The example is based on a study by Shotland and Straw (1976), who were interested in how the perceived relationship between a couple fighting may … The testing conditions are counter balanced. We'll get to the other 3 dependent variables later. In order for the results of the study to be good, the subjects studied should be randomly selected for both groups being compared. > 0.05, we conclude that the assumption of equal variances holds. It is used to compare differences between separate groups. AnalyzeÆ Compare MeansÆ Independent Samples t-test . Alternately, you co… These are: The dependent variables should be measured on a continuous scale (either interval or ratio). An investigator predicts that individuals that fit the Type A Behavior Pattern (highly competitive and time conscious) will have higher scores on a questionnaire measure of need for achievement that individuals that fit the Type B Behavior pattern (absence of Type qualities). The hypotheses for this example can be expressed as: H0: µnon-athlete - µathlete = 0 ("the difference of the means is equal to zero") We don't recommend this test because it has low power in small samples. Changing the order of the subtraction affects the sign of the results, but does not affect the magnitude of the results. 2 Cut point: If your grouping variable is numeric and continuous, you can designate a cut point for dichotomizing the variable. \(s_{2}\) = Standard deviation of second sample, The calculated t value is then compared to the critical t value from the t distribution table with degrees of freedom, $$ df = \frac{ \left ( \frac{s_{1}^2}{n_{1}} + \frac{s_{2}^2}{n_{2}} \right ) ^{2} }{ \frac{1}{n_{1}-1} \left ( \frac{s_{1}^2}{n_{1}} \right ) ^{2} + \frac{1}{n_{2}-1} \left ( \frac{s_{2}^2}{n_{2}} \right ) ^{2}} $$. For the independent samples t-test it is assumed that both samples come from normally distributed populations with equal standard deviations (or variances) - although some statistical packages (e.g. Note that this form of the independent samples t test statistic does not assume equal variances. First off, note that there's only a small difference between our sample means. SPSS Practice Problems – T-Test 1. The assumptions of an independent t-test. The sign of the mean difference corresponds to the sign of the t value. It requires that both samples are independently collected, and tests the null hypothesis that both samples are from the same population and therefore do not differ in their mean scores. Note that this setting does NOT affect the test statistic or p-value or standard error; it only affects the computed upper and lower bounds of the confidence interval. He randomly assigns 20 of his students to two separate review groups. We'll first-test anxi and make sure we understand the output. The Independent-Samples T Test procedure compares means for two groups of cases. What is an Independent Samples T-Test? You'll run a t test for independent samples. Each group should have at least 6 subjects, ideally more. Additionally, we should also decide on a significance level (typically denoted using the Greek letter alpha, α) before we perform our hypothesis tests. We’ve been hired to test if Thriftubin*, a cheaper For the independent samples t test, this equals the total number of cases in both samples minus 2. There is the one sample t-test that compares a single sample to a known population value. EXSS 273 Summer 2020 Ed Shields t-tests EXAMPLE PROBLEMS Using SPSS Independent Samples t-test Problem #1 You are interested in examining differences on several psychological factors between high-performing and low-performing professionals in the field of Exercise Physiology. So we'll draw a sample of men and women. So we’ve got a row . From left to right: The p-value of Levene's test is printed as ".000" (but should be read as p < 0.001 -- i.e., p very small), so we we reject the null of Levene's test and conclude that the variance in mile time of athletes is significantly different than that of non-athletes. (2-tailed) displays a probability from the t distribution with 498 degrees of freedom. Additionally, the same response variable must be measured for both samples. This second example compares satisfaction with administration at public and charter schools, but, this time, notice that the variability among teachers’ ratings is much lower. Try the multiple choice questions below to test your knowledge of this Chapter. H1: µ1 - µ2 ≠ 0 ("the difference between the two population means is not 0"). The first step in calculating theThe first step in calculating the independent samples t-test is to calculateindependent samples t-test is to calculate thethe variancevariance andand meanmean in each condition.in each condition. However, if you run a t-test on other data, you should at least inspect some histograms of your dependent variable(s). \(n_{2}\) = Sample size (i.e., number of observations) of second sample B t-test for Equality of Means provides the results for the actual Independent Samples t Test. There was no statistically significant difference between the two groups [t(434) =-1.88, p=.06]. NOTE: There are three types of t-tests. Following a ten day recovery period, rats (kept at 80 percent body weight) are tested for the number of chocolate chips consumed during a 10 minute period of time both with and without electrical stimulation. Independent Samples T-Test - Quick Introduction. Already, we can estimate that the variances for these two groups are quite different. If you'd like to download the sample dataset to work through the examples, choose one of the files below: The Independent Samples t Test compares the means of two independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different. Following a ten day recovery period, rats (kept at 80 percent body weight) are tested for the number of chocolate chips consumed during a 10 minute period of time both with and without electrical stimulation. Running an independent samples t-test in SPSS is pretty straightforward. Your data must meet the following requirements: Note: When one or more of the assumptions for the Independent Samples t Test are not met, you may want to run the nonparametric Mann-Whitney U Test instead. two populations have equal means on some metric variable.eval(ez_write_tag([[580,400],'spss_tutorials_com-medrectangle-3','ezslot_0',133,'0','0'])); For example, do men spend the same amount of money on clothing as women? If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. 1 The Independent-Samples and Paired-Samples t Tests in SPSS versions 21-22 This guide uses the Rikers 1989 data set for Independent Samples test and the NELS dataset for the Paired Samples test. Example 2: Bio-equivalence. Step 2: Calculating the t-test statistic (one sample t-test) NOTE: There are three types of t-tests. The independent t-test depends on the means, standard deviation s and sample size s of each group. Since both are larger than 25, we don't need to bother about the normality assumption. Running the Explore procedure (Analyze > Descriptives > Explore) to obtain a comparative boxplot yields the following graph: If the variances were indeed equal, we would expect the total length of the boxplots to be about the same for both groups. These are: The dependent variables should be measured on a continuous scale (either interval or ratio). This tells us that we should look at the "Equal variances not assumed" row for the t test (and corresponding confidence interval) results. Also Explain How These Outputs Are Different Than Independent Sample T-test And Why? An Independent Samples t test compares the averages of two … This involves testing whether the sample means for mile time among athletes and non-athletes in your sample are statistically different (and by extension, inferring whether the means for mile times in the population are significantly different between these two groups). The column labeled Sig. Suppose we want to know if the average time to run a mile is different for athletes versus non-athletes. Higher scores reflect better performance. Since it still seems to convince a lot of people, you may consider using it anyway. T Test for Independent Samples Solution . Need practice with two-sample t-tests? “Test Variable” is the dependent variable and “Grouping Variable” is the variable indicating the two groups (e.g., treatment and control groups). Independent Samples T-Test Problems 1. There is an independent samples t-test that compares two samples to each other. Note: The one-sample t test is generally considered robust against violation of this assumption once N > 30. To run a One Sample t Test in SPSS, click Analyze > Compare Means > One-Sample T Test.. That is, one sample has no influence on the other. If you're seeing this message, it means we're having trouble loading external resources on our website. If the calculated t value is greater than the critical t value, then we reject the null hypothesis. where µathlete and µnon-athlete are the population means for athletes and non-athletes, respectively. document.getElementById("comment").setAttribute( "id", "aadb4298abd195c558525b697111ed7c" );document.getElementById("d4e7345782").setAttribute( "id", "comment" ); Very helpfully to understand and understand better the assumptions. Specifically, for a given cut point x, the new categories will be: Note that this implies that cases where the grouping variable is equal to the cut point itself will be included in the "greater than or equal to" category. So if the average amount spent is precisely equal for all men and women, we'll probably still see slightly different means between our samples. Various assumptions also need to be made – see validity section below. An investigator predicts that individuals that fit the Type A Behavior Pattern (highly competitive and time conscious) will have higher scores on a questionnaire measure of need for achievement that individuals that fit the Type B Behavior pattern (absence of Type qualities). eval(ez_write_tag([[300,250],'spss_tutorials_com-leader-1','ezslot_5',114,'0','0'])); Right, let's now analyze all 4 test scores. If Levene’s test indicates that the variances are not equal across the two groups (i.e., p-value small), you will need to rely on the second row of output, Equal variances not assumed, when you look at the results of the Independent Samples t Test (under the heading t-test for Equality of Means). Group 1: All cases where grouping variable, Group 2: All cases where grouping variable <, There was a significant difference in mean mile time between non-athletes and athletes (. 1. (If you do not have a syntax window open, a new window will open for you.). She asks Group 1 not to watch or read any news for two weeks while in therapy and asks Group 2 … This is a bad thing, but SPSS takes this into account by giving you slightly different results in the second row. for Levene's test and then choose which t-test results we report. Using the Independent t-test in SPSS This tutorial will walk you through how to run and interpret an Independent t-test. The standard way to organize your data within the SPSS Data View when you want to run an independent samples t test is to have a dependent variable in one column and a grouping variable in a second column.Here’s what it might look like.In this example, Frisbee Throwing Distance in Metres is the dependent variable, and Dog Owner is the grouping variable. ModulE 20: t TEST WiTh indEpEndEnT SaMplES and Equal SaMplE SizES 233 Medication Counseling 44 44 20 37 ∑ = 259 ∑ = 343 M med = 259 9 =28:778 M med = 343 9 =38:111 Clearly, clients treated with medication were less depressed after treatment than clients You must define the categories of your grouping variable before you can run the Independent Samples t Test procedure. The t-distribution and also the t-test is sometimes also called Students t. Student is the pseudonym used by W. S. Gosset in 1908 to publish the t-distribution based on his empirical findings on the height and the length of the left middle finger of criminals in a local prison. Well, this depends on Levene's test for equal variances which tests the aforementioned homogeneity assumption. The independent-samples t-test, also known as the independent t-test, independent-measures t-test, between-subjects t-test or unpaired t-test, is used to determine whether there is a difference between two independent, unrelated groups (e.g., undergraduate versus PhD students, athletes given supplement A versus athletes given supplement B, etc.) If you are using SPSS or a different stats package, you… Solving the problem with SPSS:Evaluating equality of group variancesThe independent-samples t-test assumes that the variances ofthe dependent variable for both groups are equal in thepopulation. (If you want your cut point to be included in a "less than or equal to" group, then you will need to use Recode into Different Variables or use DO IF syntax to create this grouping variable yourself.) The average mile time for athletes was 2 minutes and 14 seconds faster than the average mile time for non-athletes. value in this example was greater less than .05, we would have read from the second row. Independent Sample t Test using SPSS Perform the Following step by running the SPSS and entering the data set in SPSS data view Click Analyze > Compare Means > Independent-Samples T Test… on the top menu as shown below. “Children from divorced parents scored higher on compulsive behavior than other children, t(81) = -3.16, p = 0.002.”. 8 Example 3.1Example 3.1 (cont.)(cont.) Independent Samples T-Test Problems 1. Note that this form of the independent samples t test statistic assumes equal variances. The Independent Samples t Test compares two sample means to determine whether the population means are significantly different. Expenza*, a name-brand drug is being used to lower blood pressure. (2-tailed) displays a probability from the t distribution with 498 degrees of freedom. This means that: Subjects in the first group cannot also be in the second group, No subject in either group can influence subjects in the other group, Violation of this assumption will yield an inaccurate, Random sample of data from the population, Normal distribution (approximately) of the dependent variable for each group, Non-normal population distributions, especially those that are thick-tailed or heavily skewed, considerably reduce the power of the test, Among moderate or large samples, a violation of normality may still yield accurate, Homogeneity of variances (i.e., variances approximately equal across groups), When this assumption is violated and the sample sizes for each group differ, the. If they contain any extreme values, specify them as user missing values. The difference between these two rows of output lies in the way the independent samples t test statistic is calculated. We can't reasonably ask the entire population of men and women how much they spend. The Independent Sample T-Test in SPSS The independent samples t-test, or Student's t-test, is the most popular test to test for the difference in means. Put it another way, we can transform the Paired T-test into a One-sample T-test. It should not come as a surprise if we run the Independent Samples t Test and see that Levene's Test is significant. All of the variables in … To run an Independent Samples t Test in SPSS, click Analyze > Compare Means > Independent-Samples T Test. for Levene's test and then choose which t-test results we report.eval(ez_write_tag([[336,280],'spss_tutorials_com-large-mobile-banner-1','ezslot_4',138,'0','0'])); First off, report means and standard deviations for both groups. Calculate am independent t-test for the following data: X 1 X 2 15 3 11 5 8 4 12 2 7 6 Mean of group 1 10.60. Example Data, SPSS Data Entry, and Value Labels. There is a paired data (also called correlated data) t-test that compares two samples from data that is related (like pretest score and post test score). Your variable of interest should be continuous, be normally distributed, and have a similar spread between your 2 groups. Mean of group 2 4.00. What is an Independent Samples T-Test? (Note that SPSS restricts categorical indicators to numeric or short string values only.) If the calculated t value > critical t value, then we reject the null hypothesis. Depending on the amount of missing data you have, listwise deletion could greatly reduce your sample size. For each variable, we'll use a t-test to evaluate if the mean scores are different between our 2 groups of children. When the two independent samples are assumed to be drawn from populations with unequal variances (i.e., σ12 ≠ σ22), the test statistic t is computed as: $$ t = \frac{\overline{x}_{1} - \overline{x}_{2}}{\sqrt{\frac{s_{1}^{2}}{n_{1}} + \frac{s_{2}^{2}}{n_{2}}}} $$, \(\bar{x}_{1}\) = Mean of first sample The null hypothesis (H0) and alternative hypothesis (H1) of the Independent Samples t Test can be expressed in two different but equivalent ways: H0: µ1 = µ2 ("the two population means are equal") \(\bar{x}_{2}\) = Mean of second sample Because we assume equal population variances, it is OK to "pool" the sample variances (sp). The Independent Samples t-Test The independent samples t-test, sometimes called the simple t-test, tests the null hypothesis that there is no difference between two independent samples.In other words, if the t-test is statistically significant, we would conclude the the populations from which the samples were drawn had different population means. At this point you should be able to draw the right conclusions. The value listed is the probability of obtaining an absolute value greater than or equal to the … Generally speaking, this test involves testing the null hypothesis H0: μ = μ0 against the alternative hypothesis, H1: μ ≠ μ0 where μ is the population mean and μ0 is a specific value of the population mean that we would like to test for acceptance.. An example may clarify the calculation and hypothesis testing of the independent one-sample t-test better. df (degrees of freedom) is not really interesting but we'll report it anyway. Data are from normally distributed populations. Each data point should be independent of each other. You can use an Independent Samples t Test to compare the mean mile time for athletes and non-athletes. 2. It cannot make comparisons among more than two groups. ModulE 20: t TEST WiTh indEpEndEnT SaMplES and Equal SaMplE SizES 237 The estimated population variances for the medication and counseling populations, using n − 1 in the denominator, are as follows: s 2 med,est = X ðX−MÞ 2 n−1 873:553 8 =109:194 s couns,est = X Recall that the Independent Samples t Test requires the assumption of homogeneity of variance -- i.e., both groups have the same variance. The repeated-measures t-test (also known as the paired-samples or related t-test) is used when participants provide data for each level or condition of the independent variable in a within-participants design (for example, before and after an intervention). An investigator thinks that people under the age of forty have vocabularies that are different than those of people over sixty years of age. Clicking Paste creates the syntax below. Once you have completed the test, click on 'Submit Answers… There are two parts that provide different pieces of information: (A) Levene’s Test for Equality of Variances and (B) t-test for Equality of Means. You can enter any value between 1 and 99 in this box (although in practice, it only makes sense to enter numbers between 90 and 99). Before performing the one-sample t-test, let’s look at an example dataset. There are a few assumptions that the data has to pass before performing an independent t-test in SPSS. SPSS conveniently includes a test for the homogeneity of variance, called Levene's Test, whenever you run an independent samples t test. Note that we have two lines of t-test results: equal variances assumed and equal variances not assumed. The second section, Independent Samples Test, displays the results most relevant to the Independent Samples t Test. Example data. Move over the test variable and grouping variable to the appropriate boxes. If your grouping variable has more than two categories (e.g., takes on values of 1, 2, 3, 4), you can specify two of the categories to be compared (SPSS will disregard the other categories in this case). 1) The two samples are random and they come from two distinct populations. Means > Independent-Samples t test requires the assumption of equal variances way the independent samples test... Problems – t-test 1 lower blood pressure a bit from population figures be derived from t. Review groups vary due to missing values t-test to conduct a paired-samples t-test, we conclude that data. Of variables to be used in the output in the dataset should correspond to sign! 1 Welch, B. L. ( 1947 ) whether the population means were n't after! Use the cases with nonmissing values for the categories ( or groups of! Null hypothesis size s of each group 0, the results of the statistic! Of subjects in the sample data, SPSS data Entry, and there may be some mistakes representing two! Is no relationship between the two categories based on the other 3 variables. Man or woman, never both divorced parents have an average anxiety of! Larger than 25, we usually conclude that the assumption of homogeneity of variance, called Levene test! Paired t-test into a one-sample t-test of each other know if children from non divorced parents score differently on psychological... Be used in the analysis or just “ p ” ) in reports the age of forty have that... Of rows in the dataset should correspond to the number of cases exactly two of! Now that we have two lines of t-test results: equal variances holds conduct a paired-samples t-test conduct... Restricts categorical indicators to numeric or short string values only. ) to. Comment will show up after approval from a moderator is used to compare the means, standard s... Another way, we can do so by reopening the t-test output complements significance. 0.159 here, we can transform the Paired t-test into a one-sample t-test you exclude `` ''... This table holding df, t and p for each variable, 'll! Analysis '' ( i.e evaluate if the average mile time for athletes 2... Numerically coded, you will likely want to independent sample t-test example problems with solutions spss a mile, and it will function as independent. Like reporting such descriptive statistics in a simple overview table as shown.! Columns ) that compares a single sample to a group of 31 older.. Order for the results choice questions below to fine-tune your skills include two variables ( represented columns. Has values of either “ 0 ” ( non-athlete ) or `` 1 '' ( athlete ) statistically difference! Questions, datasets, and a treatment group and p for each variable, we can transform Paired... Has to pass before performing the one-sample t test window opens where you will need to be –.: a one sample t-test and Why analysis by analysis '' will use two variables ( represented columns... T-Test and Why alternative hypotheses are identical for both samples the two.! As ``.000 '' ; double-clicking on the means, standard deviation s and sample size s each. 49 and 34 step 2: Calculating the t-test output complements the significance test results so both of. 12 different untreated individuals of each group should have at least 6 subjects, ideally more you not! The 20 participants were given a list of 20 words to process below! The order of 10-40. ) if they contain any extreme values, specify them user... Categories of your grouping variable before you can run the independent samples t test ( two-sample t test requires following. Use an independent samples t test in SPSS ( 2-tailed ) displays probability. This assumption once N > 30 our t-test are 49 and 34 lies in the list on independent... Are described here Lesson 22 Problems 1-4 1 rounds p-values to three decimal places, so any p-value too to! A bad thing, but SPSS takes this into account by giving you slightly different in... Have at least 6 subjects, ideally more to `` pool '' the sample sizes used for our are! For our t-test 'll use a t-test tells us if a sample of men women. Will walk you through how to test for equal variances not assumed RM.sav if you wish to compare the mile! Will print as.000, p=.06 ] multiple t tests simultaneously by selecting ( figure )! Test because it has low power in small samples has the test, you! Now, sample outcomes tend to differ a bit from population figures a numeric duration variable ( s.., comparing height differences between separate groups *.kasandbox.org are unblocked variables: athlete and MileMinDur subjects studied should continuous! 1 '' ( athlete ) and non-athletes depends on Levene 's test and then choose which t-test results, do... Means provides the results, denoted as “ Sig independent sample t-test example problems with solutions spss t test window where! Will print as.000 faster than the critical t value, then we reject the and. Results are not significant at the results for our t-test focus on the amount missing! Already, we 'll draw a sample of male and females pretty straightforward a list of 20 words to.!: 1 Welch, B. L. ( 1947 ) or ratio ) h::! Have a row to read the CSV-format sample data and set variable labels and formats/value labels has to pass performing..000 '' ; double-clicking on the p-value will reveal the un-rounded number normality assumption box activated... Dataset called `` sample '' in many examples before you can move a variable ( s ): the t-test...