psych 210: chapters 8-12
The amount of overlap between 2 distributions can be decreased in 2 ways
1) overlap decreases and effect size increases when means are farther apart. 2) overlap decreases and effect size increases when variability within each distribution of scores is smaller.
Data Transformations
1) transform a scale variable to a ordinal variable 2) Use a data transformation such as square root transformation to squeeze the data together to make it more normal **Remember, we need to apply any kind of data transformation to every observation in the data set ---> some data transformations offer advantages over others, including, the square root transformation and how it maintains scale data and allows for parametric tests to be performed
Point estimate
a summary statistic from a sample that is just one number used as an estimate of the population parameter (e.g. mean) ***A point estimate is rarely accurate
Effect size tells us how much two populations do not overlap. the less overlap --> bigger or smaller effect size?
bigger effect size
A t statistic is not as extreme as a z statistic; t statistic is more ______________
conservative When sample size increases, s approaches σ and t and z become more equal
The critical cutoffs for a 95% confidence interval are -1.96 and 1.96. What are the cutoffs for a 90% confidence interval? (chapter 8)
-1.65 and 1.65
Order effects
How a participant's behavior changes when the DV is presented for a second time
How do we get more power?
Increase alpha Conduct a one-tailed rather than a two-tailed Increase N (number of participants) All three of these techniques serve to increase the chance of rejecting null hypothesis
Factors affecting power
Larger sample size increases power Alpha level Higher level increases power (e.g. from .05 to .10) One-tailed tests have more power than two-tailed tests Decrease standard deviation Increased difference between means
Meta-analysis
Meta-analysis consider many studies simultaneously provides an average effect size across the many studies that asked the same research question. Allows us to think of each individual study as just one data point in a larger study Unpublished studies are a key to a strong meta-analysis These unpublished studies typically concluded null results and did not find a significant difference
Why would it be important to know the statistical power of your study?
On a practical level, statistical power calculations tell researchers how many participants are needed to conduct a study whose findings we can trust.
Effect Size: Just how big is the difference?
Size of a difference that is unaffected by sample size Standardization across studies As sample size increases, test statistic also increases (becoming more extreme) BUT standard error decreases and it becomes easier to reject null hypothesis
What is the difference between the z and t tests?
T test estimates a population standard deviation from a sample. Z tests are statistical tests used to determine whether two population means are different when the variances are known and the sample size is large. Use t distribution (instead of z distribution) when the standard deviation is not known and when the sample size is small (n<30)
What is the paired-samples t statistic when using M difference = 9.0, s = 6.8, N= 16? (chapter 10)
a. 1.32 b. 1.70 c. 5.13 d. 5.29 correct answer is d standard deviation/ N = standard error --> 6.8/ square root of 16 = 1.7 t = 9/1.7 = 5.29
In which statistical test do you calculate a difference score for each individual, take the mean of the difference scores, and perform a test on them to compare two sample means? (chapter 10)
a. between-groups design b. paired-samples t test c. z test d. single-samples t test correct answer is b
The paired-samples t test is an example of a ______________ test, while the independent-samples t test is an example of a _______________ test (chapter 11)
a. between-groups; within-groups b. within-groups; between-groups c. between-individuals; between-groups d. within-groups; between-individuals correct answer is b
Would an independent-samples t test be appropriate when using three groups (a control group and two experimental groups) to compare differences on an IQ test? Explain. (chapter 11)
a. yes; IQ test scores is a scale variable b. yes; the participants belong to different groups c. no; there are more than 2 groups d. no; the independent variable should be a scale variable correct answer is c
After performing a paired-samples t test as part of a hypothesis test, it is recommended by the APA the researchers also consider: (chapter 10)
a. calculating a confidence interval and a measure of effect size b. performing a power analysis to assess the risk of type 1 error c. repeating the research with a between-groups design to avoid order effects d. running a replication to confirm the findings correct answer is a
When the population mean falls in our confidence interval, we conclude that the sample: (chapter 9)
a. comes from a different population b. comes from the same population c. is not representative of the population d. was obtained in error correct answer is b
for the paired-samples t test, the comparison distribution: (chapter 10)
a. is the same as that for a single-samples t test b. is the same as that for the z test c. contains sample means based on samples of the same size d. contains means of difference scores correct answer is d (single sample = individuals scores vs paired sample = means of difference scores)
why is it necessary to used pooled variance rather than variance when conducting an independent-samples t test? (chapter 11)
a. there are two samples b. it is a first step to calculate mean differences c. we need to remove the effects of sample size d. we need to multiply this value by 100 correct answer is a
In calculating pooled variance, why are adjustments made for sample size? (chapter 11)
a. to remove the effects of sample size b. because estimates from smaller samples tend to be less accurate than those from larger samples c. to convert variance to standard deviations d. to test for type 1 and type 11 errors correct answer is b
"estimate of the spread of distribution of means" means....
standard error Just like the z distribution, in a t distribution we make the spread smaller to reflect the fact a distribution of means is less variable than a distribution of scores. ***standard error should always be smaller than standard deviation, otherwise, you have made an incorrect calculation!!!
We can also compare two samples to each other There are 2 ways to compare 2 samples:
(1) within group design; we use paired-samples t test (2) between group design; we use independent-samples t test
95% Confidence Intervals
Constructed around h0 (Null hypothesis): where we expect the sample mean to fall 95% of the time Constructed around h1 (Alternative hypothesis): where the value of the true mean is expected to fall 95% of the time
Counterbalancing
Minimises order effects by varying the order of presentation of different levels of the IV from one participant to the next **Measure such as this can reduce order effects in within-groups research designs **
Homogeneity of Variance
The two populations from which samples are selected must have equal variances F-max = s2(largest)/s2(smallest)
Characteristics of a T distribution
The uncertainty of a small sample size means that the t distributions become flatter and more spread out. As the sample size gets larger, the t distributions begin to merge with the z distribution because we gain confidence as more participants are added to the study
in an independent samples t test, each group has N minus ____________ degree(s) of freedom. (chapter 11)
a. 0 b. 1 c. 2 d. 3 correct answer is b
A 95 % confidence interval of [152, 168] is calculated. What is the sample mean? (chapter 8)
a. 16 b. 160 c. 168 d. 184 correct answer is b
To calculate df, subtract ____ from ____. (chapter 9)
a. 2; N b. 2; n c, 1; N d. 1; n correct answer is c
As effect size increases, the overlap between distributions being compared is (chapter 8)
a. increase b. decreases c. remains the same d. overlap is not compared for the distributions correct answer is b because as effect size increases, distribution becomes taller and more narrow therefore eliminating overlap
A power analysis reveals that the study being run has low power. Which method is not an appropriate way to increase statistical power? (chapter 8)
a. increase alpha b. increase the variance of the distributions c. increase the N d. decrease the standard deviation/ or use a one-sample t test correct answer is b
A cohen's d of -.82 is what type of effect size? (chapter 8)
a. large b. medium c. small d. because it is less than zero, no effect correct answer is a
a researcher calculates a confidence interval for a paired-samples t test. That interval is centered on -6.35, which is the (chapter 10)
a. sample mean difference b. sample mean c. null hypothesized mean d. calculated t statistic correct answer is a **single-samples t test = sample mean **paired-samples t test = sample mean difference
A paired-samples t test is also known as a: (chapter 10)
a. single-subjects t test b. dependent-samples t test c. single-sample t test d. z test correct answer is b **paired-samples t test = dependent-samples t test & within groups design **independent-samples t test = between groups design
a small difference between means may not be statistically significant with a small sample, but it could reach statistical significance with a large sampler because (chapter 8)
a. the overlap between distributions grows as sample size increases b. as N increases, the standard error gets smaller, reflecting less variability in sample means, which allows greater sensitivity for detecting small BUT significant differences c. as N increases, distributions get more heterogeneous, allowing small differences to be detected d. the difference between means gets larger as sample size increases correct answer is b
According to APA standards, why is it recommended to report descriptive statistics for the two samples in addition to reporting the p value? (chapter 11)
a. they help the reader calculate and interpret same size differences b. they help the reader identify type 1 error c. they help the reader identify type 11 error d. they provide additional info about the group differences that often interests the readers correct answer is d
type 2 error
is when we fail to reject the null but we should have rejected (false negative!!! Researcher accepts a false null hypothesis) too small a sample --> too small a sample
Single Sample t test
A hypothesis test in which we compare a sample from which we collect data to a population for which we know the pop. mean and properties but not the standard deviation
is a two-tail or one-tail test more conservative?
Two-tail test is more conservative compared to the single-tail test
When would you use a z test over a t test?
When standard deviation is known AND when population is large (N>30)
the critical cutoffs for a two-tailed, paired-samples t test with N=19, at a p level of 0.05, are: (chapter 10)
a. -1.734 and 1.734 b. -2.093 and 2.093 c. -2.101 and 2.101 d. -2.861 and 2.861 correct answer is c
Instead of looking up the actual sample size on the t table we look us ___________________
degrees of freedom (df) the number of scores that are "free to vary" (# of scores that can take on a different values when a given parameter is known) when we estimate a population parameter from a sample
T-statistic
distance of a sample mean from a population mean in terms of the estimated standard error T = (M − µM )/s M We use estimated standard error in the denominator which makes the t statistic smaller and thereby reduces the probability of having an extreme t statistic
File Drawer Problem
the fact that a large proportion of all studies actually conducted are not available for review because they remain unpublished in "file drawers," having failed to obtain positive results (they have null or false results). **the file drawer analysis is a statistical calculation, following a meta-analysis, of the number of studies with null results that would have to exist so that the mean effect size would no longer be statistically significant If it would take several hundred studies in researchers "file drawers" to render the effect nonsignificant , then it is safe to conclude that there really is a significant effect For most research topics, it is not likely that there are hundreds of unpublished studies Sensitivity analysis, evaluating publication bias and replication/reproducibility are other variants of the file drawer analysis Researchers are increasingly encouraging meta-analysis with fewer studies, even as few as 2 Small meta-analysis can even replace hypothesis testing
Calculating effect size
Cohen's d estimates effect size Assesses the difference between means using the standard deviation instead of standard error ("standardized difference between means") We calculate Cohen's d by dividing the difference between two means by the standard deviation. d = (M - µ)/ σ Small - 0.2 (85% overlap) **A small effect can be meaningful!! Medium - 0.5 (67% overlap) Large - 0.8 (53% overlap)
Conducting an independent-samples t test
Compare two means for a between groups design Each participant is assigned to only one condition/ one of two groups NOT both groups Distribution of differences between means
The t distributions (single-sample t test)
Comparing a sample to a population when we don't know all the details about the parameters We want to know whether we can generalize what we have learned about one sample to a larger population T tests based on t distributions tell us how confident we can be that a sample differs from the larger population
Paired-Samples t test
Comparing two sample means for a within-groups design, a situation in which every participant is in both samples; also called a dependent-samples t test
Statistical Power
The measure of our ability to reject null hypothesis, given that null hypothesis is false The probability that we will reject the null when we should An effect truly exists if we reject null hypothesis An effect does NOT exist if we fail to reject null Most affected by sample size Calculate power → Power = Effect Size × SampleSize 80% chance of correctly rejecting the null hypothesis → appropriate to conduct the study.
T distributions are more versatile than z distributions
We can use them when we don't know the population standard deviation Also, when we compare two samples
When would you use a single-sample t test? Think of a specific study.
When we want to know whether our sample comes from a particular population but we do not have full population information available to us. For instance, we may want to know if a particular sample of college students is similar to or different from college students in general.
what is the correct formula for cohen's d for a paired-samples t test? (chapter 10)
a. (X-M)/N b. (X-M)/(N-1) c. (M-µ)/s d. (M-µ)/(s-1) correct answer is c **this formula is used in z-statistic formula BUT divided by standard error instead of standard deviation **single-sample t test and paired-samples t test is (M-µ)/s --> standard deviation instead of standard error **in an independent-samples t test, cohen's d formula is (Mx-My) - (µx - µy)/ s pooled
twenty two students were assessed on a mindful measure both before and after completing a semester-long mediative yoga class. The critical t values for a two-tailed paired-samples test based on their data, with a p level of 0.05, are: (chapter 10)
a. -1.717 and 1.717 b. -1.721 and 1.721 c. -2.074 and 2.074 d. -2.080 and 2.080 correct answer is d (df = 22-1 = 21) look up 21 on t table to find corresponding critical t value
a reseacher reported a paired-samples t test as follows: t(18)= 2.69, p<0.05, d=0.82. The value of the effect size measure here is: (chapter 10)
a. 0.05 b. 0.82 c. 2.69 d. 18 correct answer is b
Taylor is looking through a statistics test for a z table, but he can find only a t table in the index. What tip would best help him find the information he needs? (chapter 9)
a. Add 1 to all the scores in the t table to find the corresponding z statistic b. go to the library to look up the z table c. use a different distribution instead of a z distribution d. use the sample size of infinity listed in the t table because it is equal to the z table correct answer is d
the interval estimate for two values overlaps. What might this indicate? (chapter 8)
a. Both points may actually have the same value in the general population, although one appears slightly higher, possibly due to uncertainty of the sample b. The range between the two points absolutely represents a genuine difference in the general population c. Both points must be equal if there is any overlap among their interval estimates because of error in estimating the population from a sample d. There is no way to tell if the difference between the two points is genuine correct answer is a
A researcher is comparing the normal curve for two studies using the deviation for individual scores. Study one depicts two samples with means close together, Study two depicts two samples with means further apart. Which has a bigger effect size? (chapter 8)
a. Study 1, because there is more overlap b. Study 1, because there is less overlap c. Study 2, because there is more overlap d. Study 2, because there is less overlap correct answer is d because the less overlap, the bigger the effect size
According to the Federal Reserve, the average credit card interest rate in 2017 was 12.54% (averaged across all credit card accounts at all reporting banks). A researcher wanted to know if college students at her institution have different interest rates compared to this national statistic. If conducting a single samples t test, which statement would serve as her research hypothesis? (chapter 9)
a. The national interest rate is higher than that of college students on average b. college students have different interests rates on average compared to the nation c. The national interest rate is not different from that of college students d. college students have the same interest rates as the nation correct answer is b
When comparing the difference between means for two distributions , what happens to the effect size as the variability within each distribution gets smaller? (chapter 8)
a. There is no change in the effect size b. the effect size decreases c. the effect size increases d. it is not possible to determine based on the information provided correct answer is c because overlap decreases and effect size increases when variability within each distribution of scores gets smaller
By increasing statistical power, the probability of making a ____________ error is ______________ (chapter 8)
a. Type 1; increased b. Type 11; decreased c. Type 1; decreased d. Type 11; increased correct answer is b because when you increase statistical power, you increase sample size and increasing sample size is only associated with type 1 errors. Therefore, the chance of making a type 11 error is decreases ** too large a sample --> type 1 error ** too small a sample --> type 11 error
It is necessary to correct for error when calculating the standard error for a t test? (chapter 9)
a. Yes; we are estimating the standard deviation of the population b. Yes; we are estimating both the mean and standard deviation of the population c. No; we already corrected the standard deviation and are now reflecting the size of the sample d. No; we are estimating both the mean and standard deviation of the population. correct answer is c
what is the confidence interval for a paired-samples t test with a mean difference of 9.2, a standard error of 0.26, and 15 df? (chapter 10)
a. [-0.55, 0.55] b. [8.74, 9.66] c. [8.94, 9.46] d. [8.65, 9.75] correct answer is d
Sample size can affect whether statistically significant differences are found, but sometimes in extremely large sample differences are found that are significant but of no real value or interest. Which standardized value helps measure the size of the difference in relation to the variability of the data rather than to the variability of the sample size? (chapter 8)
a. alpha level b. confidence interval c. effect size d. interval estimate correct answer is c because effect size is the size of a difference UNAFFECTED by sample size! effect sizes are calculated with respect to distribution of scores, so they are not inflated with increases in sample size
Sample size can affect whether statistically significant differences are found, but sometimes in extremely large sample differences are found that are significant but of no real value or interest. Which standardized value helps measure the size of the difference in relation to the variability of the data rather than to the varibility of the sample size? (chapter 8)
a. alpha level b. confidence level c. effect size d. interval estimate correct answer is c because effect size is a size of difference that is unaffected by sample size
Published literature tends to include significant findings, where the data were sufficient to reject the null hypothesis. This can lead to an inflated estimate of effect size when performing a meta-analysis. Rosenthal suggested that researchers test the level of inflation of their effect size calculations by: (chapter 8)
a. conducting additional research that would more clearly assess the relationship between variables b. pressuring the scholarly journals to publish more null findings. c. computing a file drawer analysis to see how many null findings would be needed to remove the statistical significance found d. including only studies that have strong effects in their meta-analysis correct answer is c
The process of __________ involves researchers at different institutions work together, recruiting participants and sharing methodology and data online (chapter 9)
a. convenience sampling b. open science c. crowdsourcing d. replication correct answer is c
Critical t values _____ as the degrees of freedom _____. (chapter 9)
a. decrease; increase b. increase; increase c. decrease; decrease d. decrease; approach 0 correct answer is a
what is the correct formula for calculating degrees of freedom for an independent-samples t test? (chapter 11)
a. df(total) = df(x) - df(x) b. df(total) = df(x) + df(y) c. df(total) = df(x) + x1 d. df(total) = x- - x2 correct answer is b
The symbol df stands for: (chapter 9)
a. distance from mean b. degrees of freedom c. distance from mode d. degrees of f estimation correct answer is b
credit card debt for 36 individuals was calculated for the 3-month period prior to the economic crash of 2008 and then calculated for a 3-month period 5 years later, after the economy recovered. Which of the following is an appropriate null hypothesis for this research? (chapter 10)
a. economic recoveries have no impact on debt carried by citizens b. credit card debt will be different after economic recovery compared to just prior to an economic crash c. credit card debt increases over time d. credit card debt before the economic crash will be approximately the same as that after the economic recovery correct answer is d (null means no difference)
A group of students in a research class develop an educational video about academic integrity. They are interested in whether their video can increase students' knowledge about the topic. They recruit 42 students, assess their knowledge about academic integrity, show the video, and then reassess knowledge with the same questionnaire used earlier. According to the phenomenon of order effects, performance on the test of knowledge may be: (chapter 10)
a. higher on the first administration because students are fresh and not yet fatigued b. higher on its second administration simply because the students have seen the questionnaire once before c. lower on the first administration because the video has not yet been seen d. lower on the second administration because students may become tired correct answer is b **order effects is how a participant's behavior changes when the DV is presented for a second time
A group of rats ran faster after receiving a steroid drug supplement compared to a group of rats that received no steroid drug supplement. Which type of statistical test should be used to report these results? (chapter 11)
a. independent-samples t test b. paired-samples t test c. single-samples t test d. z test correct answer is a because there is a control and experimental groups - 2 groups of different subjects
The _______________ estimate acknowledges the amount of uncertainty in the _____________ estimate by reporting the margin of error (chapter 8)
a. interval; standard error b. point; interval c. interval; point d. point; standard error correct answer is c because point estimate is a summary statistic the is represented by one number as the estimate of the population --it is rarely accurate-- interval estimate is a range of sample statistics, not just one number --finding where the true value lies in a population-- ***interval estimate, margin of error and confidence interval all represent the same idea
What is one benefit of increasing the sample size when using a t distribution? (chapter 9)
a. larger sample sizes cost less when running the experiment than small samples b. larger sample sizes reflect the parameters of the population more closely c. larger sample sizes make better graphs d. larger sample sizes distance themselves from z distributions correct answer is b **As the sample size gets larger, the t distributions begin to merge with the z distribution because we gain confidence as more participants are added to the study
The confidence interval provides _______________ the hypothesis test (chapter 9)
a. less info than b. the same info as c. more info than d. the opposite info from correct answer is c because confidence interval confirms hypothesis testing AND adds more detail **confidence intervals give us a range of possible values and an estimate of the precision for our parameter value WHILE, hypothesis tests simply tell us how confident we are in drawing conclusions about the population parameter from our sample
An independent-samples t test compares sample _______________ differences. (chapter 11)
a. mean b. median c. mode d. standard deviation correct answer is a
In Cohen's d, the further apart the means of two distributions, the _____________ the effect size is, assuming the standard deviation is held constant (chapter 8)
a. more variable b. less variable c. higher d. lower correct answer is c because the further apart the means = less overlap which means the distribution is taller and narrower and effect size is bigger
On a t table for a single-samples t test, "degrees of freedom" refers to the: (chapter 9)
a. number of restrictions enforced on people in the sample b. total sample size of the distrubution N c. number of scores that are free to vary in estimating population paramaters, N - 1 d. amount of variance in the t distribution correct answer is c
Power can be thought of as the percentage of the distribution of means, centered around your sample mean, that falls: (chapter 8)
a. outside of the null hypothesized distribution b. below the mean of the null hypothesized distribution c. more than two standard deviations from the sample mean d. within the critical regions, where the null hypothesis can be rejected correct answer is d
In Bayesian statistics, probability distributions are based on: (chapter 11)
a. population parameters b. prior beliefs or probabilities c. chance d. new data correct answer is b *** Bayesian statistics --> distributions are based on prior beliefs, posterior beliefs, likelihood and marginal
Which of the following is NOT a way to resolve issues with the file drawer problem? (chapter 8)
a. replicating a study b. evaluating publication bias c. conducting a file drawer analysis d. eliminating unpublished studies from analysis correct answer is d
If a researcher wanted to determine whether her results were specific to the sample or context used, she should: (chapter 9)
a. return her analyses to make sure they are accurate b. replicate the study with different people c. replicate the study with the same people d. throw the data away and start over again from scratch to see if she gets the same results correct answer is b
Medical researchers used a t test to compare cancer patients' recovery rates during time spent in the hospitals versus time spent in their own home to decide the best place for patients to be during recovery. Their study measured all patients' white blood cell counts while they were in the hospital and then again while all patients were at home. What type of design is this? (chapter 10)
a. single-subjects b. between-groups c. within-groups d. independent samples correct answer is c because within-groups design uses the same subjects in each condition
A cohen's d value of 0.51 indicates what effect size? (chapter 8)
a. small b. medium c. large d. no effect correct answer is b ** 0.2 = small effect, 0.5 = medium, 0.8 = large
a researcher compares the ages of 58,072 registered nurses who have or do not have leadership positions in their workplace, and finds a significant difference in age t(58,072) = 2.13, p<0.05, d=0.2. This effect size is: (chapter 11)
a. small b. medium c. large d. too small to be of any significance correct answer is d
Cohen's d measures effect size in terms of (chapter 8)
a. standard deviation b. standard error c. sum of squared error d. sample size correct answer is a
Cohen's d measures effect sizes in terms of: (chapter 8)
a. standard deviation b. standard error c. sum of squared error d. sample size correct answer is standard deviation
Which of the following reports of statistical results is in appropriate APA form? (chapter 9)
a. t(27) = 3.5, fail to reject null b. t(27) = 3.5, p< 0.05 c. t= 3.5, df= 27, reject null d. t= 3.5, df= 27, p< 0.05 correct answer is b
why is the mean difference of the comparison distribution always 0? (chapter 11)
a. the null hypothesis posits small differences b. the research hypothesis posits small differences c. the null hypothesis posits no difference d. the research hypothesis always posits negative differences correct answer is c
To conduct a single-samples t test, you need to know: (chapter 9)
a. the population mean and standard deviation, and the standard error of the sample b. all properties of the sample and the population c. the mean of the sample and all the properties of the population d. the population mean and properties of the sample correct answer is d
When there is uncertainty about the parameters of a population of interest, a t distribution is used instead of a z distribution. Is the t distribution wider or thinner than the z distribution and why? (chapter 9)
a. the t distribution is wider because we are less certain of the findings compared to the z distribution b. the t distribution is thinner because we are less certain of the findings compared to the z distribution c. they produce the same curve because both use the population mean d. they produce the same curve because both use the standard deviation of the population correct answer is a because as sample size decreases, t distribution widens and spreads out. As sample size increases, t distribution becomes more narrow, it more likely matches the z distribution and is more accurate (more certain)
Because a statistically significant effect might not be an important one, we should calculate ________________
effect size in addition to conducting a hypothesis test. We can then report whether a statistically significant effect is small, medium, or large
what is "the new statistics"
effect sizes, confidence intervals, meta-analysis & statistical power First, we compute confidence intervals, which provide a range of plausible mean differences. Second, we calculate effect sizes, which indicate the size of differences. Finally, we estimate the statistical power of the study to be sure that we have a sufficient sample size to detect a real difference.
The major difference between a paired-samples t test and a single-sample t test is that
in a paired-samples t test, we must first create difference scores for every participant because we will be working with different scores, we need to learn about a new distribution-- a distribution of means of these different scores, or a distribution of mean differences
Confidence interval
includes the mean that we would expect for the sample statistic a certain percentage of the time, were we to sample from the same population repeatedly ***We are not saying that we are confident that the population mean falls in the interval; we are merely saying that we expect to find the population mean within a certain interval a certain percentage of the time—usually 95%—when we conduct this same study with the same sample size.) Confirms findings of hypothesis testing and adds more detail The confidence level is 95%, but the confidence interval is the range between the two values that surround the sample mean when we add and subtract margin of error. Interpretation of Confidence Interval If we were to sample 5 students from the same population over and over, the 95% confidence interval would include the population mean 95% of the time
We can increase accuracy by using an _______________ when possible
interval estimate it is based on our sample statistic, range of sample statistics (not just one number) we would expect if we repeatedly sampled from the same population (e.g. confidence interval) **finding where the true value lies in a population** The terms: interval estimate, margin of error and confidence interval all represent the same idea
type 1 error
is when we reject the null hypothesis but we should not have (false positive!!! Researcher incorrectly rejects a true null) --> too large a sample type 1 error is the WORST error to make