Variance
Variance is the average of the squared deviations from the mean.
What is the formula for Variance
The sum of squares, symbolized as SS, is the sum of each score’s squared deviation from the mean. The formula for variance is: SD2= √(X-M)² / N: To calculate variance, subtract the mean (M) from every score (X) to calculate deviations from the mean; then square these deviations, sum them, and divide by the sample size (N). By summing the squared deviations and dividing by sample size, we are taking their mean.
What is standard deviation?
The standard deviation is the square root of the average of the squared deviations from the mean; it is the typical amount that each score varies, or deviates, from the mean. The most basic formula for standard deviation is: SD = √SD2². We simply take the square root of the variance.
How do we calculate the Standard Deviation
The full formula for standard deviation is: SD= √(X-M)² / N. To determine standard deviation, subtract the mean from every score to calculate deviations from the mean. Then, square the deviations from the mean. Sum the squared deviations, then divide by the sample size. Finally, take the square root of the mean of the squared deviations.
What is the Interquartile Range?
The interquartile range is a measure of the distance between the first and third quartiles.
What does the first quartile and third quartile represent?
The first quartile marks the 25th percentile of a data set. The third quartile marks the 75th percentile of a data set.
Define the interquartile range?
The interquartile range (IQR) is the difference between the first quartile (Q1), the median of the lower half of the scores, and the third quartile (Q3), the median of the upper half of the scores. The formula is: IQR 5 Q3 2 Q1.
What is the interquartile range?
The interquartile range is the distance from the 25th percentile (first quartile) to the 75th percentile (third quartile). It is often a better measure of variability than the range because it is not affected by outliers.
What is the simplest way to measure variability.
The simplest way to measure variability is by using the range, which is calculated by subtracting the lowest score from the highest score.
What does variation and standard deviation measure?
Variance and standard deviation both measure the degree to which scores in a distribution vary from the mean. The standard deviation is simply the square root of the variance: It represents the typical deviation of a score from the mean.
How do you calculate the interquartile range?
The interquartile range is calculated by subtracting the score at the 25th percentile from the score at the 75th percentile. It communicates the width of the middle 50% of the data.
What is a random sample?
A random sample is one in which every member of the population has an equal chance of being selected into the study.
What is a convenience sample?
A convenience sample is one that uses participants who are readily available. There are two main types of samples in social science research. In the ideal type (a random sample), every member of the population has an equal chance of being selected to participate in a study. In the less ideal but more common type (a convenience sample), researchers use participants who are readily available.
What does generalizability refer to?
Generalizability refers to researchers’ ability to apply findings from one sample or in one context to other samples or contexts; also called external validity.
What is Replication?
Replication refers to the duplication of scientific results, ideally in a different context or with a sample that has different characteristics.
What is a volunteer sample?
A volunteer sample, or self selected sample, is a special kind of convenience sample in which participants actively choose to participate in a study.
Explain Replication and Random Assignment?
Replication and random assignment to groups help overcome problems of convenience sampling. Replication involves repeating a study, ideally with different participants or in a different context, to see whether the results are consistent. With random assignment, every participant has an equal chance of being assigned to any level of the independent variable.
Explain what is inferential Statistics?
Data from a sample are used to draw conclusions about the larger population.
What is Random Sampling?
In random sampling, every member of the population has an equal chance of being selected for the sample.
Which is more common, Random or Convenience Sampling?
In the behavioral sciences, convenience samples are far more common than random samples.
Explain Random Assignment?
In random assignment, every participant has an equal chance of being assigned to one of the experimental conditions.
Explain why replication is beneficial?
If a study that uses random assignment is replicated in several contexts, we can start to generalize the findings.
Are random numbers random?
Random numbers may not always appear to be all that random; there may appear to be patterns.
Explain Confirmation Bias?
Confirmation bias is our usually unintentional tendency to pay attention to evidence that confirms what we already believe and to ignore evidence that would disconfirm our beliefs. Confirmation biases closely follow illusory correlations.
Explain what is illusory correlation?
Illusory correlation is the phenomenon of believing one sees an association between variables when no such association exists.
Explain Personal Probability?
Personal probability is a person’s own judgment about the likelihood that an event will occur; also called subjective probability.
Probability is the likelihood that a particular outcome—out of all possible outcomes—will occur.
What is the expected relative frequency?
The expected relative frequency probability is the likelihood of an event occurring based on the actual outcome of many, many trials.
What does a trial refer to?
In reference to probability, a trial refers to each occasion that a given procedure is carried out.
Explain Confirmation Bias?
Human biases result from two closely related concepts. When we notice only evidence that confirms what we already believe and ignore evidence that refutes what we already believe, we’re succumbing to the confirmation bias. Confirmation biases often follow illusory correlations—when we believe we see an association between two variables, but no association exists.
Explain Probability as a statistician.
In everyday life, we use the word probability very loosely—saying how likely a given outcome is, in our subjective judgment. Statisticians are referring to something very particular when they refer to probability. For statisticians, probability is the actual likelihood of a given outcome in the long run.
What is probability theory?
Probability theory helps us understand that coincidences might not have an underlying meaning; coincidences are probable when we think of the vast number of occurrences in the world (billions of interactions between people daily).
Explain an illusory correlation?
An illusory correlation refers to perceiving a connection where none exists. It is often followed by a confirmation bias, whereby we notice occurrences that fit with our preconceived ideas and fail to notice those that do not.
Explain Personal Probability?
Personal probability refers to a person’s own judgment about the likelihood that an event will occur; also called subjective probability.
What is Expected relative-frequency probability?
Expected relative-frequency probability is the likelihood of an event occurring, based on the actual outcome of many, many trials.
What does outcomes refer to?
In reference to probability, outcome refers to the result of a trial.
What does success refer to?
In reference to probability, success refers to the outcome for which we’re trying to determine the probability.
Describe the probability of an event?
The probability of an event occurring is defined as the expected number of successes (the number of times the event occurred) out of the total number of trials (or attempts) over the long run.
What are proportions?
Proportions over the short run might have many different outcomes, whereas proportions over the long run are more indicative of the underlying probabilities.
Explain a "Control Group"?
A control group is a level of the independent variable that does not receive the treatment of interest in a study. It is designed to match an experimental group in all ways but the experimental manipulation itself.
Explain "experimental group"
An experimental group is a level of the independent variable that receives the treatment or intervention of interest in an experiment.
How are the control group and the experimental group treated.
Many experiments have an experimental group in which participants receive the treatment or intervention of interest, and a control group in which participants do not receive the treatment or intervention of interest. Aside from the intervention with the experimental group, the two groups are treated identically.
What is the null hypothesis?
The null hypothesis is a statement that postulates that there is no difference between populations or that the difference is in a direction opposite of that anticipated by the researcher.
Explain the research Hypothesis?
The research hypothesis is a statement that postulates that there is a difference between populations or sometimes, more specifically, that there is a difference in a certain direction, positive or negative; also called an alternative hypothesis.
Explain an "experiment"
In experiments, we typically compare the average of the responses of those who receive the treatment or manipulation (the experimental group) with the average of the responses of similar people who do not receive the manipulation (the control group).
Explain how researchers develop hypotheses?
Researchers develop two hypotheses: a null hypothesis, which theorizes that there is no average difference between levels of an independent variable in the population, and a research hypothesis, which theorizes that there is an average difference of some kind in the population.
What do we mean by reject the null hypothesis?
Researchers can draw two conclusions: They can reject the null hypothesis and conclude that they have supported the research hypothesis or they can fail to reject the null hypothesis and conclude that they have not supported the research hypothesis.
Explain Type I Error?
A Type I error involves rejecting the null hypothesis when the null hypothesis is correct.
Describe the types of errors in hypothesis testing.
In hypothesis testing, there are two types of errors that we risk making. Type I errors, in which we reject the null hypothesis when the null hypothesis is true, are like false positives on a medical test; we think someone has a disease, but they really don’t. Type II errors, in which we fail to reject the null hypothesis when the null hypothesis is not true, are like false negatives on a medical test; we think someone does not have a disease, but they really do.
Explain Type II Error?
A Type II error involves failing to reject the null hypothesis when the null hypothesis is false.
What is a disadvantage of inferential statistics?
When we draw a conclusion from inferential statistics, there is always a chance that we are wrong.
When do we commit a Type I error?
When we reject the null hypothesis, but the null hypothesis is true, we have committed a Type I error.
When do we commit a Type II error?
When we fail to reject the null hypothesis, but the null hypothesis is not true, we have committed a Type II error.
Explain Type I errors.
Because of the flaws inherent in research, numerous null hypotheses are rejected falsely, resulting in Type I errors.