Descriptive Vs Inferential statistics Flashcards
What is a research question, and why is it important?
A research question is a question that addresses an important problem or gap in knowledge. It is complex, meaning that it requires research and investigation to find a solution. Research questions guide the direction of a study and form the foundation for gathering data and analysing results.
What is a statistic, and how does it differ from a parameter?
A statistic is a value calculated from sample data. It can vary between different samples, and it is observable. For example, the sample mean is a statistic.
In contrast, a parameter is a value or characteristic of an entire population. It is usually fixed, though it is often unknown or unknowable. The population mean is an example of a parameter.
What is a point estimate?
A point estimate is a single value estimate of a population parameter. It is often the difference in means between two samples. Point estimates provide a specific, best-guess value for the population parameter, though it may not be entirely accurate due to sampling variability.
Why do point estimates vary between samples?
Point estimates vary between samples because they are based on sample data, which can differ from one sample to another due to random sampling error. Each time a new sample is taken, the sample mean may differ, leading to different point estimates of the population parameter.
What are descriptive statistics?
Descriptive statistics are methods used to summarize the characteristics of a dataset, such as the mean and standard deviation. These statistics provide a snapshot of the data without accounting for uncertainty, as they do not involve making predictions or estimations about a broader population.
What is the difference between descriptive statistics and inferential statistics?
Descriptive statistics summarize the characteristics of a dataset (e.g., mean, standard deviation) without introducing uncertainty. They simply describe the data as it is.
Inferential statistics, on the other hand, use descriptive statistics to estimate population parameters and allow for hypothesis testing. Inferential statistics incorporate uncertainty and provide insights into how well sample data estimates the true values for the population.
What does the standard error of the mean (SEM) tell us?
The standard error of the mean (SEM) tells us how much the sample mean is expected to fluctuate from the actual population mean if we were to take multiple samples from the same population. A smaller SEM indicates that the sample mean more precisely estimates the population mean.
How is the standard error of the mean (SEM) calculated?
The standard error of the mean is calculated as:
SEM = Standard Deviation/square root of n
standard deviation is where the standard deviation is the variation within the sample, and
N is the number of observations in the sample. SEM provides an estimate of how much the sample mean might vary from the population mean.
What is the relationship between sample means and population mean?
Sample means are normally distributed around the population mean. This means that if you take multiple samples, their means will be clustered around the true population mean, and the distribution of sample means will form a bell curve, especially as the sample size increases.
What is an interval estimate, and how is it used?
An interval estimate provides a range of values within which a population parameter is expected to lie. This range accounts for the uncertainty inherent in estimating the true value from a sample. Interval estimates are commonly used in confidence intervals to indicate the possible values of a population parameter.
What is a confidence interval, and how is it related to the standard error of the mean?
A confidence interval is a range of values within which the true population parameter is expected to lie with a certain level of confidence (usually 95%). The standard error of the mean (SEM) is used to calculate the confidence interval. A 95% confidence interval is typically calculated as:
ConfidenceInterval=Mean±(1.96×SEM)
This means that 95% of sample means will fall within 1.96 standard errors of the true population mean.
What does a 95% confidence interval mean?
A 95% confidence interval means that if you were to take multiple samples and calculate a confidence interval for each, approximately 95% of those intervals would contain the true population parameter. This provides an estimate of the precision of the sample mean and the uncertainty surrounding it.
How do confidence intervals help determine whether a difference between means is real?
Confidence intervals of the difference between means allow you to assess whether a difference is statistically significant. If the confidence interval for the difference between means does not contain zero, this suggests that the difference is real and not due to random sampling error. Conversely, if zero is within the interval, the difference may not be statistically significant.
What is the role of inferential statistics in understanding random sampling error?
Inferential statistics help account for and quantify the uncertainty or random sampling error inherent in estimates. They provide methods to estimate how far off a sample estimate (e.g., sample mean) might be from the true population parameter and allow researchers to test hypotheses and make predictions despite this uncertainty.
How are confidence intervals related to the estimation of population values?
Confidence intervals are used to estimate the true population value by providing a range within which the population parameter is likely to fall. A 95% confidence interval, for example, gives us a 95% level of confidence that the true parameter is within the specified range.
