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Because we have more data and therefore more information, our estimate is more precise. As our sample size increases, the **confidence** in our estimate increases, our uncertainty decreases and we have greater precision.

Which of the following describes the effect of increasing sample size? … **There is little or no effect on measures of effect size**, but the likelihood of rejecting the null hypothesis increases.

Which of the following correctly describes the effect that decreasing sample size and decreasing the standard deviation have on the power of a hypothesis test? **A decrease in sample size will decrease the power, but a decrease in standard deviation will increase the power.**

For the independent-measures t-statistic, what is the effect of increasing the difference between sample means? **Increase the likelihood of rejecting the null hypothesis and increase measures of effect size.**

Standard Error is the square root of the variance. When the variance increases, so **does the standard error**. Since the standard error occurs in the denominator of the t statistic, when the standard error increases, the value of the t decreases.

How does the standard deviation influence the outcome of a hypothesis test and measures of effect size? **Increasing the sample variance reduces the likelihood of rejecting the null hypothesis and reduces measures of effect size**.

Which of the following would definitely increase the likelihood of rejecting the null hypothesis? **All of the** other options will increase the likelihood of rejecting the null hypothesis. A researcher selects a sample from a population with = 30 and uses the sample to evaluate the effect of a treatment.

**Larger variance decreases** the standard error but increases measures of effect size Larger variance Increases the standard error but decreases measures of effect size. Larger variance increases both the standard error and measures of effect size.

Question: How does sample variance influence the estimated standard error and measures of effect size such as r2 and Cohen’s d? a. **Larger variance decreases both the standard error and measures of effect size**. … Larger variance increases both the standard error and measures of effect size.

Our result indicates that as the sample size increases, the variance of the sample **mean decreases**.

Therefore, as a sample size increases, the sample mean and **standard deviation** will be closer in value to the population mean μ and standard deviation σ .

In general, larger samples will have smaller variability. This is because as the sample size increases, **the chance of observing extreme values decreases** and the observed values for the statistic will group more closely around the mean of the sampling distribution.

Increasing sample size makes the **hypothesis test more sensitive** – more likely to reject the null hypothesis when it is, in fact, false. Thus, it increases the power of the test.

Variability can **dramatically reduce your statistical power** during hypothesis testing. Statistical power is the probability that a test will detect a difference (or effect) that actually exists. … Even when you can’t reduce the variability, you can plan accordingly in order to assure that your study has adequate power.

Increasing the sample size tends **to reduce the sampling error**; that is, it makes the sample statistic less variable. However, increasing sample size does not affect survey bias. A large sample size cannot correct for the methodological problems (undercoverage, nonresponse bias, etc.) that produce survey bias.

The population mean of the distribution of sample means is the same as the population mean of the distribution being sampled from. … Thus as the sample size increases, the **standard deviation of** the means decreases; and as the sample size decreases, the standard deviation of the sample means increases.
## How does sample size affect statistical significance?

## How would changes in sample size affect the margin of error assuming all else remained constant?

## How does the variability of the scores in the sample influence the measures of effect size?

## Which of the following factors help to determine sample size?

## How does the principle of diminishing returns affect decisions about sample size?

## How does effect size affect power?

## How does sample size affect type 1 error?

## How does sample size affect Type 2 error?

## What happens to the t statistic when n becomes larger?

## Why does increased N make the t statistic larger?

## What happens to T when sample size increases?

Higher sample size allows **the researcher to increase the significance level of the findings**, since the confidence of the result are likely to increase with a higher sample size. This is to be expected because larger the sample size, the more accurately it is expected to mirror the behavior of the whole group.

Therefore, you not only have to present summary data, but must also be able to explain the results in a manner that is accurate and easy to understand. How would changes in sample size affect the margin of error, assuming all else remained constant? … **A larger sample size would cause the interval to narrow.**

**Increasing** the sample variance reduces the likelihood of rejecting the null hypothesis and reduces measures of effect size.

Three factors are used in the sample size calculation and thus, determine the sample size for simple random samples. These factors are: 1) the margin of error, 2) the confidence level, and 3) the proportion (or percentage) of the sample that will chose a given answer to a survey question.

In a research study what is the difference between a census and a sample? … How does the principle of diminishing returns affect decisions about sample size? **Larger populations require proportionately larger samples**. What is generally recommended sample size for qualitative studies?

The statistical power of a significance test depends on: • The sample size (n): when n increases, the power increases; • The significance level (α): when α increases, the power increases; • The effect size (explained below): when the effect size increases, the power increases.

**Changing the sample size has no effect on** the probability of a Type I error. it. not rejected the null hypothesis, it has become common practice also to report a P-value.

As the sample size increases, the probability of a Type II error (given a false null hypothesis) **decreases**, but the maximum probability of a Type I error (given a true null hypothesis) remains alpha by definition.

t-statistic

Since the square root of n is the **denominator** of that fraction, as it gets bigger, the fraction will get smaller. However, this fraction is, in turn, a denominator. As a result, as that denominator gets smaller, the second fraction gets bigger. Thus, the t-value will get bigger as n gets bigger.

Higher n **leads to smaller standard error that gives higher** t-value. Higher t-value means lower p-value infering that the difference between sample-mean (ˉX) and population-mean (μ) is significant (hence we reject the null hypothesis).